Pairwise likelihood estimation for factor analysis models with ordinal data

A pairwise maximum likelihood (PML) estimation method is developed for factor analysis models with ordinal data and fitted both in an exploratory and confirmatory set-up. The performance of the method is studied via simulations and comparisons with full information maximum likelihood (FIML) and three-stage limited information estimation methods, namely the robust unweighted least squares (3S-RULS) and robust diagonally weighted least squares (3S-RDWLS). The advantage of PML over FIML is mainly computational. Unlike PML estimation, the computational complexity of FIML estimation increases either with the number of factors or with the number of observed variables depending on the model formulation. Contrary to 3S-RULS and 3S-RDWLS estimation, PML estimates of all model parameters are obtained simultaneously and the PML method does not require the estimation of a weight matrix for the computation of correct standard errors. The simulation study on the performance of PML estimates and estimated asymptotic standard errors investigates the effect of different model and sample sizes. The bias and mean squared error of PML estimates and their standard errors are found to be small in all experimental conditions and decreasing with increasing sample size. Moreover, the PML estimates and their standard errors are found to be very close to those of FIML.