The Effects of Sampling Error and Model Characteristics on Parameter Estimation for Maximum Likelihood Confirmatory Factor Analysis

1985 ◽  
Vol 20 (3) ◽  
pp. 255-271 ◽  
Author(s):  
David W. Gerbing ◽  
James C. Anderson
2019 ◽  
Author(s):  
André Beauducel ◽  
Norbert Hilger

The model of buffered simple structure is discussed as a method for modeling cross-loadings in confirmatory factor analysis. This method introduces assumptions from item sampling theory into confirmatory factor analysis. The independent clusters model, buffered simple structure, and Bayes estimation were compared by means of a simulation study based on three different population types. Population type A had zero cross-loadings, population type B had symmetrically distributed nonzero cross-loadings, and population type C had asymmetrically distributed nonzero cross-loadings. It turned out for population A that, although the independent clusters model yields the best loading estimate, it did not outperform Bayes estimation and buffered simple structure with respect to the factor inter-correlation estimate and model fit. One reason for this unexpected result could be that the specification of zero-cross loadings is suboptimal even when only sampling error introduces some cross-loadings. For populations B and C Bayes estimation and buffered simple structure clearly outperformed the independent clusters model. Overall, the results indicate that depending on the structure of cross-loadings in the population and depending on the focus on loading estimates or factor inter-correlation estimates, different modeling approaches might be appropriate.


1983 ◽  
Vol 53 (2) ◽  
pp. 607-611 ◽  
Author(s):  
Raymond K. Tucker ◽  
Richard L. Weaver ◽  
Eileen M. Redden

30 graduate teaching assistants rated 419 students (171 men, 248 women) on assertiveness, aggressiveness, and shyness. A maximum likelihood confirmatory factor analysis produced a single factor; assertiveness and aggressiveness variables correlated positively and the shyness variable correlated negatively with the factor. These results are interpreted as indicating confusion among lay raters as to whether a syndrome of motoric behavior is assertive or aggressive.


2021 ◽  
Author(s):  
Anneke Cleopatra Weide ◽  
Vera Scheuble ◽  
André Beauducel

Difficulties in interpersonal behavior are often measured by the circumplex-based Inventory of Interpersonal Problems. Its eight scales can be represented by a three-factor structure with two circumplex factors, Dominance and Love, and a general problem factor, Distress. Bayesian confirmatory factor analysis is well-suited to evaluate the higher-level structure of interpersonal problems because circumplex loading priors allow for data-driven adjustments and a more flexible investigation of the ideal circumplex pattern than maximum likelihood confirmatory factor analysis. Using a nonclinical sample from an online questionnaire study (N = 822), we replicated the three-factor structure of the IIP by maximum likelihood and Bayesian confirmatory factor analysis and found great proximity of the Bayesian loadings to perfect circumplexity. We also investigated higher-level scores for Dominance, Love, and Distress using traditional regression factor scores, posterior mean factor scores from Bayesian confirmatory factor analysis, and weighted sum scores. We found excellent reliability (with Rtt ≥ .90) for Dominance, Love, and Distress for all scoring methods. We found high congruence of the higher-level scores with the underlying factors and good circumplex properties of the scoring models. The correlation pattern with external measures – Agreeableness, Extraversion, and Neuroticism from the Big Five and subclinical grandiose narcissism – were in line with theoretical expectations. We encourage the use of Bayesian modeling when dealing with circumplex structure and recommend the use of higher-level scores for interpersonal problems as parsimonious, reliable, and valid measures.


2021 ◽  
Vol 12 ◽  
Author(s):  
Oliver Lüdtke ◽  
Esther Ulitzsch ◽  
Alexander Robitzsch

With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood (PML) estimation, and the mean (EAP), median (Med), or mode (MAP) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo (MCMC) methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error (RMSE). We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research.


2021 ◽  
Vol 12 ◽  
Author(s):  
Anneke C. Weide ◽  
Vera Scheuble ◽  
André Beauducel

Difficulties in interpersonal behavior are often measured by the circumplex-based Inventory of Interpersonal Problems. Its eight scales can be represented by a three-factor structure with two circumplex factors, Dominance and Love, and a general problem factor, Distress. Bayesian confirmatory factor analysis is well-suited to evaluate the higher-level structure of interpersonal problems because circumplex loading priors allow for data-driven adjustments and a more flexible investigation of the ideal circumplex pattern than conventional maximum likelihood confirmatory factor analysis. Using a non-clinical sample from an online questionnaire study (N = 822), we replicated the three-factor structure of the IIP by maximum likelihood and Bayesian confirmatory factor analysis and found great proximity of the Bayesian loadings to perfect circumplexity. We found additional support for the validity of the three-factor model of the IIP by including external criteria-Agreeableness, Extraversion, and Neuroticism from the Big Five and subclinical grandiose narcissism-in the analysis. We also investigated higher-level scores for Dominance, Love, and Distress using traditional regression factor scores and weighted sum scores. We found excellent reliability (with Rtt ≥ 0.90) for Dominance, Love, and Distress for the two scoring methods. We found high congruence of the higher-level scores with the underlying factors and good circumplex properties of the scoring models. The correlational pattern with the external measures was in line with theoretical expectations and similar to the results from the factor analysis. We encourage the use of Bayesian modeling when dealing with circumplex structure and recommend the use of higher-level scores for interpersonal problems as parsimonious, reliable, and valid measures.


Sign in / Sign up

Export Citation Format

Share Document