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I have two sets of a longitudinal data that I hypothesize to measure same latent construct.I am trying to test this hypothesis using Structural equation modelling technique. Basically, I am trying to use confirmatory factor analysis in longitudinal data using SEM. My models are relatively simple CFA models.

The problem is that my sample size is small in term of SEM standards. We collected data only from 20 individuals for nearly two years (number of time points nearly equals 18) because the data collection is very expensive.

I am new to SEM and I was not able to decide if SEM is right choice for me. My question is given such a small sample size, is it a good idea to use SEM based techniques to model the data and test my hypothesis? Based on my researches, I concluded that I should not fit SEM using least squares, weighted least squares or Maximum likelihood since they require large samples which I do not have. It seems that they recommend fitting SEM using Partial least squares or Baysian approaches for small sample size but the problem is my sample size is very small. Are there any articles that discuss fitting SEM using very small sample size?

I am looking for suggestions, literatures or recomendations to fit such data with small sample size.

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  • $\begingroup$ If this is longitudinal data, I would suspect the total number of observations is of importance. So if it is 18 per subject, you should have 360 observations. $\endgroup$ – ReliableResearch May 10 '13 at 17:53
  • $\begingroup$ that would be cross sectional analysis of my data which i am quite reluctant to do...currently my model has a latent variable at each time point so there are 18 latent variables following ar(1) process..so i have only 20 unique samples $\endgroup$ – iinception May 10 '13 at 20:43
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    $\begingroup$ If your measurement model stays constant over time, I won't see any problems at least trying to fit an SEM to this -- you would really have 360 point or nearly so for your measurement part of the model (the latent part may still suffer). I personally have zero trust in PLS, and Bayesian may be too complicated unless you've spent the previous three years of your life running MCMC every day on every problem. Another class of estimation methods that may work OK with small samples are instrumental variable regressions, see the body of work of Ken Bollen on this starting from the 1996 Psychometrika $\endgroup$ – StasK May 11 '13 at 3:21
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    $\begingroup$ @iinception Have you considered latent growth curve modeling on observed variables? Usually for LGM, sample size required decreases as the number of measurement occasions increases, and some have shown that a sample size as small as 20 could work well in a simple model. Here is the reference. Muthen, L. K., & Muthen, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, (4), 599–620. $\endgroup$ – Sootica May 14 '13 at 3:48
  • $\begingroup$ @Sootica thanks for the reference i will go over it... correct me if i am wrong.i am not interested in characterizing the trajectories(which I think that LGM does) of my longitudinal variables..i am interested in studying if the two sets of measurements are measuring the same latent construct at each time point. $\endgroup$ – iinception May 14 '13 at 17:59

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