This study aims to examine the performance of adaptive quadrature (AQ) estimation method for ordinal confirmatory factor analysis (CFA). Specifically, we compared four link functions (complimentary log-log CLL, logit, log-log, and probit) of the AQ estimation method across varying factor structures, sample sizes, distributional shape of latent trait, and number of quadrature points. The study is conducted via a simulation study and using empirical data. The results demonstrate that the probit link function exhibits superiority across the vast majority of conditions, consistently yielding the highest proper convergence rates and, among successfully converged solutions, the lowest parameter recovery errors, and the best relative fit, whereas the logit generally showed the weakest performance. Additionally, a critical divergence was discovered regarding asymmetric link functions: while the probit link generally provided the best model fit across the positively skewed simulation conditions, the log-log link yielded the best relative model fit for the positively skewed empirical data. Furthermore, the study reveals the complex role of quadrature points in multidimensional spaces. Although using eight quadrature points may be necessary in more complex simulated models, it frequently causes severe estimation failures when applied to sparse real-world data.
Kabasakal et al. (Mon,) studied this question.