Weighted tests of homogeneity for testing the number of components in a mixture

An important but di-cult problem in .tting .nite mixture models is estimating and testing the number of components in the mixture. Regularity conditions do not hold for large sample likelihood theory so that likelihood ratio tests cannot easily be implemented. However, a number of homogeneity tests have been developed to test for the presence of a mixture. Weighted versions of homogeneity tests are presented that can be used to test for the presence of additional components in a mixture. These tests are easily implemented, do not require long computational times and can incorporate covariates. Examples are given to illustrate the methodology and simulation results are presented that suggest that the tests have power comparable to the bootstrap likelihood ratio test. c © 2002 Elsevier Science B.V. All rights reserved.