Hello.

I am running 9 poisson regressions with 5 predictors each, using glm with
family=gaussian.
Gaussian distribution fits better than linear regression on fit indices,
and also for theoretical reasons (e.g. the dependent variables are counts,
and the distribution is highly positively skewed).

I want to determine pseudo R^2 now. However, using the pR2() of the pscl
package offers drastically higher R^2 values than I get using linear
regressions, and that I am "used" from the dataset which I know well (it
might sound weird, but sometimes you're just skeptical of the results after
you worked a while on the data).

Now I know that linear regression fits worse and therefor r^2 might be
underestimated, but the differences are drastic:

R^2 McFadden r2ML r2CU
m1 0.13 0.27 0.32 0.42
m2 0.17 0.27 0.33 0.43
m3 0.06 0.19 0.36 0.40
m4 0.11 0.21 0.38 0.42
m5 0.14 0.26 0.39 0.45
m6 0.18 0.33 0.37 0.49
m7 0.10 0.28 0.29 0.41
m8 0.04 0.23 0.13 0.28
m9 0.07 0.31 0.12 0.36

The first column represents r^2 values obtained by linear regression
models, then comes McFadden pseudo r^2, maximum likelihood pseudo r^2, and
Cragg and Uhler's pseudo r^2.

As far as I understand, Cragg and Uhler's pseudo r^2 is similar to
Nagelkerke, which, in contrast to the other pseudo r^2 values, offers a
range between 0 and 1, so that should be my comparison. And the values are
between 3 and 7 times higher than the original r-square values.

My dependent variables self reported single questionnaire items of a
screening instrument for mental disorders, the predictors covariates like
gender and personality traits.

Thank you for your input

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