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Some remarks on estimating a covariance structure model from a sample correlation matrix

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  • Maydeu Olivares, Alberto
  • Hernández Estrada, Adolfo

Abstract

A popular model in structural equation modeling involves a multivariate normal density with a structured covariance matrix that has been categorized according to a set of thresholds. In this setup one may estimate the covariance structure parameters from the sample tetrachoricl polychoric correlations but only if the covariance structure is scale invariant. Doing so when the covariance structure is not scale invariant results in estimating a more restricted covariance structure than the one intended. When the covariance structure is not scale invariant, then the model parameters must be estimated jointly from the sample thresholds and tetrachoricl polychoric correlations. In general, when fitting a covariance structure from a sample correlation matrix one should consider the population correlation structure under the null hypothesis. This is obtained by pre and post-multiplying the covariance structure by a diagonal matrix consisting of the inverse of the square root of the diagonal of the covariance structure under consideration. We provide computer algebra code for assessing whether a covariance structure is scale invariant and for assessing the identification of threshold and correlation structures.

Suggested Citation

  • Maydeu Olivares, Alberto & Hernández Estrada, Adolfo, 2000. "Some remarks on estimating a covariance structure model from a sample correlation matrix," DES - Working Papers. Statistics and Econometrics. WS 10009, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10009
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    References listed on IDEAS

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    1. Karl Jöreskog, 1994. "On the estimation of polychoric correlations and their asymptotic covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 59(3), pages 381-389, September.
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    3. Karl Jöreskog, 1978. "Structural analysis of covariance and correlation matrices," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 443-477, December.
    4. M. Browne & A. Shapiro, 1991. "Invariance of covariance structures under groups of transformations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 345-355, December.
    5. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 507-514, December.
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