Hallo Ray,

I’m comparing the fit of two models: a 5-dimensional within item model and a 4-dimensional between item model.

1.Are these two models nested? Can deviance be used to compare them?

In the 5-dimensioanl model I have set all the correlations equal to zero while in the 4-dimensional model, dimensions are allowed to correlate. Deviance shows that the 4-dimensional model fits better.

However, when in the 4-dimensional model the correlations among the dimensions are set to zero, the 5-dimensional model fits better.

2.Which model fits better, the 4-dimensional or the 5-dimensional?

I just thought that in order to make all the conditions equal to make a fair comparison I have to set the correlations in the 4-dimensional model to zero, too. Besides, the dimensions in the 4-dimensional model are test format dimensions. We don’t expect test formats (for example, multiple-choice and gap-filling) to be correlated.

3.Does this make sense?

Thanks

Georg II