Using the item response model as developed on the multinomial distribu
tion, 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 l
imited-information test of fit for the model is developed by using res
iduals defined for the first-, and second-order marginals. Model evalu
ation based on residuals for these marginals is particularly useful wh
en the response pattern frequencies are sparse.