Hi all,

I was wondering if someone could point me to a book or papers on the use of simulated replicates on the results of a mixed method analysis, and the treatment of survey frequency (not probability) weights.

In particular, I am interested in how the construction of 100 replicates per subject, from simulation, affects the frequency weight that should be used.

The reason I am asking is that this appears to be the method used to estimate the population distribution of nutrient intakes in humans. The method uses a simulation to generate the replicates, using the mixed method estimate plus the subject's error (the error is adjusted by a pull from the random normal distribution each time) to estimate each replicate, which is then subjected to a Taylor series approximation to back-transform the nutrient data to the original scale, as the mixed method analysis and MC have been performed on data that has undergone a Box-Cox transformation.

Once the simulation is concluded, the individual weights are divided by 100 (i.e. by the number of simulated replicates per subject), and I am wading my way through SAS macro code to see if any other weight corrections were performed (age grouping level, total sample level) ahead of estimating the population distribution of nutrient intake. The reason this is important is that the population distribution will show the percentage below minimum daily nutrient intake guidelines, and the percentage exceeding maximum daily intake guidelines - both are public health issues.

I'm not clear on the correct method of handling the survey weights, and would appreciate guidance.

The reason I am asking this question is that the replicates form various related distributions obviously centred on each subject's mixed method output (they estimate a range of nutrient intakes for each subject). I'm not clear on how those replicates should be weighted, in particular because:
- subject was entered as a random effect in the mixed methods analysis, and
- there was no weighting included in the mixed methods analysis, so post hoc weighting seems to add a constraint to the data that was not incorporated during analysis.

I wondered whether Wolter (1985) Introduction to Variance Estimation (Statistics for Social and Behavioral Sciences) would be my best bet for advice, but I'm not sure how the advice would be affected by the use of a mixed methods approach.

Alternatively, have any of you worked with weighted survey data and experienced these issues? If so, how did you fix the post hoc weighting?

cheers
Michelle

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