In social, health and environmental sciences, many data are collected with a known but complex underlying structure. Over the past three decades, multilevel modeling techniques have been extensively used to account nested data structures. However the underlying data structures are often more complex and cannot be fitted into a nested structure. This complexity of the data structure may arise due to fact that the observations are cross-classified and an observation does not belong to one member of the classification. As the existing frequentist modeling approaches have limitations to analyze such data, we propose generalized linear models with crossed nonparametric random effect. For estimating the model parameters, we propose the estimating equation based on BLUP (best linear unbiased predictors) of random effects. We illustrate the methodology with analysis of the child respiratory illness data.