This paper reviews the application of the EM Algorithm to marginal maximum likelihood estimation of parameters in the latent class model and extends the algorithm to the case where there are monotone homogeneity constraints on the item parameters. It is shown that the EM algorithm can be used to obtain marginal maximum likelihood estimates of the item response functions under the minimal monotone homogeneity assumption, if restricted to finite-state latent-class models. With the marginal maximum likelihood estimates in hand for both the monotonely homogeneous latent class model and the unconstrained model with the same number of states, a direct likelihood ratio test of the monotone homogeneity hypothesis can be calculated. (Author/JAZ)