# Negative Binomial „Ancova” with planned contrasts

My DV is count, obtained from psychological questionnaire (14 questions with options ”Yes”/”No”, each yes is 1 point, thus overall result is count of yeses).

I’ve checked that Poisson distribution isn’t exactly what I’ve got (data is a bit overdispressed) and NB fits better (in comparison to Poisson – log likelihood is closer to 0 and AIC/BIC values are lower. Deviance/df = 1,153; Pearson Chi-square/df = 0,96 – which seem fair enough to me). Although 14 is obviously a bound, no one scored more than 8, so I think it should not be a problem (also all groups had same questionnaire, so the same bound).

I have 4 groups (smallest n=28, biggest n=35), which i need to compare. My hypotesis has a form of planned orthogonal contrast (-3,1,1,1 and 0,1,1,-2). In the best scenario, I would love to also include some covariates in the model, that’s why I mentioned „Ancova”.

I’ve spent last week reading stats coursebooks and articles about count data – I've finished with impression that regression is a fair option. But stats teacher I asked about it said she had no idea what I am speaking about and that I should not contrive, just use Kruks-Wallis.

So I thought that maybe I misunderstood something and that's why I wanted to ask 3 questions:

1. Assuming that distribution of the data is in fact negative binomial, is negative binomial regression an appropriate method to test an alternative hypotesis that groups differ?
2. Assuming that distribution of the data is in fact negative binomial, should negative binomial regression be considered a better fitted test for such comparison than Kruks-Wallis? (more powerfull?)
3. [If answer for 2 former questions was „yes-ish”] Is it right to implement planned orthogonal contrasts (-3,1,1,1 and 0,1,1,-2) by including 2 dummy variables coded for groups just like this (-3,1,1,1 and 0,1,1,-2) as covariates? I’m using SPSS.

1. DV describes one’s Locus of Control
2. That’s my syntax (yet without covariates), if it helps in any way:

GENLIN LOC WITH Contrast1 Contrast2 /MODEL Contrast1 Contrast2 INTERCEPT=YES DISTRIBUTION=NEGBIN(MLE) LINK=LOG /CRITERIA METHOD=FISHER(1) SCALE=1 COVB=MODEL MAXITERATIONS=100 MAXSTEPHALVING=5 PCONVERGE=1E-006(ABSOLUTE) SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 CITYPE=WALD LIKELIHOOD=FULL /MISSING CLASSMISSING=EXCLUDE /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION (EXPONENTIATED) /SAVE MEANPRED DEVIANCERESID.