A Model-Based Shrinkage Target to Avoid Non-convergence in Small Sample SEM

Abstract

Structural equation modeling is prone to a variety of problems when the sample size is small. One solution that attempts to solve the (non-convergence) problem of small sample SEM is found in shrinkage estimation, where a weighted average between the sample variance-covariance matrix (S) and a highly structured shrinkage target (T) is calculated to construct an adjusted sample variance-covariance matrix (${\mathbf{S}}_a$), which is then used as input for the analysis. Different target candidates have already been put forward in the literature, but in this paper, we propose using a model-based target matrix specifically tailored for structural equation models. Two simulation studies demonstrate the benefit of using a model-based target over other candidate targets in terms of convergence rate, bias, and MSE, but also emphasize the importance of constructing an optimal shrinkage intensity.

Keywords:

• Non-convergence
• shrinkage estimation
• small samples

Notes

1 The code that was used for these two studies can be found using the following link: https://osf.io/8qp3f/.