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.     

Normative population theory

Conclusion We have shown, contrary to the claims of Cowen, that average and critical-level utilitarianism, which do not suffer from the repugnant conclusion, do not recommend the killing of people with low but positive utilities. We have shown, in addition, that Methuselah's paradox and the repugnant conclusion do not stem from preferences that are represented by additive utility functions. Further, we have shown that Cowen's ideal participant method suffers from the repugnant conclusion.We believe that Parfit's [4] criticism of classical utilitarianism — that it satisfies the repugnant conclusion — should be taken seriously. That suggests that the ideal participant method should be rejected (along with classical utilitarianism) as a reasonable solution to the optimal population problem.We have benefited from private correspondence with T. Cowen, and the remarks of T. Hurka and an anonymous referee.