Asymptotic robustness of standard errors in multilevel structural equation models

Authors:
Ke-Hai Yuan;Peter M. Bentler
Affiliations:
University of Notre Dame, IN, USA;University of California, Los Angeles, CA, USA
Venue:
Journal of Multivariate Analysis
Year:
2006

Citing 5
Cited 0

A distribution free approach for analysis of two-level structural equation model

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Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models

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An Introduction to Multilevel Modeling Techniques

An Introduction to Multilevel Modeling Techniques

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Abstract

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical methodology was developed to analyze such data. Most of the procedures for analyzing multilevel data are derived from maximum likelihood based on the normal distribution assumption. Standard errors for parameter estimates in these procedures are obtained from the corresponding information matrix. Because practical data typically contain heterogeneous marginal skewnesses and kurtoses, this paper studies how nonnormally distributed data affect the standard errors of parameter estimates in a two-level structural equation model. Specifically, we study how skewness and kurtosis in one level affect standard errors of parameter estimates within its level and outside its level. We also show that, parallel to asymptotic robustness theory in conventional factor analysis, conditions exist for asymptotic robustness of standard errors in a multilevel factor analysis model.