A Simulation Study of Polychoric Instrumental Variable Estimation in Structural Equation Models

The Importance of Type I Error Rates When Studying Bias in Monte Carlo Studies in Statistics

“…Moreover, bias values near zero (e.g., 14.4% were ≤ .03) may simply reflect sampling error. Similar patterns appear in many studies reporting Monte Carlo results (e.g., Chung MICHAEL HARWELL 5 et al, 2018;Ye, 2015;Jin et al, 2016;Lachowicz et al, 2018;Li et al, 2011;McNeish, 2016).…”

“…For example, Harring et al (2012) used an absolute bias cutoff of .05 for structural equation modeling estimates; Jin et al (2016) and Kim et al (2016) used a relative bias cutoff of 5% for estimated factor loadings; Leite and Beretvas (2010) used 5% when examining bias after imputing missing Likert-type data; Li et al (2011) used 5% when evaluating bias in estimated correlations; Wang et al (2012) used 5% in their study of the impact of violating factor scaling assumptions, and Ye and Daniel (2017) used 5% for assessing bias in cross-classified random effect models as did Meyers and Beretvas (2006) and Chung et al (2018).…”

Selecting polychoric instrumental variables in confirmatory factor analysis: An alternative specification test and effects of instrumental variables

“…If the test for one equation indicates a non‐zero correlation between the IVs and the composite error term, researchers need to investigate whether it is caused by omitted cross‐loadings, omitted correlated errors or even both. In CFA, an omitted cross‐loading in one equation will not invalidate IVs for the other equations (Jin et al ., ), which enables us to identify the source of model misspecification in a stepwise manner. In step 1, perform the specification test on the modified model that lifts all zero loading assumptions in the initial model.…”

“…2SLS/IV has been generalized to ordinal observed variables by Bollen and Maydeu‐Olivares () and is referred to as the polychoric instrumental variable (PIV) approach. Jin, Luo, and Yang‐Wallentin () and Nestler () showed that the PIV approach produces loading estimates as accurate as ULS and DWLS if the model is correctly specified and more robust loading estimates if the model is misspecified in CFA models. Thus, the PIV approach is a promising alternative to ULS and DWLS.…”

Robustness Conditions for MIIV-2SLS When the Latent Variable or Measurement Model is Structurally Misspecified

“…Bollen (2001) provides two general conditions on MIIV-2SLS’s robustness to structural misspecification. Several other studies (Bollen, Kirby, Curran, Paxton, and Chen, 2007; Bollen & Maydeu-Olivares, 2007; Nestler, 2013; Jin, Luo & Yang-Wallentin, 2016) provide simulation evidence that the MIIV-2SLS estimator is more robust to structural misspecifications than the more widely used system wide (e.g., ML) estimators, but do not give general analytic conditions for robustness. Our goal is to provide new, specific, conditions of when the MIIV-2SLS estimator will be robust to structural misspecifications.…”