Assumptions of the Two-Step Approach to Latent Variable Modeling

Although methods for latent variable modeling that allow a joint analysis of measurement and theory have become popular, they are not without difficulties. As these difficulties have become more apparent, several researchers have recently called for a “two-step approach” to latent variable modeling in which measurement is evaluated separately from theory. This implies that programs for covariance structure analysis are not needed because factor analysis and regressions would suffice for analysis. Before a return to earlier practice using seemingly simpler analysis tools can be recommended, it seems prudent to consider the assumptions underlying a two-step approach. At least four implicit assumptions can be identified: (a) theory and measurement are independent, (b) results of factor analysis specifications can be generalized to other specifications, (c) the estimators have desirable statistical properties, and (d) the statistical test in one step is independent of the test in the other. The authors show that these assumptions cannot be met in general and that some of them are logically inconsistent. Thus any wholesale adoption of a two-step approach could have serious consequences.

[1]  R. P. McDonald,et al.  A simple comprehensive model for the analysis of covariance structures , 1978 .

[2]  P. Bentler,et al.  Models of attitude–behavior relations. , 1979 .

[3]  Louis Guttman,et al.  Measurement as structural theory , 1971 .

[4]  Claes Fornell,et al.  Issues in the Application of Covariance Structure Analysis: A Comment , 1983 .

[5]  Ronald S. Burt,et al.  Confirmatory Factor-Analytic Structures and the Theory Construction Process , 1973 .

[6]  Alan Stuart,et al.  Data-Dredging Procedures in Survey Analysis , 1966 .

[7]  P. Horan.  Causal models of measurement: some problems for theory construction , 1989 .

[8]  H. J. Larson,et al.  Biases in prediction by regression for certain incompletely specified models , 1963 .

[9]  James C. Anderson,et al.  STRUCTURAL EQUATION MODELING IN PRACTICE: A REVIEW AND RECOMMENDED TWO-STEP APPROACH , 1988 .

[10]  Empiricist measurement strategies: A critique of the multiple indicator approach to measurement , 1980 .

[11]  L. Cronbach,et al.  Construct validity in psychological tests. , 1955, Psychological bulletin.

[12]  Richard P. Bagozzi,et al.  "Issues in the application of covariance structure analysis": A further comment. , 1983 .

[13]  Kenneth A. Bollen,et al.  Outliers and Improper Solutions , 1987 .

[14]  N. Anderson.  Functional measurement and psychophysical judgment. , 1970, Psychological review.

[15]  M. Browne,et al.  Cross-Validation Of Covariance Structures. , 1983, Multivariate behavioral research.

[16]  P M Bentler,et al.  Choice of structural model via parsimony: a rationale based on precision. , 1989, Psychological bulletin.

[17]  A. Shapiro,et al.  On the multivariate asymptotic distribution of sequential Chi-square statistics , 1985 .

[18]  Peter M. Bentler,et al.  Structural modeling and psychometrika: An historical perspective on growth and achievements , 1986 .

[19]  A. Satorra,et al.  Power of the likelihood ratio test in covariance structure analysis , 1985 .

[20]  D. Kaplan.  The Problem of Error Rate Inflation in Covariance Structure Models , 1989 .

[21]  H. Hoppe.  On how not to make inferences about measurement error , 1980 .

[22]  Robert C. MacCallum,et al.  SPECIFICATION SEARCHES IN COVARIANCE STRUCTURE MODELING , 1986 .

[23]  J. L. Hall.  Stabilized lasers and precision measurements. , 1978, Science.

[24]  Richard P. Bagozzi,et al.  The degree of intention formation as a moderator of the attitude-behavior relationship , 1989 .

[25]  David Rindskopf,et al.  Structural Equation Models , 1984 .

[26]  G. Bohrnstedt,et al.  A Review of the Background and History of the First Fifteen Years of Sociological Methods and Research , 1988 .

[27]  D. Rindskopf,et al.  Some Theory and Applications of Confirmatory Second-Order Factor Analysis. , 1988, Multivariate behavioral research.

[28]  R. P. McDonald,et al.  Some algebraic properties of the Reticular Action Model for moment structures. , 1984, The British journal of mathematical and statistical psychology.

[29]  R. Burt.  Interpretational Confounding of Unobserved Variables in Structural Equation Models , 1976 .

[30]  R. Luce,et al.  What sort of measurement is psychophysical measurement? , 1972, The American psychologist.

[31]  N Cliff,et al.  Some Cautions Concerning The Application Of Causal Modeling Methods. , 1983, Multivariate behavioral research.

[32]  P. Bentler,et al.  Attitudes "cause" behaviors: A structural equation analysis. , 1981 .

[33]  S. Mulaik,et al.  Limited Information Parameter Estimates for Latent or Mixed Manifest and Latent Variable Models. , 1988, Multivariate behavioral research.

[34]  B. Muthén,et al.  A comparison of some methodologies for the factor analysis of non‐normal Likert variables , 1985 .