Dilution assays are widely used to estimate the concentration of a particular type of cell, called a limiting cell, in a population of cells from an animal. For each animal, the response vector is a set of binomial variables derived at different plating frequencies. Often extra-binomial variation is found when dilution assay data are analysed. This paper proposes a mixture model where the animal level effects are assumed to have a gamma distribution. This leads to more realistic standard errors for the estimates of the limiting cell concentrations.