Robustness of Parameter Estimation to Assumptions of Normality in the Multidimensional Graded Response Model

Chun Wang, Shiyang Su, David J. Weiss

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A central assumption that is implicit in estimating item parameters in item response theory (IRT) models is the normality of the latent trait distribution, whereas a similar assumption made in categorical confirmatory factor analysis (CCFA) models is the multivariate normality of the latent response variables. Violation of the normality assumption can lead to biased parameter estimates. Although previous studies have focused primarily on unidimensional IRT models, this study extended the literature by considering a multidimensional IRT model for polytomous responses, namely the multidimensional graded response model. Moreover, this study is one of few studies that specifically compared the performance of full-information maximum likelihood (FIML) estimation versus robust weighted least squares (WLS) estimation when the normality assumption is violated. The research also manipulated the number of nonnormal latent trait dimensions. Results showed that FIML consistently outperformed WLS when there were one or multiple skewed latent trait distributions. More interestingly, the bias of the discrimination parameters was non-ignorable only when the corresponding factor was skewed. Having other skewed factors did not further exacerbate the bias, whereas biases of boundary parameters increased as more nonnormal factors were added. The item parameter standard errors recovered well with both estimation algorithms regardless of the number of nonnormal dimensions.

Original languageEnglish (US)
Pages (from-to)403-418
Number of pages16
JournalMultivariate Behavioral Research
Issue number3
StatePublished - May 4 2018

Bibliographical note

Funding Information:
Funding: This research was supported by the Eunice Kennedy Shriver National Institutes of Child Health and Human Development of the National Institutes of Health under Award Number R01HD079439 to the Mayo Clinic in Rochester

Publisher Copyright:
© 2018 Taylor & Francis Group, LLC.


  • IRT
  • Ordinal data analysis
  • item response theory
  • maximum likelihood estimation
  • weighted least squares estimation


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