Goodness-of-fit tests for multinomial models with many parameters can be simplified using power-divergence statistics. These tests can be applied to models with large degrees of freedom and work well even with sparse data. The tests are based on Pearson's X2 and likelihood ratio G2, which have asymptotic normal distributions for increasing sample sizes. The approach used here allows for an increasing number of independent multinomials while keeping the number of classes and parameters fixed. The tests are particularly useful for quantal response models and binary data, where they act as score tests within an enlarged model. The expectation and variance of the statistics can be easily computed, especially when the sizes of the multinomials are large.