Logistic Regression on small sample size/case ratio - SPSS?

#1
Hi all - I have a small issue. I have a categorical dichotomous DV (0,1) with 4 IV's , two of which are categorical and dichotomous (0,1), and the other two are categorical but have about 16 categories (1-16). Ideally I want to estimate the likelihood of the DV outcomes given these IV's, but I my sample n=16 (with 4 cases in one category of the DV, and 12 in the other).

Is it safe to say that Logistic regression using maximum likelihood will produce highly bias odds ratios? If so, what other options do I have? I came across Penalized Likelihood /Firth method, as well as Exact Logistic regression, but NONE of those are available on SPSS.

Do you think my best bet is just a Chi Square to estimate the contingencies between the DV and the IV's, and forget about my dreams of modelling their likelihoods?
 

noetsi

Fortran must die
#2
If you make dummy variables out of the two 16 category IV you will have I believe fewer cases than categories [so you won't have any DF and no valid model]. I believe that some of the standard tests in logistic regression [wuch as the Wald Chi Square] are only asymptotically correct so 16 cases would not be enough regardless to be confident of your results. There are rules of thumb by various authors about minimum sample size for logistic regression, see Agresti for example, but there is strong disagreement on the validity of those rules of thumb.

A more basic question is what you can reliably say with only 16 cases anyhow. That seems far to small to validly generalize to anything on.

It looks to me that SPSS will do FIRTH through its R studio...http://spssx-discussion.1045642.n5....-FIRTHLOG-and-STATS-INEQUALITY-td5725639.html
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
Heck i dont know how well the 16 category fishers exact will work if you go the bivariate route.