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We've got a construct-likert-scale with an internal (8 items) and an external dimension (6 item) and there is also a 5-point item y assessing the "subjective" perception (How skilled do you think you are?).

$N$ is 250

y-Cell frequency:

extrem gering   sehr gering        gering        mittel          hoch     sehr hoch  extrem hoch 
3               2                  2             36              78       103            26 

Now we've got the hypothesis/idea that subjective perception of the construct is "more" related to the external dimension that to the internal one. In order to prove this, we used three proportional odds regressions (a: y ~ int + ext, b: y ~ int, c: y ~ ext) using the R-package rms.

Result:

  • Every LR-ChiSq p-Value is significant
  • Every Intercept and every predictor is highly significant
  • The Nakerkes' pseudo-$R^2$ differs
    • .23 for a)
    • .11 for b)
    • .22 for c)

So we used the different $R^2$-values to say "using ext "explains" more than int and including int does only minimal effects once ext is included".

What do you think of this approach? Is this even correct?

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1 Answer 1

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I think that you are thinking about this in a good way. In addition to using generalized $R^2$ to gauge predictive discrimination you can use formal likelihood ratio $\chi^2$ tests for added information as well as something I talk about in my book Regression Modeling Strategies called the "adequacy index". This is just the ratio of the likelihood ratio $\chi^2$ for a sub-model to the overall $\chi^2$ for the largest model.

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