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
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
- 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?