# Multinomial Logistic Regression, 2x2 Between Participants Design

#### lost_in_stats

##### New Member
Hello everyone,

I would really appreciate some advice on how to interpret my SPSS-Output. I have tried to figure it out myself, but haven't been able to get an answer.

I have 2 binary independent variables and 1 dependent variable with 3 categorical outcomes. So a 2x2 Design.

In order to run multinomial logistic regression analyses, I put the two Factors into the factor-box and specified the model to check for 2 main effects and 1 interaction effect. However, after running SPSS I noticed that only the interaction effect was displayed. The 2 main effects however did not appear (i.e., the Chi2 is ,000 and no significance level is shown for each of the main effect). There is also a note that says:

The chi-square statistic is the difference in -2 log-likelihoods between the final model and a reduced model. The reduced model is formed by omitting an effect from the final model. The null hypothesis is that all parameters of that effect are 0.

a) This reduced model is equivalent to the final model because omitting the effect does not increase the degrees of freedom.

HOWEVER, SPSS gave me the main effects and the interaction effect, when I defined the factors as covariates (i.e. I put the factors into the covariate-box). However, the factors are nominal, so shouldn't be defined as covariates.

Thank you very much in advance! :tup:

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#### hlsmith

##### Omega Contributor
Just for clarification your model is:
y = Bo + B1X1 + B2X2 + B2X3, y contain: 0,1,2).
So, you are putting the interaction term in the model for the 2 IV, correct?

#### lost_in_stats

##### New Member

Yes, I tested for the main effect of Factor A, main effect of Factor B and the interaction effect between the two factors. They are all part of the model. Factor A also significantly interacts with Factor B (there is kind of a cross-interaction).

When I run the analysis, only the interaction effect shows, but no main effects.

#### hlsmith

##### Omega Contributor
I have run a bunch of logistic reg in my life, but not really polytomous reg. It was my understanding that it just kicks out the same output, but for say 1 vs. 0 and then 2 vs. 0. So there are two models ran, both using the same reference outcome group. I would imagine then that your outcome should look like two traditional models that had two binary IVs and their interaction term. Is this what you are expecting? I am not an SPSS user, so no help there if it is a program issue.

Just for fun why don't you split your data (dataset #1: outcomes 0,1 and dataset #2: outcomes 0, 2) and see if everything runs fine and as expected. Do you have any sparsity in your data, say for outcome 2 no subjects have a certain combination of covariates - this doesn't seem like that, but if you have 3 outcomes it becomes a greater risk. Its sounds like the likelihood test is trying to compare your saturated model to an empty model and error, not sure if that is a multinomial thing or not???

#### lost_in_stats

##### New Member
Thanks again for you prompt reply!

Yes, I have split the outcome variable and ran a binary logistic regression analysis. The results were identical (fortunately).

But why are the main effects only displayed in the multinomial logistic regression analysis, when I treat the factors as covariates? By definition, this doesn't make any sense.

However, when I defined the factors as factors, the main effects do not show. I have attached the output for that (jpeg-file).