Ralph O. Mueller

The Reviewer's Guide to Quantitative Methods in the Social Sciences

The Reviewer’s Guide to Quantitative Methods in the Social Sciences is designed for evaluators of research manuscripts and proposals in the social and behavioral sciences, and beyond. Its 31 uniquely structured chapters cover both traditional and emerging methods of quantitative data analysis, which neither junior nor veteran reviewers can be expected to know in detail. The book updates readers on each technique’s key principles, appropriate usage, underlying assumptions, and limitations. It thereby assists reviewers to offer constructive commentary on works they evaluate, and also serves as an indispensable author’s reference for preparing sound research manuscripts and proposals. Key features include:

Structural equation modeling: Back to basics

Major technological advances incorporated into structural equation modeling (SEM) computer programs now make it possible for practitioners who are basically unfamiliar with the purposes and limitations of SEM to use this tool within their research contexts. The current move by program developers to market more user friendly software packages is a welcomed trend in the social and behavioral science research community. The quest to simplify the data analysis step in the research process has—at least with regard to SEM—created a situation that allows practitioners to apply SEM but forgetting, knowingly ignoring, or most dangerously, being ignorant of some basic philosophical and statistical issues that must be addressed before sound SEM analyses should be conducted. This article focuses on some of the almost forgotten topics taken here from each step in the SEM process: model conceptualization, identification and parameter estimation, and data‐model fit assessment and model modification. The main objective i...

Factor Analysis and Latent Structure, Confirmatory

Confirmatory factor analysis (CFA) is a mainly dis-confirmatory quantitative data analysis method that belongs to the family of structural equation modeling (SEM) techniques. CFA allows for the assessment of fit between observed data and an a prioriconceptualized, theoretically grounded model that specifies the hypothesized causal relations between latent factors and their observed indicator variables. In this article, typical steps in a CFA are introduced. First, during model specification, a model is conceptualized by indicating how latent, unobserved factors relate to measurable variables. Second, if each parameter can be expressed as a function of the variances and covariances of observed variables, model identification is assured and parameters can be estimated. Third, iterative techniques such as the maximum likelihood, generalized least squares, or asymptotically distribution free estimation methods can be utilized to estimate the unknown model parameters. Fourth, assessments of fit between observed data and the a priori specified model(s) can be made via a multitude of absolute, parsimonious, and incremental fit indices. Fifth, if data-model inconsistencies are observed, model modifications might be appropriate, provided they are consistent with underlying substantive theories and the modified model is cross-validated using an independent sample. The article closes with applied and methodological references appropriate for a more in-depth study of CFA and SEM in the social and behavioral sciences.

Confirmatory Factor Analysis

Confirmatory factor analysis (CFA) is based on the premise that observable variables are imperfect indicators of certain underlying, or latent, constructs. For example, variables used in the regression and path analytical models of Chapter 1, such as father’s education (FaEd), degree aspirations (Degre Asp), and highest held academic degree (Degree), can be thought of as imperfect indicators of the latent constructs parents’ socioeconomic status (PaSES), general academic motivation (AcMotiv), and one’s own socioeconomic status (SES), respectively. If more than one observed indicator variable is available to measure a particular latent construct, CFA allows the researcher to cluster these variables in prespecified, theory-driven ways to evaluate to what extent a particular data set “confirms” what is theoretically believed to be its underlying structure. Thus, the CFA approach to multivariate data analysis does not let a particular data set dictate, identify, or discover underlying dimensions [as is the case with other variable reduction techniques such as exploratory factor analysis (EFA) or principal components analysis (PCA)]; rather, it requires the researcher to theorize an underlying structure and assess whether the observed data “fits” this a priori specified model. In doing so, CFA provides a framework for addressing some of the problems associated with traditional ways of assessing a measure’s validity and reliability.

Linear Regression and Classical Path Analysis

In many ways, structural equation modeling (SEM) techniques may be viewed as “fancy” multivariate regression methods. Some models can be understood simply as a set of simultaneous regression equations. If the statistical assumptions of ordinary least squares (OLS) regression are met, standard OLS estimation as available in general-purpose statistical computer programs such as SPSS, SAS, or BMDP can be used to estimate the structural parameters in these models. This chapter serves to set the stage for presenting general structural equation models in Chapter 3, which include as special cases the regression and path analytical models presented in this chapter and the confirmatory factor analysis models introduced in Chapter 2. For now, the two main purposes are (1) to introduce a general SEM notation system by reviewing some important results in univariate simple and multiple regression, and (2) to discuss the multivariate method of path analysis as a way to estimate direct, indirect, and total structural effects within an a priori specified structural model. Throughout the chapter, examples based on data from a sociological study serve as an introduction to the LISREL and EQS programs. The respective manuals (Joreskog and Sorbom, 1993a,b; Bentler, 1993; Bentler and Wu, 1993) should be consulted for more detailed programming information.

General Structural Equation Modeling

The most general structural equation models treated in this book are nothing more—and nothing less—than path analytical models (introduced in Chapter 1) that involve latent variables (discussed in Chapter 2). Even though classical path analysis has important advantages over conventional univariate or multivariate regression (e.g., the estimation of direct and indirect structural effects), one major disadvantage is that a priori hypothesized structures can be analyzed only under the usually unrealistic assumption that variables in the models are measured with no or negligible error. An integration of latent variables—as previously introduced in the context of confirmatory factor analysis—into path models relaxes this assumption and allows for the estimation of direct and indirect structural effects between variables or constructs that are not directly observable but, instead, are indicated by some imperfect observable measures.