Answers.Body: <p>Here is my solution to the problem. I am posting it here in case anyone else come up with the same idea but did not know how to formulate it in mathematical notation!</p>
  
  <blockquote>
    <p>$$ \psi_i = \sum_{i=1}^9 S_i $$</p>
    
    <p>where $S_i$ is the score function and defined as:</p>
    
    <p>$$
  S_i = \cases{
    0 &amp; \text{if $\theta(x_i) &lt; Q_1$ or $\theta(x_i) = $ benign/neutral} \\
    0.5 &amp; \text{if $Q_1 \leq \theta(x_i) &lt; Q_3$ or $\theta(x_i) = $ possibly damaging/uncertain} \\
    1 &amp; \text{if $\theta(x_i) \geq Q_3$ or $\theta(x_i) = $ damaging}
  }
  $$</p>
    
    <p>The $\theta(x_i)$ is the pathogenicity or conservation score for variant $x$ as defined by model $i$ and $Q$ denotes the quartile range for scores from M-CAP, CADD, GERP and Phylop models.</p>
  </blockquote>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-08-18T09:47:56.360Z
Answers.Text: If Q are quartiles, then the last line for damaging shouldn't be $>Q_3$?
Answers.UserDisplayName: llrs
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2018-03-31T15:59:05.397Z
Answers.Text: @Konrad and Reza : Can you look into this problem and provide some suggestions. https://math.stackexchange.com/questions/2716192/how-to-convert-a-detailed-mathematical-statistical-compuational-process-into-ma
Answers.UserDisplayName: everestial
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-08-17T19:47:04.523Z
Answers.LastActivityDate: 2017-08-18T17:39:08.600Z
Answers.LastEditDate: 2017-08-18T17:39:08.600Z
Answers.UserDisplayName: RJF
Body: <p>This is a cross-post from <a href="https://math.stackexchange.com/q/2380215">Mathematics forum</a>. As no one has answered it yet, I fIgured post here as well.</p>
  
  <p>I would like to describe a transform I used to rank my data points. I have recoded my variable columns from $10$ measurements with different range to $n$ (for each measurement) where $n \in \{0,0.5,1\}$.    </p>
  
  <p>For columns where measurements were expressed as categorical values I simply recoded the categorical value to either $0$, $0.5$ or $1$ and for continuous variables I recoded the lower quartile as $0$, interquartile as $0.5$ and upper quartile as $1$ and finally I summed the recoded values to produce a single score $\sum n_{i1,..i10} $ for each row. </p>
  
  <p>I am trying to write my method and I'd like to have it in mathematical notation. I was wondering if anyone could help me with this!  </p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-02T22:09:59.793Z
Comments.Text: Maybe try https://stats.stackexchange.com/
Comments.UserDisplayName: Alex Reynolds
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-03T07:54:34.203Z
Comments.Text: What do you mean by "have it in mathematical notation"? Can you give an example of something you consider "in mathematical notation"?
Comments.UserDisplayName: bli
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-03T07:55:28.047Z
Comments.Text: Also, it would be good to include the link to the cross-post
Comments.UserDisplayName: bli
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-03T09:29:36.913Z
Comments.Text: Hi bli, Thank you for your comment. By mathematical notation I mean mathematical representation of my transform. I am including the link as you suggested!
Comments.UserDisplayName: RJF
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-04T09:45:14.693Z
Comments.Text: Your question is not very clear to me. So can you please try to explain it with some example. Then we may able to help you.
Comments.UserDisplayName: Arijit Panda
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-04T09:56:07.130Z
Comments.Text: Have you looked at the dataframe I uploaded in Mathematics forum?
Comments.UserDisplayName: RJF
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-04T10:27:43.863Z
Comments.Text: Yes, I did. But still it not clear.
Comments.UserDisplayName: Arijit Panda
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-09T21:10:13.680Z
Comments.Text: I think the problem with your question is two-fold. 1) you don't provide any reproducible data so that we can grasp the details of how you calculate this "rank" score. [See this post for an example how you would make a reproducible example in R to get an idea of what we mean by "reproducible example"](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) 2) there is not likely to be a mathematical notation for what you have done, because there is no mathematical formula to convert strings ("I", "II", "III") into numbers. One way that you could potentially solv
Comments.UserDisplayName: Reilstein
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-10T08:22:08.330Z
Comments.Text: I think that "mathematical notation" does not necessary have to consist in "formulas". One could probably define a bijection between a set of strings and a set of numbers, in proper mathematical notation, and that would validly describe a conversion procedure.
Comments.UserDisplayName: bli
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-10T14:56:35.360Z
Comments.Text: Yeah you are probably right that there is some valid way of describing the rank score. I imagine in this case it would be something more akin to a key than notation/formula, but if you have an idea how to describe it why don't you add an answer?
Comments.UserDisplayName: Reilstein
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-08-10T15:16:41.953Z
Comments.Text: As you pointed out, it is difficult to grasp the details of what the OP wants. Besides, it's been a long time since I last wrote maths formally.
Comments.UserDisplayName: bli
Tags: <modelling>
Title: Mathematical notation for formulating a rank score
ThreadText: # Mathematical notation for formulating a rank score
  
  (Asked by: username_0 on 2017-08-02)
  
  This is a cross-post from [Mathematics forum](https://math.stackexchange.com/q/2380215). As no one has answered it yet, I fIgured post here as well.
  
  I would like to describe a transform I used to rank my data points. I have recoded my variable columns from $10$ measurements with different range to $n$ (for each measurement) where $n \in \{0,0.5,1\}$.
  
  For columns where measurements were expressed as categorical values I simply recoded the categorical value to either $0$, $0.5$ or $1$ and for continuous variables I recoded the lower quartile as $0$, interquartile as $0.5$ and upper quartile as $1$ and finally I summed the recoded values to produce a single score $\sum n\_{i1,..i10} $ for each row.
  
  I am trying to write my method and I'd like to have it in mathematical notation. I was wondering if anyone could help me with this!
  
  **Tags:** modelling
  
  > **Comments:**
  > **username_1**: Maybe try https://stats.stackexchange.com/  
  > **username_2**: What do you mean by "have it in mathematical notation"? Can you give an example of something you consider "in mathematical notation"?  
  > **username_2**: Also, it would be good to include the link to the cross-post  
  > **username_0**: Hi bli, Thank you for your comment. By mathematical notation I mean mathematical representation of my transform. I am including the link as you suggested!  
  > **username_3**: Your question is not very clear to me. So can you please try to explain it with some example. Then we may able to help you.  
  > **username_0**: Have you looked at the dataframe I uploaded in Mathematics forum?  
  > **username_3**: Yes, I did. But still it not clear.  
  > **username_4**: I think the problem with your question is two-fold. 1) you don't provide any reproducible data so that we can grasp the details of how you calculate this "rank" score. [See this post for an example how you would make a reproducible example in R to get an idea of what we mean by "reproducible example"](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) 2) there is not likely to be a mathematical notation for what you have done, because there is no mathematical formula to convert strings ("I", "II", "III") into numbers. One way that you could potentially solv  
  > **username_2**: I think that "mathematical notation" does not necessary have to consist in "formulas". One could probably define a bijection between a set of strings and a set of numbers, in proper mathematical notation, and that would validly describe a conversion procedure.  
  > **username_4**: Yeah you are probably right that there is some valid way of describing the rank score. I imagine in this case it would be something more akin to a key than notation/formula, but if you have an idea how to describe it why don't you add an answer?  
  > **username_2**: As you pointed out, it is difficult to grasp the details of what the OP wants. Besides, it's been a long time since I last wrote maths formally.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_0 on 2017-08-17. Score: 1
  
  Here is my solution to the problem. I am posting it here in case anyone else come up with the same idea but did not know how to formulate it in mathematical notation!
  
  > $$ \psi\_i = \sum\_{i=1}^9 S\_i $$
  >
  > where $S\_i$ is the score function and defined as:
  >
  > $$
  > S\_i = \cases{
  > 0 & \text{if $\theta(x\_i) < Q\_1$ or $\theta(x\_i) = $ benign/neutral} \\
  > 0.5 & \text{if $Q\_1 \leq \theta(x\_i) < Q\_3$ or $\theta(x\_i) = $ possibly damaging/uncertain} \\
  > 1 & \text{if $\theta(x\_i) \geq Q\_3$ or $\theta(x\_i) = $ damaging}
  > }
  > $$
  >
  > The $\theta(x\_i)$ is the pathogenicity or conservation score for variant $x$ as defined by model $i$ and $Q$ denotes the quartile range for scores from M-CAP, CADD, GERP and Phylop models.
  
  > **Comments:**
  > **username_5**: If Q are quartiles, then the last line for damaging shouldn't be $>Q_3$?  
  > **username_6**: @Konrad and Reza : Can you look into this problem and provide some suggestions. https://math.stackexchange.com/questions/2716192/how-to-convert-a-detailed-mathematical-statistical-compuational-process-into-ma  
  
  ---
  
  