# Building separate logistic regression models for each categorical variable

I am building a binary logistic regression model. I am not sure if using the variables as interactions is a better choice than building separate models for level of a categorical variable. Is there a way to determine this? For ex, there are 2 categorical variable with 2 levels each - 1.Regions - East and West 2.AGI - High and Low The response variable behaves differently for each level i.e. East has higher number of positives response and so does high AGI. here is my question - Is it good to build separate models for each level i.e. have 4 models East and high, East and Low, etc.? Or use the 2 as categorical variables in one model? How do you determine when to split the data into separate models? I have built separate models when i knew the behaviour of the data (independent variables) are different in each level of a categorical variable.

Thanks!

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## 1 Answer

You do not need to determine this a priori. You can build the same models in a unified framework if the highest order model has interactions between the two dichotomous covariates and the other predictors. That way you would allow separate intercepts and slopes for the other covariates. The decision should should be made on the basis of the underlying knowledge in the domain of investigation, anyway. Is it meaningful to consider comparisons of high and low AGI (whatever that might be) as being something that is independent of Region?

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Thanks DWin. I personally think the segments should be made based on business logic but wanted to know if there was a statistical way to determine this. Also, hese be introduced as independent variables or should i include the interaction terms. If so, how do i determine if the interactions need to be added? I plotted the average response (binary) against the interaction terms to check for a trend. Some interaction terms have the same average response rate. For e.x. East-Male and East-Female have similar response rate. Can i use them as independent variables? Thanks! –  Nik S Feb 21 '13 at 15:31
Yes. You can test for homogeneity of Sex effect within AGI category in a regression framework by comparing Y~ AGI + Sex with Y ~ AGI * Sex. –  DWin Feb 21 '13 at 18:34