Measurement model quality, sample size, and solution propriety in confirmatory factor models

Sample size recommendations in confirmatory factor analysis (CFA) have recently shifted away from observations per variable or per parameter toward consideration of model quality. Extending research by Marsh, Hau, Balla, and Grayson (1998), simulations were conducted to determine the extent to which CFA model convergence and parameter estimation are affected by n as well as by construct reliability, which is a measure of measurement model quality derived from the number of indicators per factor (p/f) and factor loading magnitude. Results indicated that model convergence and accuracy of parameter estimation were affected by n and by construct reliability within levels of n. Sample size recommendations for applied researchers using CFA are presented herein as a function of relevant design characteristics.