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I'm comparing plausible models selected a-priori to predict a binary response variable. I used binary logistic regression in SPSS20 and obtained AIC=-2*LogLikelihood+2k where k is the number of parameters in the model. Using the GLM procedure (binary logistic) I get provided with AIC, AICc, BIC etc. straight away, however, the output differs from the binary logistic regression output (and results in different ranking of the models).

Why do the outputs using binary logistic regression vs GLM (binary logistic) differ? And which approach should I use?

Thanks heaps!!

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    $\begingroup$ With logarithms, it is rare for a multiplicative comparison (e.g., "factor of 10") to be meaningful. Is it perhaps the case that the two procedures return a constant difference in the log likelihoods (for datasets of a fixed size)? $\endgroup$
    – whuber ♦
    Commented Apr 23, 2012 at 1:50
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    $\begingroup$ good point - there is no constant difference in the log likelihoods the output values are seriously different and result in different ranking of the models. $\endgroup$
    – ulnberg
    Commented Apr 23, 2012 at 5:54

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I'm sorry you had to wait so long for an answer. I believe your problem is caused by the same issue in SPSS that prompted my question here.

In SPSS, binary logistic regression is done casewise. The 0/1 responses is modelled as Bernouilli(p), with p given by the logistic equation.

Under the generalized linear model menu, SPSS looks to see if the covariates have common values. If you have categorical variables (or ordinal) with a small number of outcomes, it is quite possible that a number of responses would stem from the same covariate conditions - as in a contingency table. SPSS then models the outcomes as binomials. The asymptotic distribution of the maximum likelihood estimates and variances are different (assuming the number of conditions remains constant) than what you get from the casewise model. The coefficients have the same estimates, but you get a different deviance statistic, different asymptotic chi-squared and different AIC.

My opinion is that you should go with binary logistic if a) you want to compare nested models and/or b) the number of categories is likely to increase with increased sample size.

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  • $\begingroup$ Thanks Placidia. When asking my peers the general notion was to use the binary logistic regression menu rather than the more convenient approach via GLM. However, I still struggle to understand what happens to my data in the SPSS black box. I neither want to compare nested models nor do the number of categories increase with increased sample size. Still results make more sense using the binary logistic approach. $\endgroup$
    – ulnberg
    Commented Feb 4, 2013 at 22:19

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