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Generalized semiparametrically structured ordinal models.

ABSTRACT: Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form, and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. Global effects and category-specific effects are distinguished; the latter allow the effect to vary across response categories. A general framework is developed in which global as well as category-specific effects may have unspecified functional form. The framework extends various existing methods of modeling ordinal responses. The Wilkinson-Rogers notation is extended to incorporate smooth model parts and varying coefficient terms, the latter being important for the smooth specification of category-specific effects.

SUBMITTER: Tutz G

PROVIDER: S-EPMC3464104 | biostudies-literature | 2003 Jun

REPOSITORIES: biostudies-literature

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Generalized semiparametrically structured ordinal models.

Tutz Gerhard G

Biometrics 20030601 2

Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form, and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. Global effects and category-specific effects are distinguished; the latter allow the effect to vary across response categories. A gener ...[more]

PMID: 12926711

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Project description:Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

Dataset Information

Generalized semiparametrically structured ordinal models.

Publications

Generalized semiparametrically structured ordinal models.

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