THE INFLUENCE OF ORGANIZATIONAL CULTURE, SELF-EFFICACY, WORK MOTIVATION AND JOB SATISFACTION ON THE PERFORMANCE OF UMN AL-WASHLIYAH LECTURERS IN MEDAN

This study aims to answer several hypotheses about the direct influence of organizational culture, self-efficacy, work motivation, and job satisfaction on work motivation, job satisfaction, and lecturer performance. The research technique used proportional random sampling to a sample of 152 of 246 lecturers UMN Al-Washliyah Medan, with research instruments using questionnaires with the scale Likert. Then the data is processed and analyzed with path analysis, thus producing an analysis with a coefficient of path 0.30 on the direct influence of organizational culture on work motivation, path coefficient 0.43 on the direct influence of self-efficacy on work motivation, path coefficient 0.47 on the direct influence of organizational culture on job satisfaction, coefficient of path 0.28 on the direct influence of self-efficacy on job satisfaction, path coefficient 0.22 on the direct influence of organizational culture on performance, the coefficient of line 0.15 on the direct influence of self-efficacy on lecturer performance, the coefficient of line 0.23 on the direct influence of work motivation on lecturer performance, and the coefficient of path 0.28 on the direct influence of job satisfaction on lecturer performance. From the results of the analysis, to improve the performance of lecturers need to be made various efforts, among others, by improving organizational culture, self-efficacy, work motivation, and job satisfaction.

[115] There are two theories that provide different explanations for the factors that influence performance. Colquitt explain through the Organizational Behavior Integration Model that organizational culture indirectly affects organizational performance and commitment through job satisfaction, stress, motivation, trust, fairness, ethics, learning, and decision making (Colquitt, Lapine, & Wesson, 2009, p. 8). Furthermore, Robbins and Judge through the Organizational Cultural Relationship Model with Performance and Satisfaction explained that organizational culture directly influences performance (Robbins & Judge, Organizational Behavior, 2011, p. 608). Based on the explanation of organizational behavior integration model, it can be known that performance is not directly influenced by organizational culture, while the Organizational Cultural Relationship Model with Performance and Satisfaction explains that performance is directly influenced by organizational culture. The difference in explanation of the two theories is the gap in the explanation of factors that influence performance, so it needs to be researched in order to get empirical support.
Based on some research results can be confirmed that job satisfaction is an important factor for performance improvement. Symptoms of low job satisfaction can result in low quality of work, slow work, lack of work, moving jobs, behaving negatively towards the organization. The high job satisfaction desired by the members of the organization can be attributed to the positive results expected by the employees. High job satisfaction is a sign that the organization is well managed so that there is improvement and quality of work.
From the picture above shows that the performance of lecturers at UMN Al-Washliyah Medan needs to get serious attention in order to improve the quality of education. The selection of UMN Al-washliyah as a place of research, because of the tendency and the majority of problems in UMN Al-Washliyah Medan related to the problems of lecturer performance, organizational culture, self-efficacy, work motivation, and job satisfaction. While this research is focused on the performance of UMN lecturers Al-Washliyah Medan.

B. Method
The method used in this research is called the survey method. Looking at the problems studied, this type of survey research belongs to the research category "explanatory or confirmatory ", namely research that explains causal relationships and hypothesis testing (Singarimbun & Efendi, 1989, p. 4) This research includes expose factors that are causal, because the purpose of this research is to uncover causality relationships between research variables, namely: organizational culture, self-efficacy, work motivation and job satisfaction to the performance of lecturers. The data collected in this study are the facts of the symptoms of the five variables without being given special treatment of these variables.
To obtain data on organizational culture variables, variables of self-efficacy, work motivation, job satisfaction variables, and the performance of lecturers used indirect Vol. 1, Issue. 2, Dec 2020E-ISSN: 2746 data collection techniques that is with. In descriptive research, concepts or constructs of variables are described into questions and statements in questionnaires. This enables the collection of empirical data relevant to an analysis.
The procedure used to measure all the variables studied is the Likert method. This method is to express the respondent's feelings towards his work by choosing the alternative answers that are already available. Although the procedures used are the same, alternative answer options and indicators differ between instruments to measure variables with each instrument to measure other variables.
The preparation of the instrument statements considers the ease of filling by respondents, so that the preparation pays attention to several important things, among others: (a) avoidingdubiousor ambiguous statements, (b) avoiding words that are too abstract, (c) not using suspicious words or antipathy.
To find out the accuracy of the instruments used in this research, testing is carried out to obtain the validity of the instrument. A valid instrument is obtained by performing a content validity analysis, and construct validity. In its implementation sought internal consistency and discarded the details of weak statements, so that obtained a good questionnaire batteries and qualified to be used as a research data collection tool.
Then the data is describedbyusing descriptivestatistics, whichis done using the help of spss for Windows program application version 21. Through the use of statistics obtained average score (mean), median, mode, standard deviation, and variance of each variable so that the research variable data can be described in question.

Research Results
After calculation of the path analysis with two models, i.e. (1) the influence of organizational culture (X1) on work motivation (X3), (2) the influence of self-efficacy (X2) on work motivation (X3), (3) the influence of organizational culture (X1) on job satisfaction (X4), (4) the influence of self-efficacy (X2) on lecturer job satisfaction (X4), (5) influence of organizational culture (X1) on lecturer performance (X5), (6) influence of self-efficacy (X2) on lecturer performance (X5) , (7) the influence of lecturer work motivation (X3) on lecturer performance (X5), (8) the influence of job satisfaction (X4) on lecturer performance (X5). After the calculation using statistical application, the results of analysis of the structure of the test model are obtained as follows: The Influence of Organizational Culture, Self-Efficacy, Motivation… [117] From the calculation of the path analysis directly in the previous model analysis, the influence of organizational culture on lecturers' work motivation is 0.33. The tcount coefficient value of 4.89 is greater than the ttable α(0.05) = 1.98 and the ttable α(0.01) = 2.61.
Hence the first hypothesis that there is no direct influence of organizational culture on work motivation or referred to as H0 is rejected.
Thus, the results of the first hypothesis analysis provide findings that organizational culture is very significant direct influence on the work motivation of lecturers. This means that the better the organizational culture that occurs in the form of innovation and risk-taking, attention to detail, orientation of results, orientation of people, orientation of the team, aggressiveness, and stability will be even better in terms of responsibility in carrying out tasks, having a feeling of pleasure in working, always Based on previous findings, it can be concluded that work motivation can be directly influenced directly by organizational culture.
The second hypothesis, the results of the calculation of path analysis directly in the analysis of the previous model, the influence of self-efficacy on work motivation of 0.43.
Thus, the results of hypothetical analysis can be stated that self-efficacy is very significant direct influence on work motivation. That is, the better self-efficacy in the form of challenging, having high confidence, taking difficult work as a challenge, assuming failure is the result of less maximal effort, quickly rising and restoring confidence due to failure, not easily stressed and depressed, obeying the applicable rules, and always providing a good example will also be better in terms of responsibility in carrying out tasks , having the pleasure of working, always trying to outperform others, prioritizing the achievements of what he does, working in the hope of wanting to get incentives, happy to get praise from what he does, having clear and challenging goals, there is feedback on his work, always trying to meet his life needs and work needs, and working in the hope of getting attention from friends and superiors.
Based on the findings in this second hypothesis, it can be concluded that both poor work motivation can be directly influenced by the poor self-efficacy that a person has.
The third hypothesis, the results of the calculation of path analysis directly in the analysis of the previous model, the influence of organizational culture on job satisfaction obtained a coefficient value of 0.47. The coefficient of tcount is 6.86 greater than the value of ttable, α(0.05) = 1.98 and ttable α(0.01) = 2.61. Therefore, the third hypothesis stating that there is no direct influence of organizational culture on job satisfaction or H0 is rejected.
Thus, the results of the analysis of the third hypothesis provide findings that organizational culture is very significant directly affect job satisfaction. This means that the better the organizational culture applied by the increasing job satisfaction that a person has in terms of promotion opportunities, the job itself, salary, co-workers, workplace and supervision.
Based on previous findings it can be concluded that good job satisfaction can be directly influenced by the bad culture of the organization applied.
The fourth hypothesis, the results of the calculation of path analysis directly in the previous model analysis, the effect of efficacy on job satisfaction of 0.28. The coefficient value of tcount is 4.05 greater than the value of ttable α(0.05) = 1.98 and table ttable α(0.01) = 2.61. Therefore, the hypothesis that there is no direct influence of self-efficacy on teacher job satisfaction or referred to as H0 is rejected.
Thus the results of hypothetical analysis that states that self-efficacy is very significant direct influence on job satisfaction can be received empirically. That is, the better self-efficacy in the form of facing challenges, having high confidence, considering difficult work as a challenge, assuming failure is the result of less than maximum effort, quickly rise and restore confidence due to failure, not easily stressed and depressed, adhere to the applicable rules, and always set a good example then the better job satisfaction has in terms of seriousness in carrying out work , work knows no time, work hard without expecting rewards, there is pride in work, and there is a sense of responsibility.
Based on the findings of research on this hypothesis it can be concluded that high low job satisfaction can be directly influenced by the good of a person's poor self-efficacy.
The fifth hypothesis, the results of the calculation of path analysis directly in the analysis of the previous model, the influence of organizational culture on the performance of lecturers obtained a coefficient value of 0.22. The coefficient value of tcount is 3.12 greater than the value of ttable α(0.05) = 1.98 and ttable α(0.01) = 2.61. Therefore, the hypothesis that there is no direct influence of organizational culture on the performance of lecturers or referred to as H0 is rejected.
Thus the results of hypothetical analysis that states that organizational culture directly affects the performance of lecturers can be accepted empirically. This means that the better the organizational culture applied in the form of innovation and risktaking, attention to detail, orientation of results, orientation of people, orientation of the team, aggressiveness, and stability, the better the performance of lecturers in the form of increased activities in the field of education and teaching, research, community service, and supporting activities.
Based on the findings in this hypothesis, it can be concluded that the poor performance of lecturers can be directly influenced by the poor organizational culture applied.
The sixth hypothesis, the result of calculation of path analysis directly in the analysis of the previous model, self-efficacy directly affects the performance of lecturers by 0.15. The coefficient value of tcount is 2.23 greater than the value of ttable α(0.05) = 1.98 and table ttable α(0.01) = 2.61. Therefore, the hypothesis that there is no direct influence of self-efficacy on the performance of lecturers or referred to as H0 is rejected.
Thus the results of hypothetical analysis that states that self-efficacy is very significant directly affect the performance of lecturers can be accepted empirically. That is, the better self-efficacy in the form of activities like to face challenges, have high confidence, consider difficult work as a challenge, consider failure is the result of less than maximum effort, quickly rise and restore confidence due to failure, not easily stress and depression, adhere to the applicable rules, and always set a good example, then the better the performance of lecturers in terms of improving the quality of learning.
Based on the findings in this hypothesis, it can be concluded that the poor performance of lecturers can be directly influenced by the poor self-efficacy.
The seventh hypothesis, the results of the calculation of path analysis directly in the analysis of the previous model, the influence of work motivation on the performance of lecturers by 0.23. The coefficient value of tcount is 2.48 greater than the value of ttable α(0.05) = 1.98 and ttable α(0.01) = 2.61. Therefore, the hypothesis proposed that there is no direct influence of teacher's work motivation on the performance of lecturers or referred to as H0 is rejected.
Thus, the results of hypothetical analysis that states that work motivation is very significant have a direct effect on the performance of lecturers. That is, the better the work motivation that includes responsibility in carrying out the task, having a feeling of pleasure in working, always trying to outperform others, prioritizing the achievements of what he does, working in the hope of wanting to get incentives, happy to earn praise from what he does, having clear and challenging goals, there is feedback on his work, always trying to meet his life needs and work needs , and work in the hope of getting attention from friends and superiors, the better the performance of lecturers in terms of implementation of activities in the field of education and teaching, research, community service, and other supporting activities to improve the quality of learning.
Based on the findings in this hypothesis, it can be concluded that the poor performance of lecturers can be directly influenced by poor work motivation.
The eighth hypothesis, the results of the calculation of path analysis directly in the previous model analysis, the effect of job satisfaction on lecturer performance of 0.28.
The coefficient value of tcount is 3.04 greater than the value of ttable α(0.05) = 1.98 and table ttable α(0.01) = 2.61. Therefore, the hypothesis that there is no direct influence of job satisfaction on the performance of lecturers or referred to as H0 is rejected.
Thus, the results of the eighth hypothesis analysis that states that job satisfaction is very significant have a direct effect on the performance of lecturers. That is, the better job satisfaction includes the opportunity of promotion, work itself, salary, colleagues, workplace and supervision, the better the performance of lecturers in terms of carrying out activities or activities in the field of education and teaching, research, community service, and other supporting activities to improve the quality of learning. Based on the findings in this hypothesis it can be concluded that the performance of lecturers directly can be influenced by good job satisfaction.

Discussion
Based on the results of the research on the first hypothesis stated that organizational culture has a positive effect on work motivation. This means that if the organizational culture is good, then the motivation of work will increase in a positive direction. In terms of increased work motivation it is asserted by Colquitt that motivation is "a set of energetic forces that originates both within and outside an employee, initiates work-related efforts, and determines its direction, intensity, and persistence", (Colquitt, Lapine, & Wesson, 2009, p. 8). A set of energetic forces that originate both inside and outside the worker in this case the teacher, starting a work-related business, determining its direction, intensity, and perseverance.
Organizational culture is also a gentle force/unconscious, but easily disseminated, its presence is not realized by members but obeyed by its members. Generally culture is below the threshold of consciousness, because it involves assumptions that are taken for granted assumptions about how a person can see, think, act and feel and react to his environment. Unconsciously the organizational culture of something that is not negotiable, rarely discussed, believed to be true, accepted as something true and nonnegotiable. However, it has a significant influence in shaping the behavior of the members of the organization. From this it can be concluded that the high low motivation of work is strongly influenced and determined by the poor culture of the organization in the workplace.
The results of the second hypothesis test showed that organizational culture has a positive effect on job satisfaction. This is demonstrated by a strong desire or with the sincere desire of the member to remain or become a member of that organization. This means that in an organization that has high job satisfaction, then the intention of members to leave the organization will no longer exist, will even further strive to advance the organization in accordance with the wishes of the organization, and will be willing to accept and implement the values and norms that the organization builds well.
Job satisfaction gives birth to feelings of pleasure, pride, joy, and other similar feelings that express a conformity between hope and reality in relation to a person's assessment of the work that has been done. If the leader gives attention and praise to the work of the lecturers, then they will feel happy and cause satisfaction in working. . 1, Issue. 2, Dec 2020E-ISSN: 2746 [122]

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The results of the third hypothesis test showed that organizational culture has a positive effect on lecturers' performance. This illustrates that a healthy organizational culture can encourage openness from both workers and leaders so as to foster work motivation in the direction between workers and leaders in order to create a good work system.
Organizational culture is controlling and direction in shaping the attitudes and behaviors of members within an organization. Individually or in groups a person will not be separated from the culture of the organization and in general members of the organization will be influenced by the diversity of existing resources.
Organizational culture also relates to the emphasis of the process on the individual (employee) in identifying himself with the values, rules, and objectives of the organization and making the individual have the desire to maintain his/her membership in the organization. Organizational culture is a means to achieve organizational goals, so that with organizational culture can spur performance to be able to achieve organizational goals. So that by achieving the objectives of the organization, they will also feel their success in working and of course will also provide additional reciproge to the members of the organization.
Based on the explanation above, it can be concluded that the performance of lecturers is influenced by the good culture of the organization in the workplace.
The results of the fourth hypothesis test showed that self-efficacy has a positive effect on work motivation. Effectiveness in work is very related to the existence of work motivation and organizational culture. Feeling good about work is one of the factors that can increase motivation in work. Self-efficacy is related to expectations in enabling selfinvolving personalities. In other words, perceived self-efficacy refers to a person's perception of their capacity to react to future situations.
Perceived self-efficacy differs from what can seem to be a similar concept to selfesteem. Self-esteem refers to a thorough evaluation of people's personal worth.
The self-efficacy that is felt is different from self-esteem in two ways. i.e. selfefficacy is not a global variable, but rather a thing that is generally owned differently by everyone in different situations, perceived self-efficacy is not an abstract concept of personal worth, but an assessment of what one can do. Thus, the motivation is achieved when self-efficacy is strong or low in the person. This empirical proof shows that self-efficacy has a direct effect on work motivation.
Thus it can be stated that the high low motivation of work is determined by how the state of self-efficacy develops in the work environment.
The results of the fifth hypothesis test stated that self-efficacy has a positive effect on lecturers' job satisfaction. Tschannen-Moran, Hoy and Hoy (1998:98) revealed that self-efficacy has a strong impact on academic achievement, principals and students, and teachers. Stephen P. Robbin and Mary Louther (2007:101) said there is a relationship of self efficacy, motivation and performance. Because it looks at the attitude of the view towards the work, the view of the self in the work, able to finish the work, trying to find a way to get the job done, have confidence, be able to learn from experience and be able to respond to situations, and conditions that vary with a positive attitude.
Baron and Byrne (Greenberg & Robert, 2000, p. 17) argue that self-efficacy is an individual's assessment of his ability or competence to perform a task, achieve a goal, and produce something. Meanwhile, Jess Feist (Feist, 2008, p. 80) states that self-efficacy is an individual's belief that they have the ability to control their work against their own environmental events.
Individuals with high self-efficacy tend to perform certain tasks, even if they are difficult tasks. Individuals who have high self-efficacy consider failure as a result of a lack of hard effort, knowledge, and skills. Individuals who doubt their ability (low self-efficacy) will avoid difficult tasks because the task is seen as a threat to them. While individuals who have low self-efficacy do not think about how good it is to deal with difficult tasks.
When faced with difficult tasks, they reduce their efforts and quickly give up. They are also slow to fix or regain their self-efficacy when they face failure.
The results of the sixth hypothesis test showed that self-efficacy has a positive effect on lecturers' performance. This is evidenced by the higher the self-efficacy, the better the performance of lecturers in teaching and educating. These findings suggest that there is a positive influence of various aspects of self-efficacy on improving lecturer performance. Each increase in the self-dimension measurement score was followed by an increase in the lecturer's performance dimension measurement score (Bandura, 1997).
According to bandura, the aspect of self-efficacy is the fantor of individual teachers to do and achieve something, so it can be seen as one of the contributors to the effectiveness of the learning and teaching process. Vol. 1, Issue. 2, Dec 2020E-ISSN: 2746 Thus, self efficacy is very important in supporting the creation of an effective performance. Basically, to build good performance takes a fairly long time and gradually.
It may be that on the way it will experience different ups and downs over time.
The results of the seventh hypothesis test showed that work motivation has a positive effect on lecturers' performance. In this test proves that lecturers who have high work motivation will have a high awareness of their responsibilities as an educator to achieve their goals. The lecturer's awareness in understanding himself as an educator will be seen from his commitment where his behavior in working.
Similarly, Sutrisno (Sutrisno E. , 2011, p. 111) mentioned that motivation is something that can cause excitement. So, someone who has motivation, will certainly make a harder effort if they believe the effort will result in a good performance assessment.
This process proves that the high low performance of lecturers is determined by the high low work motivation owned by the lecturers themselves.
The results of the eighth hypothesis test showed that job satisfaction has a positive effect on lecturers' performance. Job satisfaction is a person's general attitude towards his work. A person with a high level of satisfaction shows a positive attitude towards his work, while those who are dissatisfied with his work show a negative attitude towards his work. Job satisfaction is also demonstrated by an individual's general attitude towards his or her work. In Gibson's statement (Gibson, 2007, p. 107), job satisfaction is part of the motivational process. Therefore, the level of job satisfaction in the organization can be shown by results such as the attitude of the member of the organization, the change of work of the member of the organization, the death or absence, delay, and flexibility that is common in an organization.
Lecturers in carrying out their duties will always interact with their environment.
Lecturers who have satisfaction in working will feel the results of good work/high. On the contrary, if he feels dissatisfied in his work, then he gets poor work/low. Job satisfaction is a positive attitude that concerns self-adjustment to his work, if the lecturer is satisfied with his/her job, it will have a positive and proud attitude, as well as assess his work highly, because the situation and working conditions can meet his needs, desires, and expectations.
This process proves that the high level of low performance of lecturers is determined against the high low job satisfaction felt at work.

D. Conclussion
Based on the evidence of the eight hypotheses proposed, the findings and discussion of the results of previous research, can then be drawn several conclusions as follows: 1. Organizational culture manifested in innovation and risk-taking, attention to detail, orientation of results, orientation of people, team orientation, aggressiveness, and stability affect the realization of high lecturer work motivation with encouragement from within, encouragement from outside the self, and adequate rewards. The low motivation of lecturers' work is determined by the poor organizational culture in the institution.
2. Self-efficacy manifested in the likes of facing challenges, having high confidence, consider difficult work as a challenge, consider failure is the result of less than maximum effort, quickly rise and restore confidence due to failure, not easily stress and depression, adhere to the applicable rules, and always give a good example of the realization of high work motivation with the encouragement from within, selfencouragement, and sufficient rewards.
3. Organizational culture manifested in innovation and risk-taking, attention to detail, orientation of results, orientation of people, team orientation, aggressiveness, and stability affect the realization of job satisfaction drawn in promotional opportunities, the job itself, salaries, colleagues, workplace and supervision. 4. Self-efficacy manifested in the likes of facing challenges, having high confidence, consider difficult work as a challenge, consider failure is the result of less than maximum effort, quickly rise and restore confidence due to failure, not easily stressed and depressed, adhere to the applicable rules, and always give a good example of the effect on the realization of job satisfaction in terms of seriousness in carrying out work , work knows no time, work hard without expecting rewards, there is pride in work, and there is a sense of responsibility. 5. Organizational culture embodied in innovation and risk-taking, attention to detail, orientation of results, orientation of people, team orientation, aggressiveness, and stability directly affect the performance of lecturers drawn from the fields of education and teaching, research, community service, and other supporting activities. 6. Self-efficacy manifested in the likes to face challenges, have high confidence, consider difficult work as a challenge, consider failure is the result of less than Vol. 1, Issue. 2, Dec 2020E-ISSN: 2746 [126] maximum effort, quickly rise and restore confidence due to failure, not easily stressed and depressed, adhere to applicable regulations, and always give a good example of the impact on the realization of the performance of lecturers drawn from the field of education and teaching , research, community service, and other supporting activities.
7. Work motivation illustrated responsibility in carrying out tasks, having a feeling of pleasure in working, always trying to outperform others, prioritizing the achievements of what he does, working in the hope of getting incentives, happy to earn praise from what he does, having clear and challenging goals, there is feedback on his work, always trying to meet his life needs and work needs, and work in the hope of getting attention from friends and superiors directly affect the performance of lecturers in terms of implementation of activities in the field of education and teaching, research, community service, and other supporting activities to improve the quality of learning.
8. Job satisfaction reflected in promotion opportunities, work itself, salaries, colleagues, workplaces and supervision affects the performance of lecturers in the fields of education and teaching, research, community service, and supporting activities.


ORGANIZATION OF THE PRIMARY ACCOUNTING OF THE MANUFACTURING INVENTORIES AND THE FEATURES OF THEIR REFLECTION IN THE ACCOUNTING POLICY OF THE ENTERPRISE

ORGANIZATION OF THE PRIMARY ACCOUNTING OF THE MANUFACTURING INVENTORIES AND THE FEATURES OF THEIR REFLECTION IN THE ACCOUNTING POLICY OF THE ENTERPRISE Abstract. The organization of the store manufacturing accounting was studied. The order of accounting policy formation of the enterprises in the organization of the store accounting. The main outstanding issues related to the store accounting are analyzed. Based on the research, it is established that the accounting is directed at management and accounting policy is one of the elements of the accounting system. So it must be considered in conjunction with management because in modern conditions the focus of accounting policy is the impact on the results of management, in other words making management decisions. In the result of the research the elements of accounting policy in the store accounting organization, information that should be specified in the Order on accounting policy of the enterprise are determined. But it should be noted that the above elements are not exhaustive and the company can expand and supplement them, taking into account their information and technological needs. Based on the analysis of the requisite composition of the primary documents for the accounting of the stocks’ movement and the study of the needs of the enterprise management system, the authors have developed and proposed a new document «Fuel usage statement». It has the following details such as the name of the enterprise, brand and the state number of the car, trailer, cargo information, customer information, fuel consumption, speedometer indicators at the beginning and at the end of the day, the units of measurement, positions, full name and the signatures of responsible persons. The proposed list of details is optimal and contains all the required as well as additional details that are elements of convenience. The usage of this document will ensure that information about the fuel consumption at the enterprise is received. It is necessary to ensure the efficient organization of workflow at all stages of store accounting, to approve the forms of primary documents of the store accounting for the rational organization of the store accounting at the enterprise. Scheduling fuel flow records covers the steps of creating, verifying, processing and storing a document. The created workflow schedule for fuel usage helps to improve the work of the accounting service, to reduce the cases of untimely documents processing, its loss, to reduce the deadlines for reporting, to increase the responsibility of employees at all levels for timely preparation, usage and processing.

Для раціональної організації обліку запасів на підприємстві необхідно забезпечити ефективну організацію документообігу на всіх стадіях обліку запасів, затвердити форми первинних документів з обліку запасів. Складання графіка документообігу відомості використання пального охоплює етапи створення, перевірки, обробки та зберігання документа. Розроблений графік документообігу відомості використання пального сприяє поліпшенню роботи бухгалтерської служби, зниженню випадків несвоєчасної обробки документів, їхньої втрати, скороченню термінів складання звітності, підвищенню відповідальності працівників усіх рівнів за своєчасність їх складання, використання та опрацювання. Introduction. In order to carry out the economic activity of the enterprise they use industrial inventories that are an important and dominant part of current assets and the sufficient volume and expedient use of these inventories is a prerequisite for ensuring the continuity of the production process at the enterprise. The usage of motor vehicles is an industrial necessity for many enterprises in modern conditions of management. Fuel and lubricants are a specific item in the operation of motor transport that has a significant proportion in the total expenses of the enterprise. Solving the problem of the effective development and growth of production potential of economic entities requires the creation of an effective system of inventory management that can provide the information needs of the availability and movement of enterprise inventory. Particular attention is needed to the organization of inventory accounting and use of fuel, specially its documentary support. Consequently, inventory management occupies the central place in the accounting system of the enterprises. A clear and high quality inventory organization ensures the organizational, economic, technological and informational unity of streaming processes and allows to combine cost savings with a quick response to consumer inquiries.
Research's analysis and problem statement. The question of the organization and the methods of inventory accounting, inventory management and the peculiarities of accounting policy formation in the part of accounting inventories are highlighted in the works of well-known native and foreign economists. The study of economic literature about the organization of accounting and inventory management, as well as the formation of accounting policies in the field of inventory accounting showed that some of the theoretical provisions in this direction need to be refined and improved. In particular, there are following main issues: -definition of elements of the accounting policy in the part of accounting of inventories in order to ensure the provision of complete, timely and reliable information about the company's manufacturing resources; -study the composition and structure of the primary documents in accounting for the availability and movement of stocks in order to rationally organizing their accounting.
The purpose of the article is to study theoretical and practical aspects of inventory accounting and determine the directions for its improvement.
Research results. A prerequisite for a rational organization of production is providing the enterprise with an appropriate quantity of production inventory. Manufacturing inventories are an integral part of an enterprise's assets because of their economic content, they are objects of labor, they have a significant impact on the financial results of the entity, since they occupy the largest share in the structure of the enterprises expenses in various sectors of the economy. The feature of production stocks is that they serve a single production cycle and their cost is completely transferred to the cost price of the manufactured product. Therefore, an important factor in the sustainable development of the enterprise is the availability of industrial stocks and their rational usage.
The correct organization of inventory accounting is a prerequisite for a stable business activity in modern economic conditions. One of the important issues of accounting organization at the enterprise is the formation of its accounting policy. In accordance with the Law of Ukraine «Accounting and Financial Reporting in Ukraine» [7] and NP(C)BO1 «General Requirements to Financial Reporting» [8], business entities choose the structure and composition of accounting policies independently that gives them wide opportunities in choosing the options for organizing the accounting process.
In general, accounting policy is a set of methods, ways, principles, methodologies and accounting procedures, targeted at generalizing accounting and the implementation of strategic and current goals and objectives. However, it is necessary to pay attention to the fact that the modern accounting policy went out beyond the system of accounting only, it should be considered in connection with management. Consequently, accounting policy is a mechanism for managing the accounting, that is carried out on the basis of the choice and development by the entity of the methods (options), rules and procedures regarding to the organization and methods of accounting, compilation and reporting based on generally accepted principles and on the specifics of the enterprise's activities for obtaining complete, objective, reliable and unbiased information in order to make informed management decisions [9, p. 30]. It should be noted that this definition is absolutely objective because in modern conditions the main direction of accounting policy is the impact on the results of management, that means the adoption of managerial decisions.
Documentation of the accounting policy of enterprises is realized through the «Order about accounting policy», that is an internal rule that regulates the organization of the accounting process of the enterprise. In the accounting policy of the enterprises should be reflected only positions of the organization of inventory accounting, for which there is an alternative or those for which it is necessary to develop a method of accounting independently. Table 1 presents accounting policy elements in the part of the organization of inventory accounting and their alternatives. Table 1 The elements of the accounting policy in the part of the organization of inventory accounting

The elements of the accounting policy object Alternative variants of the inventory accounting
The forms of the primary accounting documents It is installed independently by the enterprise based on industry specifics and management needs. It is using to reflect the facts of economic activity, for which there are the standard forms of the documents; not standard forms of documents and also the forms of documents for internal accounting reporting The working plan of accounts It is developed in accordance with the Accounts Plan of assets, capital, liabilities and business operations of enterprises and organizations [9]. It contains synthetic and analytical accounts for the formation of the accounting system in order to display timely and complete information in accounting and reporting. The units of the inventory accounting It is selected by the enterprise independently in accordance with the requirements of the Regulation (Standard) of accounting 9 «Inventories» [10] by the name or a homogeneous group (type) of inventories The method of accounting of the transport-storing expenses It is selected by the enterprise independently in accordance with the requirements of the Regulation (Standard) of accounting 9 «Inventories» [10]: by direct assignment of transport-storing expenses to the initial value of the unit of the inventory; by the average percentage (provided summarizing the amount of the transportstoring expenses for separate subaccount and their subsequent distribution) The method for assessing stock disposal It is selected by the enterprise independently in accordance with the requirements of the Regulation (Standard) of accounting 9 «Inventories» [10]: -the identified cost of the corresponding unit of inventory; -the average weighted cost; -the cost of the first time in stock inflows (FIFO); -regulatory expenses; -selling prices The rules of the document circulation and processing of accounting information It is installed by the enterprise independently based on industry specifics and management needs. The structure of the document circulation should ensure the timely income of the necessary information for accounting and control over the movement of inventories The organization of the analytical inventory accounting It is installed by the enterprise independently based on industry specifics and management needs. Analytical accounting accounts are used to control the storage and movement of inventories. On the analytical accounts inventories are recorded according to their types, places of storage, materially responsible persons, suppliers. The organization of the warehouse inventory accounting It is installed by the enterprise independently based on industry specifics and management needs. Warehouse accounting is organized according to the types of inventories, by the storage locations, by quantity and by batches of production inventory The internal control system It is installed by the enterprise independently based on industry specifics and management needs. The control over the organization of data of operational and current accounting should be carried out by the department of account. The supply service must provide the control over the implementation of the contracts, the timely income and posting of inventories Source: based on [11; 12].
Consequently, the definition of its elements in the accounting of inventories is of great importance at the stage of formation of the accounting policy of the enterprises. Therefore, the development of the «Order about accounting policy» of the entity is an important element of accounting that will ensure the provision of complete, timely and reliable information about the company's production inventories.
For creation an effective system of inventory accounting, it is necessary to ensure timely and qualitative information obtaining during its creation. The source of such information is the original document that is a written certificate of economic transaction, which gives legal force to the accounting records [13, p. 69]. Documentation is a complex and multifaceted process that is extremely important for accounting, analysis and control [14, p. 68]. Consequently, the completeness and quality of displaying information about inventories in accounting registers and financial reporting depends on the correct and rational organization of the documentation circulation of inventories.
Different economic processes of the movement of inventories, namely their income, storage, usage and transfer, characterize modern enterprise. Each of the listed processes should be documented and therefore, it should find its reflection in the primary accounting documents.
That's why the very choice of forms of primary documents in the inventory movement is an important element of the accounting organization. This is a guarantee of correct and complete information provision of the management system of the enterprise when making managerial decisions. Any business transaction that is reflected in the accounting and that is not confirmed by the original document is illegal. The document is the beginning and the basis of its management in accounting [15, p. 184].
In accordance with the Law of Ukraine «About the Accounting and Financial Reporting in Ukraine» [7], the basis for the accounting of business operations is primary documents. For the control and ordering of data processing on the basis of primary documents, consolidated accounting documents may be drawn up.
Primary documents are drawn up on forms of standard and specialized forms approved by the relevant state authority. The documentation of business operations can be done using selfprepared forms that must contain the requisite details or details of the standard or specialized forms [16].
In the process of documenting the movement of inventories, enterprises may use in their own discretion: -unic forms of primary accounting records for inventory accounting; -self-developed forms of documents that have mandatory requisites defined by law.
In order to improve the process of documentation of fuel flow operations, it is necessary to create the optimal amount of accounting and information support for fuel consumption, taking into account the objective needs of individual management levels. Thus, in order to confirm fuel exenses of the enterprise, it is expedient to use the documents that satisfy the information needs of inventory management of the enterprise and comply with legal requirements about the reliable documents.
Primary and consolidated accounting documents may be drawed up in paper or electronic form and must have the following requisites [7]: 1) the name of the document (form); 2) date of creation; 3) the name of the enterprise on whose behalf the document is drawn up; 4) the content and the volume of the business transaction, the unit of measurement of the economic transaction; 5) the positions of the persons responsible for conducting the economic transaction and the correctness of its execution; 6) personal signature or other data that allows to identify the person who participated in the conduction of the economic transaction.
We have developed and proposed a new document «Fuel Use Report» based on the analysis of the requisite composition of the primary documents of inventory accounting and the study of needs of the enterprise management system. This document has the following requisites ( Table 2) This document is filled out on a daily basis in the context of materially responsible persons and vehicles.
The proposed list of the requisites is optimal and contains all obligatory, as well as additional requisites that are the elements of convenience. The full usage of this document will ensure the receipt of information about fuel expenses of the enterprise.
The proposed document can be used as a cumulative for a week or a month, for example. It will be a little modified and will have an additional requisition «date of creation». The use of the proposed original document will provide operational reporting of information to the management staff.
For optimal organization of the fuel write-off procedure by the enterprise, it is recommended to develop an order of the enterprise about the streamline use of the company's car that will approve the form of the document to be used as the primary document for the write-off of fuel.
The orderliness of the document circulation will significantly increase the efficiency of the management of the enterprise. The speed and precision of obtaining the information necessary for the management decision depends on the clarity and efficiency of the movement, the processing of the documents and their transfer to execution. For that reason, it is necessary to develop a chart of the document circulation at the enterprise, as well as the schedules of the document circulation for business documentation.
Drawing up of the schedule of the document circulation of information about the usage of fuel (Table 3) consists of the stages of creation, verification, processing and storage of the document. It helps to find out the issues through which the executors the document passes, in which sequence the document moves, which technological operations with the document are carried out by each particular executor. The schedule of the document circulation of information about the usage of fuel improves the work of the accounting service, reduces the cases of late processing of documents, their loss, reduction of reporting time and increase the responsibility of employees of all levels for the timeliness of their drawing up, usage and processing. To do this each executor should be provided by a copy of the schedule of document circulation that specifies the time of the submission of the original document and the units of the enterprise to which it should be delivered.
Conclusions. Based on the conducted researches it has been established that accounting is directed at the management and accounting policy is one of the elements of the accounting system. It should be considered in connection with the management because in modern conditions the main direction of accounting policy is the influence on the results of management, that is, on making managerial decisions. The accounting policy of inventories is essential for the efficient accounting organization. So far as expediency, validity and detailing of the inventory accounting process needs for the determination of the results of the enterprise and the adoption of effective managerial decisions. In the result of the research, the constituent elements of the accounting policy in the part of the inventory accounting organization were determined; the necessary information that should be specified in the «Order about accounting policy of the enterprise» was identified. However, it should be noted that the above elements are not exhaustive and the enterprise can expand and supplement them, taking into account their information and technological needs. For a rational organization of inventory, accounting at the enterprise it is necessary to ensure the efficient organization of the document circulation at all stages of inventory accounting and to approve the forms of primary documents of the inventory accounting. Further researches should be aimed at optimizing primary inventory accounting.


extfieldsofstudy:
Mathematics
Computer Science

text:
A statistical machine learning approach for benchmarking in the presence of complex contextual factors and peer groups

The ability to compare between individuals or organisations fairly is important for the development of robust and meaningful quantitative benchmarks. To make fair comparisons, contextual factors must be taken into account, and comparisons should only be made between similar organisations such as peer groups. Previous benchmarking methods have used linear regression to adjust for contextual factors, however linear regression is known to be sub-optimal when nonlinear relationships exist between the comparative measure and covariates. In this paper we propose a random forest model for benchmarking that can adjust for these potential nonlinear relationships, and validate the approach in a case-study of high noise data. We provide new visualisations and numerical summaries of the fitted models and comparative measures to facilitate interpretation by both analysts and non-technical audiences. Comparisons can be made across the cohort or within peer groups, and bootstrapping provides a means of estimating uncertainty in both adjusted measures and rankings. We conclude that random forest models can facilitate fair comparisons between organisations for quantitative measures including in cases on complex contextual factor relationships, and that the models and outputs are readily interpreted by stakeholders.

1. Introduction. Benchmarking has been used to make quantitative comparisons in many sectors, such as health, government and education (Klassen et al., 2009). Two challenges with benchmarking are the variability and uncertainty of contextual factors hampering direct comparisons (Dimick, Staiger and Birkmeyer, 2010), and the correct interpretation of results by the intended audience (Wilson and Piebalga, 2008;Pope, 2009). Quantitative measures must therefore be adjusted for contextual factors before a fair comparison to be made between organisations. For example, when evaluating overall academic performance in schools, a contextual factor is the composition of backgrounds of students, which is known to affect academic performance (Redden and Low, 2012). Any difference in raw academic performance between two schools may be the result of real differences in the effectiveness of teaching strategies, or could be the result of different student backgrounds, so the effect of background must be taken into account before a fair comparison can be made.
Generally, organisations should only be compared with other similar organisations, because even if efforts are made to adjust for differences in contextual factors, comparison between dissimilar organisations risks substantial influence from unknown (and thus not adjusted-for) factors. In addition, comparisons become less valid as the qualitative differences between organisations grow. This is solved by separating groups into similar organisations, called here peer groups, within which comparisons are safer. A major early finding for strategic groups, a related theoretical group for commercial firms, was that similar strategies of firms were associated with differential performance outcomes depending on the strategic Keywords and phrases: benchmarking, peer grouping, ranking, random forest, data visualisation. group (Cool and Schendel, 1987). Thus the organisation's context is important for interpreting performance, and that comparisons may need to be restricted to within groups of similar organisations to ensure fairness.
Quantitative assessment can provide a means of ranking and/or partial comparison, though appropriate adjustment for the known contextual factors is required for it to be fair and useful. Most previous methods have used a linear regression approach to adjust for such factors (O'Malley et al., 2005;Kreutzer and Wood, 2007;Holzer and Minder, 2011). In one study (Holzer and Minder, 2011), the authors noted that the residuals are skewed to the right, which indicates the linear model is a poor fit, since residuals are assumed to be symmetric in linear regression. This could be a sign that the model was under-fitting, and that more complex relationships were present, or that the distribution of unmodelled error was asymmetric, rendering a linear model inappropriate depending on sample size. In another study, subtle departures from linearity were detected by binning the continuous variable and creating a set of dummy variables (O'Malley et al., 2005).
Another methodology is to first partition organisations using the contextual factors by clustering on similarity into a set of clusters of relatively homogeneous individuals (Zafra-Gómez, López-Hernández and Hernández-Bastida, 2009), which may comprise the peer groups. The raw measurement of two organisations may then be compared without the need to adjust, since substantial differences in contextual factors have been accounted for in the clustering.
There are some examples of more complex regression models for benchmarking. Zimmerman et al. (2006) used cubic splines to model the effects for three continuous variables. The method predicted the length of stay of patients in Intensive Care Units, adjusting these values for continuous contextual factors such as age, acute physiology score and prior length of stay such that their effect was nonlinear. A subset of the data was used as a hold-out to measure the predictive accuracy of the fitted model. While it is clear that a linear model would not have captured clear nonlinear relationships in the data, it is not clear to what extent the use of splines improved the predictive accuracy.
The task of adjusting a quantitative measure so comparisons can be made across different values of one or more contextual factors fits into the broader field of risk adjustment, which is popular in both actuarial science (Li et al., 2013) and health (Warmerdam et al., 2018). Several regression tree and random forest approaches have been developed to adjust risk factors in the presence of large numbers of contextual factors (Li et al., 2013) and interactive effects (Buchner, Wasem and Schillo, 2015;van Veen et al., 2017). The importance of interactions in adjustment was recognised by Goldstein and Spiegelhalter (1996) in a study of student examination results. Goldstein and Thomas (1996) noted that the inclusion or exclusion of a variable in an adjustment model substantially influenced the resultant adjusted values. The authors emphasised the importance of including all possible influences beyond control of the organisation in the model, or the resulting measures will be misleading.
In this paper, we propose using a random forest model with a statistical learning approach to adjust quantitative measures for contextual factors accurately in the presence of both nonlinearity adjusting for peer-groups as well, and compare its accuracy to a linear regression model. We estimate the uncertainty in adjusted comparative measures and rankings, and use the approximate predictive distribution as a benchmark against which an individual organisation's adjusted measure can be compared and understood. To ensure all stakeholders can understand the random forest adjustment model and outputs, we The resulting statistical learning model provides a better representation of the underlying value addition of organisations and a better basis for comparison, while also retaining interpret-ability for all stakeholders.

Methods.
To provide meaningful and fair comparisons based on the quantitative measure, we introduce the benchmarking problem as being equivalent to the statistical learning problem of regression. We use the random forest, an algorithmic model popular in statistical learning, as the means of adjusting the raw quantitative measure for the contextual factors. In order to estimate uncertainty in benchmarking outputs (adjusted measures and rankings) we use bootstrapping, which is also a key component in the random forest model. We then use an approximate predictive distribution as a benchmark for which individual measures can be compared. Finally, we introduce two visualisations used to communicate the benchmarking outputs without the need for domain knowledge in statistical learning.
2.1. Measure Adjustment as Regression. The problem of adjusting comparative measures for contextual factors corresponds to the statistical machine learning problem of regression, which seeks to find the most accurate model for predicting a response, which corresponds to the raw quantitative measure, given covariates, which correspond to the contextual factors. Therefore, throughout this work these two pairs of terms will be used interchangeably. Once they have been taken into account, the residual variation has no dependence on the contextual factors, so it provides a better representation of differences between organisations.
Mathematically, the adjusted comparative measures corresponds to the regression residual. Let there be n organisations in the cohort. Let the observed comparative measure value, which will be referred to as the raw measure, for unit i be denoted y i , with all n values denoted by y = (y 1 , ..., y n ). Let there be J contextual factors, which are coded into the vector x i ∈ R L where J ≤ K, with the entire cohorts contextual factors given by X = (x 1 , ..., x n ). Then we may propose that the variation in y i is partially attributable to the contextual factors x i , with this relationship described by a function f (x). Therefore, we can write an equation for y i as where the residual e i represents random variation not attributable to the contextual factors, and is distributed by an error distribution. The function f represents the expected raw measure value given the contextual factors x i . A correctly adjusted measure should allow different units i and j to be compared, even if the values of their contextual factors are different.
Given an approximation of f ,f , the residual is calculated to be the difference between the observed value y i and the estimated value given the contextual factorsf (x i ): The approximation to the functionf is done by fitting a regression model to the available data. Here we use a random forest model, which is described in Section 2.3.

Bootstrap Uncertainty Estimation.
Given the residuals are only estimates of the true deviation of the observed response y i from the expected value f (x i ) given contextual factors, it is important to quantify the uncertainty around the point estimates. This uncertainty is then used to evaluate whether there is evidence for differences in the adjusted measure in pairwise comparisons, as well as in ranking with uncertainty. Bootstrapping (Efron, 1979) is a method of approximating the error sampling distribution using only the data itself, without the need for a parametric model. Bootstrap resamples are created by first sampling observations from the data n times with replacement to form a resample D (b) = y (b) , X (b) . The regression model is then fit to D (b) to get an approximatef (b) . The statistics of interest are the residualsê , which are called the bootstrap replicates. When this is done repetitively many times, an approximate sampling distribution of the residuals is formed from the distribution of the replicates.
imsart-aoas ver. 2020/08/06 file: main-document.tex date: November 18, 2020 2.3. Random Forests. The random forest (Breiman, 2001) is an ensemble learning approach, and is composed of the average prediction of many individual decision tree models. Each tree is 'grown' from a random bootstrap resample of the data. At each node in the tree, a random subsample of the covariates is drawn, and then from this subsample the best cut is chosen to minimise prediction error. The prediction given by the forest is equal to the average prediction from the trees.
The number of covariates randomly drawn per node is a tuning parameter m try , which is chosen by cross-validation to prevent over-or under-fitting. Two popular measures of generalised accuracy are the root mean squared error of prediction, and the R 2 , which estimates the proportion of variance in the response explained by the model. The other parameter, n tree , is the number of trees in the forest, and it does not require tuning since there is no risk of overfitting. The computation time of the fitting algorithm does however increase with the number of trees and the improvement in accuracy becomes progressively smaller as new trees are added. It is therefore common practice to inspect the prediction accuracy of subsets of trees of different sizes to investigate if the prediction accuracy has levelled out or if more trees need to be added.
An advantage of the random forest over other models is that it has an inbuilt estimate of generalised (also called out-of-sample) error, called the out-of-bag error. Usually crossvalidation is required, separating the data the model is fitted on to the data where error is estimated, however this is not required in random forests. For a given observation in the data, by selecting only trees in the forest which are not fitted using it, one can use their averaged prediction instead of the average over the entire forest. Provided there are sufficient trees in the forest, every observation will have some trees which are not fitted using it, and so the process can be used to get an out-of-bag prediction for every observation. The resulting error estimate calculated from out-of-bag predictions is an unbiased estimate of the generalised error.
2.4. Ranking. Ranking is the problem of ordering the organisations from highest to lowest based on adjusted measure. A single "point estimate" of rank can be extracted from the residual estimates, but like the residuals themselves the ranking is not known exactly. Bootstrapping allows for ranking uncertainty to be quantified by ranking each set bootstrap residual replicates for many bootstrap resamples, providing a sampling distribution for the rank of each observation.
2.5. Approximate predictive distribution. To evaluate adjusted comparative measures, one needs to compare it against a reasonable benchmark distribution, which characterises the typical range one would expect for the organisation. For this we chose to use the approximate predictive distribution for the raw measure for a "new" organisation with the same associated contextual factors as the given organisation.
Bootstrapping can be used to approximate the predictive distribution by refitting the model for many bootstrap resamples and calculating bootstrap residual replicates for each observation. This has been shown for linear regression Stine (1985) and non-parametric regression Kumar and Srivistava (2012). Combining the replicates of all observations gives the approximate predictive distribution. However, even if the out-of-bag residuals are used in random forest, because an observation is sometimes chosen more than once for a bootstrap resample, the out-of-bag residual may use one bootstrap draw of an observation to predict for another bootstrap draw from the same observation. One could find the subset of trees which contain none of the bootstrap draws from an observation, but in practice this can result in only a few trees being available if the observation was drawn multiple times for a bootstrap resample.
Instead, we considered a modification to approximate the predictive distribution using only the residuals of observations not in the current bootstrap resample, called here the Outof-Resample residuals. To estimate this distribution we used a bootstrapping scheme: For B resamples b = 1, ..., B: Given there is an approximate 63.2% chance that an observation will be chosen for given resample (Efron and Tibshirani, 1997), only 0.378B bootstrap replicates will be retained for each observation on average. Therefore, more bootstrap iterations are required for the individual observations. However, to get the predictive distribution, we can use the entire set of replicates from all observations. A draw from the predictive distribution for a given x is equivalent to randomly picking a residual from the error distribution and adding it to the expected value f (x). The bootstrap predictive distribution simulates this as randomly picking an observation i from 1 to n, then randomly picking a resample b where D (b) does not contain i, and then adding the residualê To compare the predictive distribution to an organisation's adjusted measure, the distribution is then centred to 0, which we called the residual sampling distribution.
By combining the bootstrap residual replicates from all organisations, there are approximately 0.378Bn samples of this predictive distribution. This method assumes that the residual distribution is homogeneous over the covariate space, because the observation i is randomly sampled from the entire cohort.
A problem with this approach is that because at any given bootstrap resample, around a third of residuals are missing, it is not possible to compare residual values and extract a full ranking. To allow comparison between all pairs of observations, as is required for ranking, we used a multivariate normal approximation to the bootstrap residual distribution to get rank distributions. The covariance matrix, computed using pairwise complete observations, was not positive definite, so the closest positive definite matrix was obtained by eigendecomposition. Means, medians, standard deviations, and interquartile ranges of samples from the approximate normal were compared with the same statistics for the bootstrap residuals to determine if the fit was reasonable. Additionally, the same analysis was performed to compare pairwise statistics such as mean difference and correlations were computed to determine if the second-order relationships were well approximated.
With an approximate distribution for the predictive distribution as a benchmark, an individual organisation's adjusted measure and associated uncertainty can be viewed relative to this benchmark. We chose to use the Probability Integral Transform (Angus, 1994) to transform the organisation's bootstrap replicates into percentiles of the predictive distribution. Therefore, if an organisation's confidence interval bounds were within the predictive distribution's lower or upper tail, it would be clear that the organisation's adjusted measure was low or high respectively.
In addition to comparison relative to the cohort, comparison relative to an organisation's peer-group can also be computed. To do this, instead of combining bootstrap residual replicates from the entire cohort, only the replicates from the organisations in the peer-group are used, and the organisation's bootstrap residual replicates are compared to this peer group predictive distribution. Under this method, the assumption is that the predictive distribution is homogeneous over the peer-group, rather than the entire cohort.
2.6. Communicating Random Forests and Adjusted Measures with Uncertainty. The random forest has a measure of variable importance based on the out-of-bag error (Breiman, 2001). For each variable, the out-of-bag prediction is calculated after permuting the values of the variable, thus removing its capacity to assist in prediction. The resulting increase in the mean squared error is a measure of the variable's importance. We also utilised a measure of variable group importance, since variables could be grouped into subsets based on correlation. This measure uses the same principle of permuting values, but on a group level to remove the entire variable groups' contribution to prediction (Gregorutti, Michel and Saint-Pierre, 2015).
Hierarchical clustering was utilised to group variables based on correlation, and a cut-off of 0.7 was used, such that variables would only be clustered together if their linear correlation was greater than 0.7 or less than -0.7.
Partial dependence plots are visualisation methods for interpreting the marginal effects of predictor variables. For a particular predictor variable, partial dependence plots display the expected predicted value for a given value of the predictor, after marginalising out the effect of the other predictor variables. The resulting plot indicates where the predicted value increases and decreases in response to the predictor, however it should be treated with caution when there is statistical dependence between the predictor variable in question and the other predictor values.
Because stakeholders often prefer simpler, intuitive visualisations rather than statistical graphics, we developed two methods of presenting the required information for interpreting the adjusted comparative measure. A simple, single dimensional "spirit-level" plot was developed for communicating the value of the comparative measure of an organisation relative to its cohort or peer-group. The axis of the spirit-level are percentiles from 0 to 100% of the bootstrap-estimated predictive distribution, where 0% represents the lowest bootstrap replicate, and 100% the highest replicate. Guidance lines are given for 10%, 25%, 50%, 75%, and 90%, indicating what range the top 10%, lowest 10%, and quartiles of raw measures are likely to take, given the predictive distribution for the organisation. To further facilitate interpretation, the associated quantile values are given above the guidance lines, and these values are shifted by the predicted value of the organisation in question, so these values are specific to the organisation and can be compared with the organisation's actual measured value.
The organisation's actual adjusted measure is not known exactly as it is a function of the fitted value, which is uncertain. To communicate this uncertainty, we depict it using a horizontal 90% confidence interval for the organisation's own adjusted measure in terms of the percentiles of the predictive distribution.
To provide an understanding of how the random forest adjusts comparative measures to a non-technical audience, the mean adjusted measure of the most similar organisations is also plotted on the spirit level plot. In addition, one-dimensional plots for the contextual factors depict the values of the organisation in question, the most similar organisations, and the peer-group. The values are converted to percentiles of the data distribution using probability integral transform for the empirical cumulative distribution. This ensures they are simple to interpret. The organisation can thus see if they are close to their neighbours and to their peer-groups for the important variables (as judged by random forest importance).
2.7. Case Study: Benchmarking of service provision. The methodology developed was used to apply quantitative benchmarking to a set of organisations involved in providing services to clients. A total of 14 client demographic summary statistics were calculated for each organisation, which describe socioeconomic status, ethnicity, gender, regionality/remoteness and age. To preserve confidentiality, these variables have been relabelled as covariate-X, where X is a number, so their exact meaning is obscured. The raw comparative measure was calculated for each organisation, and this is also anonymised for confidentiality reasons, although it relates to the amount of service provision, where a higher value indicates an organisation has provided services to a greater degree.
Data were transformed where required to reduce skewness: proportions were transformed using a logit distribution, while count and positively skewed variables were log-transformed. The response was log-transformed before the random forest was fitted. Peer-groups were constructed based on the covariates using a constrained clustering algorithm developed in a previous paper (under review).
All data processing and analysis was carried out in R (R Core Team, 2020). All R scripts required to perform the analysis are publicly available online (https://github.com/ danwkenn/peer-group-benchmarking).
3. Results. The smallest cross-validation root mean squared error was for an m try = 4 variables, though the highest R 2 was for around m try = 2 to m try = 3 (see Appendix). The differences in accuracy between m try values were however very small compared to the estimated standard deviations for both accuracy metrics, so there was no indication that any given m try value was substantially better than any other . Therefore, the value of m try was fixed to 4 for the final model. The cross-validated R 2 value was approximately 0.57 (SE: 0.12), meaning the model explains approximately half of the variation in the response with covariate variation. The parameter n tree , which is the number of trees, was chosen to be 300, and the out-of-bag accuracy was found to have reached near-optimal values.
The partial dependence plots (Figure 1) showed that the most important variable, covariate 8, had a monotonic positive effect on the response, increasing rapidly before leveling off in a single step. The variable was also not highly correlated with any other variables, so this is not affected by dependencies. Other variables, covariate 26 and covariate 10 had similar effects, while covariate 4 had a small, positive, mostly linear effect. The plot for covariate 14 indicated a non-monotonic effect, however the error bars were wide, likely due to high correlation with other variables.
The variable importance measures (see Figure 1) indicated two dominant covariates. The most important variable for predicting response was covariate 8, which is related to cultural and linguistic diversity in clients. Covariate 26, which is related to client age, was also important. Interestingly, the peer-grouping dummy variables, labelled cluster2 and cluster3, did not feature prominently. This is to be expected, as the peer-groups were created using the covariate data, so any differences between the peer-groups would likely be accounted for in the covariates.
The group variable importance (see Figure 1) again noted the importance of covariate 8, as well as covariate 26 grouped with covariate 27, which are both age-related. The group of covariate 14 and covariate 18 were also important, with both of these being related to regionality. There was some indication that a group of covariates 10, 16, and 20, which related to remoteness and indigenous ethnicity were important for predicting the the response. Again, the peer group variables did not feature highly.
3.1. Comparison with Linear Regression. The average cross-validation error (root mean squared error) for linear regression was 0.86 (SD: 0.29), compared to 0.69 (SD: 0.13) for the random forest. These values are comparable, however the cross-validation error for the two methods are highly correlated and dependent on the data. A bootstrap estimate of the difference in out-of-sample error was 0.30 (SD:0.12), showing that the random forest was consistently more accurate than the linear regression. Based on the R 2 values, the random forest explained an average of 30.5% (SD: 13.1%) more of the variation in the response than linear regression.  showing the effect of predictors after marginalising over the effects of all other predictors. Rug-plots are are included at the bottom of each plot to incidate where the actual data is concentrated. Bottom-left shows variable importance, as measured by increase in mean squared error for all 13 covariates, and peer group. The peer-group differences are represented by the two dummy variables cluster3 and cluster2, representing the change from Peer Group 1 to Peer groups 3 and 2 respectively. Bottom right shows the group variable importance calculated using mean increase in mean squared error. Variables were grouped using heirarchical clustering with a correlation cut-off of 0.7.
Analysis of the residuals showed that the LR model failed to fully account for the relationship between the response and the covariates 10, 14 and 26, as residual patterns could be seen in the residual scatter-plots (see Figure 2). This was particularly pronounced for covariate 14, where the residuals of organisations with intermediate values were on average less than 0. Here, the linear regression model is over-estimating the organisation's expected raw measure, and thus is not flexible enough to account for the nonlinearity in this variable's effect. The linear regression was also unable to fully account for the step-wise relationship between the raw measure and covariate 8, although this is not visible in the residual plots since the step occurs close to the minimum of the data. Therefore, the overall result is that the LR model is biased due to under-fitting, resulting in larger residual uncertainty overall, and at an individual organisation level specific biases occur in residual estimation.
3.2. Estimation of the residual sampling distribution. For 10,000 bootstrap resamples, 200,000 residual replicates were calculated, with approximately 73,000 being out-ofresample residuals. There was a marked difference in distribution between the entire set of bootstrap residual replicates and the out-of-resample replicates. We found over 50% of the bootstrap residual replicates were equal to 0. In contrast, none of the out-of-resample replicates were equal to 0, which is to be expected, since no observations are used in their own prediction. The result was the distribution of the entire set having a much lower standard deviation and sharply peaked around 0 (see Figure 3), compared to the subset of out-of-resample replicates.
There was some indication of multimodality in the out-of-resample residual distribution, however the modes did not correspond to peer group. There were small differences between the width, center and shape of the bootstrap residual distributions for specific peer groups, although they were mostly overlapping. Peer-group 2 had a wider range than 1 and 3, although this was mostly due to longer tails since the interquartile ranges were comparable. The similarity of means to medians indicated symmetry of residual distribution in each of the peer-groups, although there was some multimodality present as well. This implies that with respect to the raw measure, there is approximately the same probability that an organisation will be above its expected raw measure as below. This was not the case for Peer Groups 1 and 3, which exhibited positive and negative skew respectively.
We compared several statistics to investigate whether the normal approximation was accurately portraying the centres spreads, and correlations between the bootstrap residuals (see Figure 4). The means of the normal approximation matched the bootstrap residual means exactly, which is to be expected given the method uses the bootstrap means, and the medians were also similarly precise. The standard deviations were well correlated, but there was a small positive bias of around 0.018. The interquartile ranges were also well correlated with a larger positive bias. The pairwise differences were highly accurate, as expected, although there was a small positive bias on the standard deviations of the pairwise differences. There was a good correspondence with the correlations, although for highly correlated pairs (Pearson's R 2 > 0.5) the normal approximation counterparts were systematically less correlated.  The probabilities that the difference is less than 0 appeared to be unbiased, with small discrepancies. Therefore, given these probabilities are the basis for ranking we determined that approximation was accurate enough for use in ranking.
3.3. Rankings. Rankings with associated 90% confidence intervals, modes (most likely rank) and mean were computed from the normal approximation samples (see Figure 5). There was substantial variation in the width of these intervals, ranging from 2 to 100, with the greatest widths occuring when the mean residual was close to 0. It was evident that the standard error and mean of residuals was a very good explanation for the size of the confidence inimsart-aoas ver. 2020/08/06 file: main-document.tex date: November 18, 2020 terval ranks. The standard error tended to set an upper limit to the confidence interval range, under which there was some variability, which was controlled by the absolute value of the mean of the residual. The result of this was a high degree of precision in rank for the highest and lowest-ranked observations and a wide range for middle observations. Residual standard error was partially controlled by the number of close observations, as there was a small correlation (R 2 = 0.11) between the standard error and the mean distance between the nearest 10 observations. Therefore, the uncertainty in ranking is most acute for non-extreme organisations, with proximity to other organisations being a small factor.
3.4. Communicating Benchmarking Results. We devised a two-plot system for communicating the adjusted comparative measure values to non-technical audiences. The first is the spirit-level plot, which expresses the organisation's measure and associated uncertainty with respect to either the predictive distribution for the entire cohort, or for the individuals associated peer-group. The residual sampling distribution was recentered to be around the predicted raw measure for the organisation, and guiding values were transformed to the scale of the raw comparative measure. By using values of the raw comparative measure, an organisations's representative can understand the scale of the plot without having to understand the variable transformations used in the analysis, or the adjustment model used. In addition, the percentiles of the guiding values are provided, enabling a probabilistic insight into the intervals. Some accompanying text was placed under the spirit-level giving guidance as to the interpretation of the graphic: The above plot shows your [quantitative measure], adjusted for context (red dot) relative to the entire cohort/peer group. Your measurement also includes a horizontal error bar, because there is some measurement error around the adjustment. The bar indicates the values for which we have 90% confidence your adjusted value lies, relative to the rest of the cohort. The spirit level shows the range of possible adjusted values for the entire cohort/peer group. Each of the horizontal guidance lines shows a percentiles. For example, the 90% guidance line on the right of the plot indicates that according to the model, there is a 90% probability that the value of [quantitative measure] of an organisation with your clients would be equal to or below this value. The other dots on the plot are the adjusted values for the 10 most similar organisations to you, based on the client demographics.  The densities shown are not useful to a non-technical audience, however they provide a visual link between the spirit-level plots and the bootstrap predictive distributions in which they are based, and may be useful for analysts. Differences between the cohort-and peer-group spirit plots can be explained by discrepancies between the distributions. The percentile plots (see Figure 7) show the organisation's covariate values against the cohort, the peer-group, and the 10 nearest neighbors. The covariates shown are chosen using the random forest variable importance measure. In the case of the highest adjusted measure observation, the organisation is well surrounded by the neighbors and typical the peer group, and this justifies the adjusted measure given in the spirit-level plot. For the lowest adjusted measure organisation however, the value for covariates 8 and 10 were quite different from the 10 nearest neighbors, although not atypical for the peer-group. In such a situation, it may be indicating that in the multidimensional parameter space this organisation is somewhat of an extreme value, and would justify removal from the data-set or making the organisation in question not subject to quantitative comparisons.
4. Discussion. In this paper we fitted a random forest model as the adjustment model for a comparative measure for a data-set with complex contextual factor effects, and incorporated the effects of peer grouping. This model choice, which was informed by out-of-sample predictive accuracy, was shown to outperform the linear regression method in both accuracy, and in reducing bias in estimation of each organisation's adjusted measure. We developed a benchmark using bootstrapping relative to which organisations' measure values can be evaluated, and a procedure for approximating rank uncertainty. Importantly, the benchmark that an organisation is compared against can be cohort-level, or specific to their peer-group, to ensure comparison are valid. We used a novel visualisation as means of communicating the random forest model and the adjusted measures to technical and non-technical audiences. Although the random forest was used for this work, most of the analysis presented could be described as model-agnostic. The bootstrapping for residual distributions, normal approximation for ranking, as well as the spirit-level and percentile plots could all be used with other statistical learning regression models. The importance measures used here are specific to random forests, however, variable importance has been studied for Generalised Additive Models (Goetz, Guthrie and Brenning, 2011), linear regression (Grömping, 2015), and gradient boosting machines (Friedman, 2001). We found in this case that the random forest out-performed linear regression, but this is likely to be a function of the data. In general, we recommend using an out-of-sample prediction accuracy measure to determine the best model for benchmarking.
The random forest in this case study performed well because of nonlinear relationships between the response and the covariates. The step-wise relationship found for covariate 8 close to its minimum value is easily modelled by the random forest, since the binary cuts of regression trees approximate step function relationships well. The linear regression by contrast failed to approximate this relationship well as well as non-monotonic relationships seen in other variables. In addition to superior accuracy, the random forest's inbuilt importance measure is useful for identifying which variables are key to predicting the comparative measure, and thus important for adjusting. A second advantage of the random forest is the out-of-bag prediction, which is useful for preventing overfitting in predictions. However, for bootstrap approximation of the predictive distribution is was critical to include only out-of-resample replicates to prevent a strong negative bias in residual uncertainty estimates. This is important because to ensure fair comparisons, adjusted measures must be independent of contextual factors and be presented with an accurate estimate of uncertainty to avoid overconfidence in ranking or comparisons to a benchmark.
For parametric models such as linear regression, the value of the standard error is easily attributable based on proximity of the given observation to the data mean, however this is not the case for random forests. The uncertainty in rank confidence intervals was very well explained by the mean and standard error of the residuals, which is to be expected. However, there was more difficulty in explaining the standard error of residuals themselves as the proximity of an observation to other observations only partially explained it. It is likely that regions where there is a strong effect of covariates have greater uncertainty than at locations where the mean response is relatively constant. Therefore, Euclidean distance may not be a sophisticated enough measure to describe proximity, and further work may reveal a measure which can better reflect the available information in the data for prediction at a given point, and thus the residual uncertainty.
A limitation of this work is that the bootstrapping scheme cannot directly recover full rankings. Our solution, the use of a normal approximation to the joint residual distribution, is only correct to mean and standard deviation, and it was evident there was small deviations in correlation between residuals. A more sophisticated approach could use available three-way and higher order correlations to achieve a closer approximation to the bootstrap distribution. Another approach could leverage the fact that for each bootstrap replicate, it is possible to obtain a partial ranking based on the non-missing bootstrap residuals, so ranking aggregation procedures may be useful to establish a full representative ranking (For an example see Ailon, Charikar and Newman (2008)).
The bootstrap provided a means of approximating the predictive distribution of the residuals given model uncertainty. A key assumption of the use of it as a benchmark is that the error distribution is homogeneous over all organisations. This assumption is partially relaxed by making peer-group-specific distributions, however it does not control for sub-peer-group changes in the error distribution. One option might be to use only the closest neighbouring observations to form a predictive distribution for a given observation. However, determining how many neighbours are used requires balancing a trade-off between the number of observations used and how locally-specific the predictive distribution is.
We found that there were only small differences in the bootstrap residual distributions between peer-groups, indicating a similar spread of comparative measures for organisations within them. This was further seen in the spirit-level plots, where the relative adjusted measure percentiles for organisations did not change markedly. This is however not an indication that comparisons such as difference calculation or ranking can be done between organisations across peer-groups in general. As in the industry organisation economics literature for strategic groups, disparate organisations may employ the same strategy yet yield different results in terms of performance. It is therefore imperative that comparisons be made only within peer-groups of similar organisations.
The critical challenges in benchmarking are developing appropriate and meaningful metrics for comparing organisations from data, and then interpreting those metrics in context so as to ensure fair and valuable comparisons. This work has produced tools for the second challenge, using a principled, statistical learning approach. While it is tempting to account for contextual factors using linear regression, we have shown that the random forest provides a more comprehensive adjustment in real data with complex effects. We have shown that the random forest adjustment model can be explored and understood by computing relative variable importance and partial dependence plots, and that outputs such as ranking and comparison with a benchmark can be computed with bootstrap-approximated uncertainty. Finally, we have developed visualisations which can be interpreted with minimal domain knowledge, expressing both the adjusted measure relative to an intuitive benchmark, ensuring all stakeholders are able to use this information for organisational learning. KM and DK are supported by an ARC Laureate Fellowship (FL150100150). The authors would like to acknowledge the agency which contributed financial support towards this research.