What are the solutions for small sample in SEM?

Question

is bootstrap a solution? I use Lisrel 8.8 (the student version) and bootstrap actually does not work in it. Bootstrap S has N/A values.

Answer 1

As @Jeremy Miles says, bootstrapping in small samples often leads to convergence issues. Additionally, with bootstrapping, while certain assumptions may be relaxed, additional assumptions are made (e.g., for more information on bootstrapping, see this CV post, and for more details about bootstrapping in the context of SEM, see this CV post).

There are, however, two relatively new approaches to SEM that show promise when the sample size is small. These are Bayesian SEM(BSEM) and Factor Score regression (FSR).

In BSEM, instead of priors are specified for each parameter, and estimation is conducted (typically) using MCMC. If adequate information is available to select priors (i.e., informative priors are used), then few would argue with such an approach. However, adequate information to construct such priors is often unavailable, and researchers often use non-informative priors and/or default priors. If you decide to use the BSEM approach, make sure you are aware of the problems that can arise due to the use of improper priors with small samples (e.g., see Smid & Winter, 2020).

FSR is a method that has received considerable attention in the last decade and Devlieger & Rosseel (2017) introduce it well in their abstract -

In the first step, factor scores are calculated for the latent variables, which are used to perform a linear regression in the second step. However, this method results in incorrect regression coefficients. Croon (2002) developed a method that corrects for this bias. We combine this method of Croon (2002) with path analysis, resulting in FactorScore Path Analysis. This method results in correct path coefficients and has some advantages over SEM: it requires smaller sample sizes, can handle more complex models and the method is less sensitive to misspecifications, because of its stepwise nature. In conclusion, this method can be a suitable alternative for SEM, when one is dealing with a complex model and small sample sizes.

References

Croon, M. (2014). Using predicted latent scores in general latent structure models. In Latent variable and latent structure models (pp. 207-236). Psychology Press.

Devlieger, I., & Rosseel, Y. (2017). Factor score path analysis: An alternative for SEM?. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 13(S1), 31.

Smid, S. C., & Winter, S. D. (2020). Dangers of the defaults: A tutorial on the impact of default priors when using Bayesian SEM with small samples. Frontiers in Psychology, 11, 611963.