

Stability of sequenced models 

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I have 107,025 children's responses to standardized mathematics instruments administered in three waves (wave 1  37 items; wave 2  36 items; wave 3  31 items). I am conducting the analysis in the sequence: EFA, LCA, FMA, LTA. My ultimate concern is with model stability throughout the process because it seems to me that with each step in the process, the solution space inevitably increases. I am concerned that the total possible response pattern space  the distribution of possible response patterns  is much much larger than my sample size (2^37 vs 2^16.076 (approx 107,025) for wave 1). In this respect, my model may be misspecified. I see one of three possible directions to mitigate my unease. 1. Take a number of random samples (say 5,000) of the original linked dataset and run parallel EFA, LCA, FMA, and LTA analyses. Bump up the BLRT and LMRLRT random draws. Compare. 2. Reduce the number of items per wave to <= 16 (i.e., 2^16 = 65,536 which is < 107,025) run entire sample. 3. Reduce the number of items per wave to <= 16, take random samples (say 5,000) and compute estimates. Compare. Could you please advise me as to which of these (or, perhaps a new one I haven't considered) might satisfy my concerns? 


Number 1 sounds good. 

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