How to Estimate the Polynomial Model using M-Plus?

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Dear list,

we have repeated measurements of persons, where we want to estimate a random intercept for each person. This random intercept is understood as an interindividual differences variable. In a subsequent step, the conditional modes/BLUPs of the random intercept should predict some outcome variable.

We are aware that due to the shrinkage the random effects are driven towards the overall mean. Therefore we lose some of the interindividual variability which we actually would like to have. On the other hand, our within-person regressions are very noisy and based on few data, and we think that the partial pooling leads to better estimates, compared to an OLS-regression within each person.

However, Reinhold Kliegl et al. (2010) write:
"[…] one is tempted to carry on with the conditional-mean predictions based on the LMM parameter estimates to compute, for example, correlations with other background variables such as IQ or age that may be available for each subject. Unfortunately, however, this would be an erroneous step and would take the LMM-based predictions too far. First, given that conditional means represent a compromise between the subjects’ means and the estimate of the population mean, they must obviously not be treated as independent observations."

Now my questions are:
- How problematic is it to use random intercepts as predictor variables in subsequent analyses?
- Do you know any other analysis where random intercepts (or something functionally equivalent) can be used as predictors?

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关键词：Polynomial estimate nomial model Using subsequent understood actually repeated overall