Pairwise Likelihood Estimation for factor analysis models with ordinal data
2011 (English)Report (Other academic)
Pairwise maximum likelihood (PML) estimation is developed for factor analysis models with ordinal data fitted both in an exploratory and confirmatory set-up, and its performance is studied and compared with full information maximum likelihood (FIML) and a three-stage limited information estimation method. More specifically, estimates and standard errors ob- tained from PML are compared with those obtained from FIML and those from robust un- weighted least squares (3S-RULS). All three methods provide very close estimates and stan- dard errors. However, the PML estimates and standard errors are on average slightly closer to FIML than the 3S-RULS are. The advantage of PML over FIML is mainly computational. The computational complexity of FIML increases with the number of factors or observed variables depending on the model formulation, while that of PML is affected by neither of them. Contrary to 3S-RULS, in PML, all model parameters are simultaneously estimated and therefore the final estimates reflect all the sampling variability. In the 3S-RULS method the standard errors of the parameter estimates in stage three do not incorporate the variability of the estimates obtained in step one. Furthermore, PML does not require the estimation of a weight matrix for computing correct standard errors. The performance of PML estimates and their estimated asymptotic standard errors are investigated through a simulation study where the effect of different models and sample sizes are studied. The bias and mean squared error of PML estimators and their standard errors are found to be small in all experimental conditions and decreasing with the sample size.
Place, publisher, year, edition, pages
Uppsala: Department of Statistics, Uppsala University , 2011. , 31 p.
Working paper / Department of Statistics, Uppsala University, 2011:4
composite maximum likelihood; factor analysis; ordinal data; maximum likelihood; 3-stage estimation; item response theory approach
IdentifiersURN: urn:nbn:se:uu:diva-162090OAI: oai:DiVA.org:uu-162090DiVA: diva2:458843