LL of the Null model - CBC/HB

Question

Hi,

I'm trying to determine the LL of the null model for a HB run model. I understand from other posts that the model LL is determined by:

A) For each respondent, take the natural log of the RLH and multiply it by the number of tasks completed by that respondent: LN(RLH)*#Tasks.  This gives you the LL per respondent.

B)  Multiply that amount by the number of respondents, giving you the total LL across respondents.

However, I don't know how to determine the LL for the null model. I want to find this out to determine a McFadden's R^2.

Keith mentions in another post that Perct.cert is the same as McFadden's R^2 but with values in the. 5-.7 or higher range this would make the model fit extremely good as McFadden's R^2 in the range of .2-.4 represent values of extremely good fit. So I'm a little confused.

I'd love some direction here.

Jasha

Answer 1

Jasha,

The model fit of .2 to .4 is from an old paper about aggregate logit models, not respondent-level models - I don't usually see people compute McFadden's rho-squared for HB models, so I'm not sure what my target would be there.

The LL for the null model is easy.  If each of your questions has, say 4 alternatives, then a null model with all utilities=0 would choose by chance alone and you'd expect to get 25% correct.  

Now follow steps A and B in your post, except use 0.25 instead of RLH and you'll have the null model's log likelihood.

If you have varying numbers of alternatives across sets or a dual response none that contributes to your model then the null LL calculation will be more complicated.