Skip to main content
SpringerLink
Log in

Covariance structure analysis via specification searches

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Iterative model modification (specification searches) has become common practice in applications of covariance structure modeling techniques. The present analysis examines the reliability of a method for carrying out specification searches based on Lagrange multiplier and Wald tests. Results are compared to specification searches performed by means of likelihood ratio tests. Our findings indicate that neither of both methods is significantly superior to the other and that even in connection with very large samples, results from these search procedures can be relied upon only under favorable conditions. The authors therefore suggest the application of specification searches in a more restricted framework in which the parameters in that part of the model that is not subject to the search procedure are fixed. It is demonstrated that this concept enhances the likelihood of success of specification searches significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aitchison J, Silvey S D (1958) Maximum likelihood estimation of parameters subject to restraitss. Annals of Mathematical Statistics 29: 813–828

    Article  MathSciNet  MATH  Google Scholar 

  • Anderson J C, Gerbing D W (1982) Some methods for respecifying measurement models to obtain unidimensional construct measurement. Journal of Marketing Research 19: 453–460

    Article  Google Scholar 

  • Anderson J C, Gerbing D W (1987) Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, to appear

  • Balderjahn I (1988) Die Kreuzvalidierung von Kausalmodellen. Marketing ZFP 10: 61–73

    Google Scholar 

  • Bearden W O, Sharma S, Teel J E (1982) Sample size effects on chi square and other statistics used in evaluating causal models. Journal of Marketing Research 19: 425–430

    Article  Google Scholar 

  • Bentler P M (1983) Some contributions to efficient statistics in structural models: Specification and estimation of moment structures. Psychometrika 48; 493–517

    Article  MathSciNet  MATH  Google Scholar 

  • Bentler P M (1985) Theory and implementation of EQS: A structural equations program. Los Angeles: BMDP Statistical Software, Inc.

    Google Scholar 

  • Bentler P M (1986b) Lagrange multiplier and Wald tests for EQS and EQS/PC. Los Angeles: BMDP Statistical Software, Inc.

    Google Scholar 

  • Bentler P M (1986b) Structural modeling and Psychometrika: An historical perspective on growth and achievements. Psychometrika 51: 35–51

    Article  Google Scholar 

  • Bentler P M, Bonett D G (1980) Significance tests and goodness-of-fit in the analysis of covariance structures. Psychological Bulletin 88: 588–606

    Article  Google Scholar 

  • Bentler P M, Chou C P (1986) Statistics for parameter expansion and contraction in structural models. Paper presented at American Educational Research Association meetings, San Francisco

  • Bentler P M, Dijkstra T (1985) Efficient estimation via linearization in structural models. In P.R. Krishnaiah (Ed.), Multivariate Analysis-VI (9–42) Elsevier Science Publishers, Amsterdam

    Google Scholar 

  • Bentler P M, Weeks D G (1979) Interrelations among models for the analysis of moment structures. Multivariate Behavioral Research 14: 169–185

    Article  Google Scholar 

  • Bentler P M, Weeks D G (1980) Linear structural equations with latent variables. Psychometrika 45: 289–307

    Article  MathSciNet  MATH  Google Scholar 

  • Boonsma A (1985) Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation. Psychometrika 50: 229–242

    Article  Google Scholar 

  • Breusch, T S, Pagan A R (1980) The Lagrange multiplier test and its applications to model specification in econometrics. Review of Economic Studies 47: 239–253

    Article  MathSciNet  MATH  Google Scholar 

  • Browne M W (1974) Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal 8: 1–24

    MathSciNet  Google Scholar 

  • Browne M W (1982) Covariance Structures. In: D. M. Hawkins (Ed.), Topics in Applied Multivariate Analysis (72–141). Cambridge University Press, Cambridge

    Google Scholar 

  • Browne M W (1984) Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology 37: 62–83

    MathSciNet  MATH  Google Scholar 

  • Cliff N (1983) Some cautions concerning the application of causal modeling methods. Multivariate Behavioral Research 18: 115–126

    Article  Google Scholar 

  • Cudeck R (1985) A structural comparison of conventional and adaptive versions of the ASVAB. Multivariate Behavioral Research 20: 305–322

    Article  Google Scholar 

  • Cudeck R, Browne M W (1983) Cross-validation of covariance structures. Multivariate Behavioral Research 18: 147–167

    Article  Google Scholar 

  • Dobratz A (1989) Kontraktion and Expansion von Strukturparametern in Kovarianzstrukturmodellen, Diplomarbeit, Institut für Entscheidungs-theorie und Unternehmensforschung, Universität Karlsruhe

  • Engle R F (1984) Wald, likelihood ratio, and Lagrange multiplier test in econometrics. In Z. Griliches and M. Intriligator (Eds.), Handbook of Econometrics (239–253) North-Holland, Amsterdam

    Google Scholar 

  • Fornell C (1983) Issues in the application of covariance structure analysis: A comment. Journal of Consumer Research 9: 443–448

    Article  Google Scholar 

  • Fornell C (1986) A second generation of multivariate analysis: Classification of methods and implications for marketing research. Working paper, University of Michigan, Ann Arbor

    Google Scholar 

  • Gaul W, Homburg C (1988) The use of data analysis techniques by German market research agencies. Journal of Business Research 17: 67–79

    Article  Google Scholar 

  • Gerbing D W, Anderson J C (1984) On the meaning of within-factor correlated measurement errors. Journal of Consumer Research 11: 572–580

    Article  Google Scholar 

  • Gerbing D W, Anderson J C (1985) The effect of sampling error and model characteristics on parameter estimation for maximum likelihood confirmatory factor analysis. Multivariate Behavioral Research 20: 255–271

    Article  Google Scholar 

  • Gerbing D W, Hunter J E (1982) The metric of the latent variables in the LISREL-IV analysis. Educational and Psychological Measurement 42; 423–427

    Article  Google Scholar 

  • Homburg C (1989) Exploratorische Ansätze der Kauslanalyse als Instrument der Marketingplanung, Verlag Peter Lang, Frankfurt a.M.

    Google Scholar 

  • Homburg C (1991) Cross-validation and information criteria in causal modeling. Journal of Marketing Research 28: 137–144

    Article  Google Scholar 

  • Homburg C, Dobratz A (1991) Iterative Modellselektion in der Kausalanalyse. Zeitschrift für betriebswirtschaftliche Forschung 43: 213–237

    Google Scholar 

  • IMSL (1982) IMSL Library. Reference Manual Vol. 2, 9th edn. International Mathematical and Statistical Libraries, Houston

    Google Scholar 

  • Jöreskog K G (1967) Some contributions to maximum likelihood factor analysis. Psychometrika 32: 443–482

    Article  MathSciNet  MATH  Google Scholar 

  • Jöreskog K G (1969) A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 34: 183–201

    Article  Google Scholar 

  • Jöreskog K G (1973) A general method for estimating a linear structural equation system. In A. S. Goldberger, O. D. Ducan (Eds.), Structural Equation Models in the Social Sciences (85–112), Seminar Press, New York

    Google Scholar 

  • Jöreskog K G (1977) Structural equation models in the social sciences: Specification, estimation, testing. In P. R. Krishnaiah (Ed.), Applications of statistics (265–287), North-Holland, Amsterdam

    Google Scholar 

  • Jöreskog K G, Sörbom D (1982) Recent developments in structural equation modeling. Journal of Marketing Research 19: 404–416

    Article  Google Scholar 

  • Jöreskog K G, Sörbom D (1984) LISREL VI: Anllysis of linear structural relationships by maximum likelihood, instrumental variables and least squares methods, Scientific Software, Inc., Mooresville

    Google Scholar 

  • Lee S Y (1985) On testing functional constraints in structural equation models. Biometrika 72: 125–131

    Article  MathSciNet  MATH  Google Scholar 

  • MacCallum R (1986) Specification searches in covariance structure modeling. Psychological Bulletin 100: 107–120

    Article  Google Scholar 

  • Rao C R (1948) Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society 44: 50–57

    Article  MATH  Google Scholar 

  • Saris W E, de Pijper W M, Zegwaart P (1979) Detection of specification errors in linear structural equation models. In K. F. Schuessler (Ed.), Sociological Methodology 1979 (151–171), Jossey-Bass, San Francisco

    Google Scholar 

  • Saris W E, Satorra A, Sörbom D (1987) The detection and correction of specification errors in structural equation models. In C. C. Clogg (Ed.), Sociological Methodology 1978 (105–129), American Sociological Association, Washington

    Google Scholar 

  • Satorra A (1987) Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, to appear

  • Sörbom D (1975) Detection of correlated errors in longitudinal data. British Journal of Mathematical and Statistical Psychology 28: 138–151

    MATH  Google Scholar 

  • Sujan H (1986) Smarter versus harder: An exploratory attributional analysis of salespeople's motivation. Journal of Marketing Research 23: 41–49

    Article  Google Scholar 

  • Tanaka J S, Bentler P M (1984) Quasi-likelihood estimation in asymptotically efficient covariance structure models. Proceedings of the American Statistical Association: 658–662

  • Wald A (1943) Tests of statistical hypothesis concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society 54: 426–482

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Christian Homburg, Mausbergweg 96, 6720, Speyer

    Ch. Homburg

  2. Andreas Dobratz, August-Macke-Str. 12, 7842, Kandern

    A. Dobratz

Authors
  1. Ch. Homburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Dobratz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Homburg, C., Dobratz, A. Covariance structure analysis via specification searches. Statistical Papers 33, 119–142 (1992). https://doi.org/10.1007/BF02925318

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925318

Keywords

Search

Navigation