Articlegreen1985

A Comparison of Several Goodness-of-Fit Statistics

154 citations0/0 files storedApplied Psychological Measurement

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Psychometric Methodologies and Testing Statistical Distribution Estimation and Applications Statistical Methods and Bayesian Inference

Abstract

A study was conducted to evaluate four goodness- of-fit procedures using data simulation techniques. The procedures were evaluated using data generated ac cording to three different item response theory models and a factor analytic model. Three different distribu tions of ability were used, as were three different sam ple sizes. It was concluded that the likelihood ratio chi-square procedure yielded the fewest erroneous re jections of the hypothesis of fit, whereas Bock's chi- square procedure yielded the fewest erroneous accep tances of fit. It was found that sample sizes some where between 500 and 1,000 were best. Shifts in the mean of the ability distribution were found to cause minor fluctuations, but they did not appear to be a major issue.

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References

1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1972Estimating Item Parameters and Latent Ability when Responses are Scored in Two or More Nominal Categories 1973A Goodness of Fit Test for the Rasch Model 1981Using Simulation Results to Choose a Latent Trait Model 1984Testing the Conditional Independence and Monotonicity Assumptions of Item Response Theory

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1990Fitting the Two-Parameter Model to Personality Data 2003Assessing Goodness of Fit of Item Response Theory Models: A Comparison of Traditional and Alternative Procedures 2003A Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model 1991The Distributional Properties of Rasch Item Fit Statistics 1990A Comparison of Item- and Person-Fit Methods of Assessing Model-Data Fit in IRT 2010Performance of the generalized S-X2 item fit index for the graded response model 2018Validation of two PROMIS item banks for measuring social participation in the Dutch general population 1994A Conditional Item-Fit Index for Rasch Models

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