Sample Size Requirements for Estimation of Item Parameters in the Multidimensional Graded Response Model

Shengyu Jiang, Chun Wang, David J. Weiss

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87 Scopus citations


Likert types of rating scales in which a respondent chooses a response from an ordered set of response options are used to measure a wide variety of psychological, educational, and medical outcome variables. The most appropriate item response theory model for analyzing and scoring these instruments when they provide scores on multiple scales is the multidimensional graded response model (MGRM) A simulation study was conducted to investigate the variables that might affect item parameter recovery for the MGRM. Data were generated based on different sample sizes, test lengths, and scale intercorrelations. Parameter estimates were obtained through the flexMIRT software. The quality of parameter recovery was assessed by the correlation between true and estimated parameters as well as bias and root-mean-square-error. Results indicated that for the vast majority of cases studied a sample size of N = 500 provided accurate parameter estimates, except for tests with 240 items when 1000 examinees were necessary to obtain accurate parameter estimates. Increasing sample size beyond N = 1000 did not increase the accuracy of MGRM parameter estimates.

Original languageEnglish (US)
Article number109
JournalFrontiers in Psychology
StatePublished - Feb 9 2016

Bibliographical note

Funding Information:
Research reported in this publication 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 Minnesota through a subcontract to the University of Minnesota. The content is solely the responsibility of the authors and does not necessarily reflect the official views of the National Institutes of Health.

Publisher Copyright:
Copyright © 2016 Jiang, Wang and Weiss.


  • graded response model
  • item parameters
  • multidimensionality
  • parameter recovery
  • sample size


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