st: scale correction factor in logistic regression

["Bontempo, Daniel E" <deb193@ku.edu>]

Hello statalist -

I have been looking at meresc.ado which computes scale correction factor (SCF) and variance scale correction factor (VCF) for multilevel logit models to rescale model coefficients and level-2 variances into the scale of the corresponding empty model variance.

If I may ask you to consider an additional question, would a statistic like the median odds ratio (MOR) be invariant to rescaling? 

The formula is provided by Merlo & Larsen(2006), or cited by Rabe-Hesketh & Skrondal's MLMUS 3rd ed. in section 10.9.2: 

MOR = exp(  sqrt(2*Vu0) * .6745), which depends directly on the random intercept variance (Vu0). 

My intuition wants to say that this formula would work with the rescaled random intercept variance, but my algebra is poor and sometimes it makes a difference if scaling is done before or after taking exponent.

I have formed some ratios of OR/MOR and scaled-OR/scaled-MOR and thre is generally some discrepancy that looks to be more than rounding. Of course perhaps this ratio is not what I want to do in the 1st place.

Any comment on the issue of the invariance of the MOR to the rescaling done in meresc.ado would be greatly appreciated.

-Daniel Bontempo


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