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I am having trouble finding any resources to help me interpret my logistic regression results. I'm using SPSS, but I don't think that matters a whole lot. I understand the odds ratio concept (as well as a beginner can), but the real confusion for me is in determining significance of independent categorical variables with more than two categories. Nearly all examples I find have theirs coded as 0 or 1. With my independent variables, I have as many as 17 categories for one variable.

Specifically, here is an example:

For the "crash type" variable as a whole, the significance is .027 (significant)

Then there are 18 categories for "crash type," none of which individually show significance in the model.

(See image.)

How do I interpret this or report this? Would it be to say that crash type is a significant factor, but no specific type is? That doesn't exactly sound logical, does it? And vice versa... for a categorical variable which is significance "overall," but an individual category is... how to go about this?

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When dealing with categorical variables with more than two categories (i.e., that manifest as multiple terms in the model) you need to assess the inclusion of the variable using a test that includes the entire variable, and not just particular model terms for specific categories. Hence, it is essentially useless to look at the individual T-tests in the coefficient estimates table. Categorical variables like this can be assessed using partial F-tests that take account of the whole variable, as manifested by the set of all its terms (see e.g., here).

In order to conduct a partial F-test on a categorical variable you need to fit your regression model with and without that variable included, and record the residual sum-of-squares in each case. You can then calculate the F-statistic for the test and the associated p-value. This test will allow you to test the hypothesis that there is a relationship between the categorical variable and the response variable.

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  • $\begingroup$ So let's say that I test a variable and determine that it indeed significantly contributes to the model. How do I interpret, in words, the significance of this variable when none of its categories individually are significant? "The crash type variable is significant, however no specific type of crash yields explanatory value...?" Is this occurrence a sign that I am missing an interaction of some kind? $\endgroup$
    – Bkk
    Commented Jan 30, 2019 at 17:18
  • $\begingroup$ The notion of "significance" applies to quantities of evidence, not variables. So you would usually just say, "There is statistically significant evidence (at such-and-such significance level) of a relationship between [regressor variable] and [response variable]." There is no reason to mention individual T-tests at all --- these are misleading when applied to a categorical variable with more than two categories. $\endgroup$
    – Ben
    Commented Jan 30, 2019 at 22:10

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