Lower bounds on sample size in structural equation modeling

Abstract

Computationally intensive structural equation modeling (SEM) approaches have been in development over much of the 20th century, initiated by the seminal work of Sewall Wright. To this day, sample size requirements remain a vexing question in SEM based studies. Complexities which increase information demands in structural model estimation increase with the number of potential combinations of latent variables; while the information supplied for estimation increases with the number of measured parameters times the number of observations in the sample size – both are non-linear. This alone would imply that requisite sample size is not a linear function solely of indicator count, even though such heuristics are widely invoked in justifying SEM sample size. This paper develops two lower bounds on sample size in SEM, the first as a function of the ratio of indicator variables to latent variables, and the second as a function of minimum effect, power and significance. The algorithm is applied to a meta-study of a set of research published in five of the top MIS journals. The study shows a systematic bias towards choosing sample sizes that are significantly too small. Actual sample sizes averaged only 50% of the minimum needed to draw the conclusions the studies claimed. Overall, 80% of the research articles in the meta-study drew conclusions from insufficient samples. Lacking accurate sample size information, researchers are inclined to economize on sample collection with inadequate samples that hurt the credibility of research conclusions. Guidelines are provided for applying the algorithms developed in this study, and companion software encapsulating the paper’s formulae is made available for download.