I am running 9 regressions with 5 predictors each. The dependent variables are ordered, but have been treated before as count (and have a Gaussian distribution).
I ran the 9 regressions using the MASS package, using both 1) glm with family=gaussian, and 2) polr
The estimates of the models are very similar.
I want to determine pseudo $R^2$ now, and use the
pR2function of the PSCL package.
Again, $R^2$ values are basically identical for Gaussian and ordered models
However, the pseudo $R^2$ values are drastically higher than I had expected.
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 is $R^2$ obtained using linear regression models, the second McFadden pseudo $R^2$ , the third Maximum likelihood pseudo $r^2$, the fourth Cragg and Uhler's pseudo $r^2$, which is similar to Nagelkerke.
As far as I understand, Cragg and Uhler's pseudo $r^2$ has a range of 0-1, in contrast to the other pseudo $r^2$ values, and should be the one I should use. The values are between 3 and 7 times higher than the $r^2$ values obtained from linear regression models. Now I understand that linear regression doesn't fit very well because of the ordered nature of the variable, but a increase of 3-7 times sounds a bit too much.
Also my dependent variables are self reported single questionnaire items of a screening instrument for mental disorders, the predictors covariates like gender and personality traits. I am just skeptical that 40 or 50% variance can be explained by my covariates.
Maybe you have input on what might have gone wrong.