Single or multiple model. How to know beforehand? I am building a probability of default model based on behavioral information. The dataset is a loan portfolio, which contains 4 types of loans: mortgage, unsecured loans, car loans and credit cards. The goal is to predict the credit quality of the client after loan issuance based on his behavioral information, such as current account balances, overdue amounts, days past due and various other factors. In order to enhance the model performance I was thinking of splitting the model into several sub-models for different types of clients. For example we could split the dataset into two subsets, clients with and without overdue payments, and then fit separate models for each sub-segment.
Questions:

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*Are there any quantitative ways to establish if it would be beneficial to split the model into sub-models? The usual approach is to fit a variety of models and see what works best, however I find this approach to be quite rudimentary and time consuming.


*If yes, how could we identify the optimal segments that the data should be split into? In my example I gave a split based the presence of overdue payments, however, another way could be to create separate models based on the products that the client has.
So far I was doing such splits simply based on business logic and data availability, however it would be great to find an algorithmic way to do so as well.
I am limited to only using logistic regression due to regulatory requirements

Ask yourself: are there any general properties of loans that are shared between different types of loans? Saying it differently, can things learned from one kind of loan be transferred to another kind of loan? If yes, it may be beneficial to have a single model. You would end up with both more data and more diverse data.
On another hand, it may be more practical to have many smaller models. Often it would be easier to build a model that performs well for a particular kind of data, rather than building one that works equally well for all the kinds of data. Another practical reason for many models is that you can have different people working on the models independently, while a single model usually can be improved only by a single person or team at the same time. Validating smaller, more focused, models may be easier as well. The model would have a business purpose, with a smaller models, you need to sell each of the models to a single stakeholder, with one-size-fits-all model, you need to satisfy all the stakeholders at the same time--it might be hard.
How to split? Combine "similar things" together, split the "dissimilar things". There's no single rule on how to do that. The key consideration is here if combining the data is beneficial in terms of the model being able to learn some of the characteristics that would be useful for all the data. You would need both domain expertise and exploratory data analysis to guide you.
