Analysis of Residuals for the Multinomial Item Response Model

Mark Reiser

79 citations0/0 files storedPsychometrika

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

Abstract

Using the item response model as developed on the multinomial distribution, asymptotic variances are obtained for residuals associated with response patterns and first-, and second-order marginal frequencies of manifest variables. When the model does not fit well, an examination of these residuals may reveal the source of the poor fit. Finally, a limited-information test of fit for the model is developed by using residuals defined for the first-, and second-order marginals. Model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse.

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References

1992Fundamentals of item response theory 1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1989Latent Variable Models and Factor Analysis 1987On the Relationship between iTem Response Theory and Factor Analysis of Discretized Variables 1992A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model 1970Fitting a Response Model for n Dichotomously Scored Items 1987A Nonparametric Approach for Assessing Latent Trait Unidimensionality 1978Contributions to Factor Analysis of Dichotomous Variables

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