Assessing the Effect of Model Misspecifications on Parameter Estimates in Structural Equation Models

Model misspecifications may have a systematic effect on parameters, causing biases in their estimates. In the application of structural equation models, every interesting model is fallible. When simultaneously evaluating a model, it is of interest to study whether all parameters are affected by a misspecification. This paper provides three procedures for evaluating such an effect: (1) analyzing the path, (2) using a functional relationship, and (3) using a significance test. Analyzing the path is illustrated through a confirmatory factor model. This method is ad hoc but intuitive. A more rigorous approach is built upon the concept of orthogonality of two sets of parameters. When parameter a is orthogonal to parameter b, omitting parameter b will not affect the estimation of parameter a. The functional relationship of two sets of parameters is used to check their orthogonality. The distribution of the difference between estimates based on different models is obtained, which provides a Hausman–like way to check significant parameter differences that are due to biases. Examples illustrate that these procedures can provide valuable information on identifying parameter estimates that are systematically affected by a model misspecification.     

On the Utility of Robust and Resampling Procedures1

Abstract Kassab (1990) makes an important methodological contribution by urging the use of robust regression methods in the study of community economic impacts and by indicating the utility of the bootstrap in assessing standard errors in robust regression. By introducing the notion of a contaminating distribution, we reconcile differences between her claim that ordinary least squares (OLS) regression is biased when outliers are present and standard linear model theory that does not make assumptions about the shape of the residual distribution in proving OLS an unbiased estimator. The contaminating distribution provides a framework for rural sociologists to link their statistical assumptions to a substantive understanding of the phenomena being studied. We suggest an alternative regression estimation strategy that may be more robust than the technique she uses. We also discuss an approach to bootstrapping that is more appropriate for macro-level social indicator data than the one she describes. An appendix discusses the software available for implementing these methods.     

RACE, GENDER, CLASS CONSCIOUSNESS AND UNION SUPPORT: AN ANALYSIS OF SOUTHERN TEXTILE WORKERS

This paper examines race and gender differences in class consciousness and union support among a random sample of textile workers in a small North Carolina city. Class consciousness is treated as an ordinal variable consisting of class verbalization, class action orientation, and endorsement of egalitarian change. Union support denotes a recognition of the union's instrumental role in improving work and working conditions. The analysis reveals that blacks are significantly more class conscious and prounion than whites. On the other hand, males and females tend to share similar levels of class consciousness and union support. Comparisons by race, within gender and by gender, within race, are provided for finer distinctions and extended discussion. A multiple classification analysis reveals that racial differences persist and that gender differences remain unimportant when the covariates of age, job dissatisfaction, education, income, and skill are considered.     

Premarital cohabitation and subsequent marital

Married couples who began their relationship by cohabiting appear to face an increased risk of marital dissolution, which may be due to self-selection of more dissolution-prone individuals into cohabitation before marriage. This paper uses newly developed econometric methods to explicitly address the endogeneity of cohabitation before marriage in the hazard of marital disruption by allowing the unobserved heterogeneity components to be correlated across the decisions to cohabit and to end a marriage. These methods are applied to data from the National Longitudinal Study of the High School Class of 1972. We find significant heterogeneity in both cohabitation and marriage disruption, and discover evidence of self-selection into cohabitation.