Multiple Logistic Regression Interpretation for Dependent Variables with Multiple Levels

[#1]

I am trying to run a multivariate logistic regression. The dependent variable has two categories, and the first independent variable has five groups, and the second independent variable has two groups. 

Once I run the model (use Fit Model), the parameter estimates section reports the coefficient/beta value for four of the five groups for the first independent variable and one of the two groups for the second independent variable. I assume the parameter estimates reports one less than the number of categories for each variable because it chooses one group as the comparison group?

My second question has to do with the odds ratio generated. It seems like there is an odds ratio for combination of each of the five (and two) groups with each other, for a total of 25 (and 4) odds ratio. JMP shows it as Level1/Level 2. These odds ratio don't correspond to the coefficients under the parameter estimates section (since they do not equal to e^coefficient). What do these odds ratio represent? 

[#2]

Hi Mark, I am running a multivariable logistic regression, the linear predictor consists of the overall mean (intercept), an independent variable with 5 levels, and another independent variable with 2 levels. 

My main question is why the odds ratio for two non-reference categories (i.e. category 1 and 4) equals e^(parameter estimate for category 1)/e^(parameter estimate for category 4), but this equation does not work when one of the categories is the reference category (category 5).    

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[#3]

Your posts were caught in the spam filter, not sure why.

[#4]

I assume that your dichotomous response is using binary logistic regression, or the nominal logistic platform in JMP after launching from Fit Model dialog. The model is log( odds( target ) / odds( non-target ) ) = linear predictor. This linear equation may be back-transformed to probability( target | X ) = F( linear predictor). The odds ratio is just the predicted odds for the target versus the predicted odds for the non-target. The logits for target and non-target for the binary case is the simplest to back-transform.

There is a lot of background information here to help answer your question.

[#5]

useful information