On maximum likelihood estimation in sparse contingency tables (Q1080593)

Log-linear and logistic models can be fitted to data in contingency tables either by an iterative-proportional fitting algorithm or by an iteratively reweighted Newton-Raphson algorithm. Both algorithms provide maximum likelihood (ML) estimates of the expected cell frequencies and of the parameters of the model. When random zeros occur in the contingency table, numerical problems may be encountered in obtaining the ML estimates when using one or both of the algorithms. Problems in the estimation of the model's parameters, expected cell frequencies and degrees of freedom are described. An explicit formula is given for the evaluation of the degrees of freedom.