Maximum likelihood estimation for a special type of grouped data with an application to a dose-response problem

A short-cut method is given for calculating grouped maximum likelihood (ML) estimates when the data are relatively coarsely grouped in some directions, but more finely grouped in others. The algebraic details are then worked out for a dose-response problem that generates data of this kind. The situation envisaged is a variation on the usual quantal response problem in that dosage levels are taken to be random but grouped. Finally, the method is applied both to real and simulated response data conforming to this pattern and shown to work well in practice.