A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

Abstract

We conducted a Monte Carlo study to investigate the performance of the polychoric instrumental variable estimator (PIV) in comparison to unweighted least squares (ULS) and diagonally weighted least squares (DWLS) in the estimation of a confirmatory factor analysis model with dichotomous indicators. The simulation involved 144 conditions (1,000 replications per condition) that were defined by a combination of (a) two types of latent factor models, (b) four sample sizes (100, 250, 500, 1,000), (c) three factor loadings (low, moderate, strong), (d) three levels of non-normality (normal, moderately, and extremely non-normal), and (e) whether the factor model was correctly specified or misspecified. The results showed that when the model was correctly specified, PIV produced estimates that were as accurate as ULS and DWLS. Furthermore, the simulation showed that PIV was more robust to structural misspecifications than ULS and DWLS.

Reflections on Partial Least Squares Path Modeling

“…It is noteworthy that IVE has been gaining prominence in the SEM domain, due mainly to the work of Bollen and his colleagues (Bollen & Bauer 2004;Bollen, Kirby, Curran, Paxton, & Chen, 2007;Bollen & Maydeu-Olivares, 2007;Kirby & Bollen, 2009; see also Nestler, 2013aNestler, , 2013b. Given the promising results of this work, the potential transportability of IVE methods to the PLS-PM context should be examined in future research.…”

Using Instrumental Variables to Estimate the Parameters in Unconditional and Conditional Second-Order Latent Growth Models

“…He showed that (a) the IVs that can be used are the other indicators contained in the latent variable model, and (b) they can be determined solely by the model structure. Moreover, (c) the 2SLS/IV approach can be used with continuous as well as categorical indictors (Bollen & Maydeu-Olivares, 2007), it yields estimates that are as accurate as those provided by other estimation procedures, and it provides even better estimates when variables are nonnormal or when structural misspecifications occur (Bollen, Kirby, Curran, Paxton, & Chen, 2007;Nestler, 2013). These points speak for applying the 2SLS/IV approach for estimating the parameters in a second-order LGM.…”

“…One additional value of the 2SLS/IV approach is that the estimator can be more robust to specification errors than ML (Bollen, 1996;Nestler, 2013). The reason for this is that ML uses information from the whole system of model specifications to estimate the model parameters.…”

How the 2SLS/IV estimator can handle equality constraints in structural equation models: A system‐of‐equations approach

“…Given that other studies have compared the performance of the 2SLS/IV approach to established estimators (e.g., Bollen et al ., ; Nestler, ), we decided to focus only on the relative bias, the standard error bias, and the root mean square error of the parameters that were constrained to be equal. That is, we compared the performance of ML to the 2SLS/IV system‐of‐equations approach in the estimation of the intercepts and factor loadings of the indicators in the case of the CFA model and the latent regression coefficients in the case of the SEM model.…”

“…Also, the 2SLS/IV approach can be extended to estimate the parameters of latent interactions (Bollen & Paxton, ). Simulation studies have found that the 2SLS/IV estimator provides estimates that are as accurate as those provided by other estimation procedures when applied to CFA models (Bollen et al ., ; Nestler, ) and SEM models (Bollen et al ., ). It provided even better estimates when the observed variables were non‐normal or when structural misspecifications occurred (see Bollen et al ., ; Nestler, ).…”