Structural equation models with small samples: A comparative study of four approaches

The purpose of this study was to evaluate the performance of estimation methods (Maximum Likelihood, Partial Least Squares, Generalized Structured Components Analysis, Markov Chain Monte Carlo) when applied to structural equation models with small samples. Trends in educational and social science research require scientists to investigate increasingly complex phenomena with regard for the contextual factors which influence their occurrence and change. These additional layers of exploration lead to complex hypotheses and require advanced analytic approaches such as structural equation modeling. A mismatch exists between analytic technique and the realities of applied research. Structural equation modeling requires large samples in general and even larger samples for complex models; for applied researchers, large samples are often difficult and even impossible to obtain. The unique contribution of this study is the simultaneous evaluation of these four estimation methods to determine the analytic conditions under which each method might be of value to researchers. A simulation study with a 3x3x2x2x4 factorial design was conducted. The design and data features of interest were sample size (50, 300, 1000), number of items per latent variable (3, 5, 7), degree of model misspecification (correctly specified model, misspecified model), nature of the relationships between items and latent variables in the measurement models (reflective, formative), and the four estimation methods named. Rate of convergence, bias of goodness of fit and estimates of model parameters and standard errors, and accuracy of standard error estimates were evaluated to determine the ability of each estimation method to recover model estimates under each experimental condition. The results indicate that when applied to normally distributed data, Maximum Likelihood generally outperforms the other three estimation methods across experimental conditions. The present study used simulated data to evaluate the performance of four estimation methods when applied to relatively simple structural equation models with small samples and normally distributed data, but future research will need to evaluate the performance of these methods with more complex models and data that is not normally distributed.