I am interested in comparing cross-sectional prevalence estimates across waves of PATH data. Per the PATH user guide (p. 61), is it not appropriate to compute separate estimates for each wave and compare by assessing confidence interval overlap. They recommend creating a stacked (or long) dataset with a wave indicator, which I have done. The user guide goes on to say "the subsequent analyses must include the newly created wave indicator variable and the design correctly specified in a software package designed to capture sample variability described in Appendix A....Manipulating the files as described above and using the appropriate variance estimation will correctly reflect these correlations."
After applying the recommended survey set command in Stata, I have tested out several lines of code (some from Appendix A) to compare estimates by wave indicator (e.g., chi-square, regression with categorical wave as a predictor). However, it is unclear to me whether performing these simple tests (for example, a chi-square test comparing prevalence of smoking by wave indicator) with the recommended survey specification (weighted with BRR variance estimation) is accounting for the correlation between participants across waves (since they are mostly the same people). Is it? If not, what is the recommended statistical approach to do so? Several statisticians have recommended using mixed models but it seems to me that this would have been specified in the user guide if needed. There is no specific guidance on this type of analysis in Appendix A.