An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures

May 19, 2011

Levy, R., & Hancock, G. (2011). An Extended Model Comparison Framework for Covariance and Mean Structure Models, Accommodating Multiple Groups and Latent Mixtures Sociological Methods & Research, 40 (2), 256-278 DOI: 10.1177/0049124111404819 

Abstract 

Roy Levy, Arizona State University, Tempe, AZ, USA, roy.levy@asu.edu

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Testing the Stability of an Acquiescence Style Factor Behind Two Interrelated Substantive Variables in a Panel Design

February 7, 2010

Jaak B. Billiet and Eldad Davidov Testing the Stability of an Acquiescence Style Factor Behind Two Interrelated Substantive Variables in a Panel Design  Sociological Methods & Research 2008 36: 542-562.

This article addresses the question of to what extent one type of response style, called acquiescence (or agreeing response bias), is stable over time. A structural equation modeling approach Read the rest of this entry »


Enno Siemsen and Kenneth A. Bollen Least Absolute Deviation Estimation in Structural Equation Modeling Sociological Methods & Research 2007 36: 227-265.

February 7, 2010

Least absolute deviation (LAD) is a well-known criterion to fit statistical models, but little is known about LAD estimation in structural equation modeling (SEM). To address this gap, the authors use the LAD criterion in SEM by minimizing the sum of the absolute deviations between the observed and the model-implied covariance matrices. Using Monte Carlo simulations, the authors compare the performance of this LAD estimator along several dimensions (bias, efficiency, convergence, frequencies of improper solutions, and absolute percentage deviation) to the full informationmaximum likelihood (ML) and unweighted least squares (ULS) estimators in structural equation modeling. The results for LAD are mixed: There are special conditions under which the LAD estimator outperforms ML and ULS, but the simulation evidence does not support a general claim that LAD is superior to ML and ULS in small samples.

Key Words: least absolute deviation • structural equation modeling • robust estimation • small sample research


Ellen L. Hamaker, Conditions for the Equivalence of the Autoregressive Latent Trajectory Model and a Latent Growth Curve Model With Autoregressive Disturbances, Sociological Methods & Research 2005 33: 404-416.

February 7, 2010

Curran and Bollen combined two models for longitudinal panel data: the latent growth curve model and the autoregressive model. In their model, the autoregressive relationships are modeledbetween the observed variables. This is a different model than a latent growth curve model with autoregressive relationships between the disturbances. However, when the autoregressive parameter is invariant over time and lies between-1 and 1, it can be shown that these models are algebraically equivalent. This result can be shown to generalize to the multivariate case. When theautoregressive parameters in the autoregressive latent trajectory model vary over time, the equivalence between the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances no longer holds. However, a latent growth curve model with time-varying autoregressive parameters for the disturbances could be considered an interesting alternative to the autoregressive latent trajectory model with time-varying autoregressive parameters.

Key Words: latent growth curve model • autoregressive latent trajectory model • autoregression • structural equation modeling