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Total LL for split samples

So when running the HB on split samples, can the total LL (computed as the sum across respondents of the LN(RLH)*#tasks) be summed across the two sub-samples to be compared with the total LL across respondents from the pooled model? Or is this conceptually wrong?

Thanks in advance!
related to an answer for: Follow up on LL
asked May 17, 2015 by anonymous

1 Answer

0 votes
This is the sort of thinking one brings from Latent Class, where the goal is to maximize the LL.

HB does not have as a goal to maximize the LL of the fit to respondents' choices.  In fact, it purposefully gives up a lot of fit at the individual level to the individual's choices in favor of making sure the respondents seem to be drawn from higher density areas of a multivariate normal distribution, according to population means and covariances.  

If your two groups have quite different preferences, then the compromise toward population means and variances will yield higher individual-level fit to respondents' choices than when using a pooled model.  So, it's probably the case that you will obtain higher individual-level fit on average across respondents when using a segmented model.  However, segmented models also have lower sample size within each HB model to stabilize the means and especially the covariances.  So, the better individual-level fit isn't necessarily an indication of better quality.  There may be some overfitting, for example.
answered May 18, 2015 by Bryan Orme Platinum Sawtooth Software, Inc. (132,290 points)