I have a dependent/response variable that is categorized into 7 different levels with 1 being least significant and 7 being most significant. I have 20 plus independent/predictor variables that are nominal, ordinal, interval and ratio data that I want to utilize. I know I cannot use regular logistic regression because my dependent/response variable is not binary. I am pretty sure I need to use multinomial logistic regression but am unsure. Any ideas?
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$\begingroup$ Look into ordinal logit. $\endgroup$– generic_userMar 24, 2017 at 16:56
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$\begingroup$ @generic_user That looks like it should work! So I can use any data type of predictor variable for this as well? $\endgroup$– AlexMar 24, 2017 at 17:16
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In your situation, beyond each method's assumptions, there are several considerations that could affect a choice between one of the logistic regression techniques (ordinal or multinomial) and a simpler, probably more familiar ordinary least squares or linear regression.
Suppose you have very few cases scored 1 or 7; linear regression would handle those data better, and with logistic you might not be able to obtain estimates for certain groups for certain main effects, let alone interaction effects.
Also, consider your audience: will they require a particular level of rigor (will they be aware of or care about the differences in underlying assumptions), and will they be able to easily interpret a given technique's typical sort of results.
Then there is the matter of analytical flexibility: there are some diagnostic procedures that can be done only with, or more informatively with, linear regression.
One solution you might find appealing is to create a linear model for the R-squared, coefficients, and diagnostics it offers, and then an ordinal logistic model for the probabilities of being in certain groups, as well as for p-values--if you use them. (Drawback: variable selection might turn out quite differently between the two.)
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$\begingroup$ I do not believe linear regression would work because my dependent is not continuous The 1-7 would be ordinal and be similar to rankings with 1 being least significant and 7 being most significant. I am working with point data that was assigned values based on a kernal density test tool in ArcGIS. I am thinking ordinal logistic regression would be the best choice here because I can use multiple forms of data types for the predictor variables and my response variable can have 7 different options based on the different density outputs. (Correct me if I am wrong!) $\endgroup$– AlexMar 24, 2017 at 18:28
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$\begingroup$ I agree that there plenty of cons to go with the pros of OLS here, and you may well be heading in the best direction. But wouldn't you agree that few people would balk at linear regression with a non-continuous dependent variable (DV) in, say, 12 categories. And you'll find many people using OLS on DVs with fewer categories than 7. Even, sometimes, binary DVs (the "linear probability model"). I'd say some of those people have good arguments for doing so. Cheers ~ $\endgroup$– rolando2Mar 24, 2017 at 18:57