I have a dependent variable that ranges from 0-11, and it's the number of Covid-19 precautions the respondent took (mean: 7.4, SD: 1.5). I'm not sure which estimator to use. The obvious model (poisson) has a higher AIC and BIC than many of the other options.

If I rely on AIC and BIC alone, the models that are most preferred are OLS regression and
Code:
glm ... family(bin 11) link(logit)
I think the generalized linear model with binomial distribution makes more sense than OLS regression, but I'm hesitant because these aren't really "independent trials" as the binomial distribution would assume. That is, a person who took "at least 10 precautions" is more likely to take the eleventh precaution.

Any thoughts? By the way, my sample size is small (N=114) in case that matters.

Thanks,
Max

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P.S. Here are the AIC & BIC values:

Poisson: AIC = 485, BIC = 510
Ordered logit: AIC = 412, BIC = 450
OLS: AIC = 412, BIC = 436
GLM, binomial distribution: AIC = 413, BIC = 438
Truncreg: AIC = 411, BIC = 439