Analysis of residuals for the multinomial item response model

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.