# Extended Binary Logistic regression - multinomial regression or something else?

I wonder whether you could help me decide which statistical test to use. Briefly, I am testing whether personality (Big Five) predicts problem solving, in N = 282 participants. For personality, the IV, I have for each participant their mean score for each of the Big Five (so in essence continuous). So in essence there are 5 IVs; each of the Big Five personality traits. Problem solving method, the DV has four levels; fail, method A, method B and method C, and thus is categorical.

As I see it, it is an extension of binary logistic regression, with four DV categories instead of two. So this would suggest I should use a multinomial regression. However, because of the way that multinomial regression uses ‘subpopulations’, I have many ‘missing values/zero frequency cells’ because clearly not every score of each personality trait has DV value. Does anyone have any suggestions about how to run such an analysis (I am an SPSS user!). Is it perhaps a set of binary logistic regressions?

Many thanks indeed.