I have performed first an ordinal logistic regression analysis (using function clm) that included all explanatory variables. Then I chose the best candidate models with AICc
Generally pseudo-R^2 measures are problematic because R^2 is not defined for models where the total variance to be explained is not fixed. In an ordinal model like the clm() type model - which is an ordered logistic regression - the total variance and variance explained are not constant. At heart this model is a series of binary logistic regressions with cumulative thresholds. Thus the underlying model at each threshold is binomial and the variance of the model is a function of the binomial probability (and var fora binomial distribution is greatest when P = 0.5 and hence variance = .5^2 = 0.25. If the P value were 0.1 the variance would be 0.1*).9 = 0.09.
There are various workarounds - but none in my view wholly satisfactory. The following chapter may be useful (it is an online supplement to my book):
Chapter Pseudo-R2 and related measures. Online Supplement 4 to Serio...
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