Models and parameters of finite mixtures of multivariate normal densities c
onditional on regressor variables are specified and estimated. We consider
mixtures of multivariate normals where the expected Value for each componen
t depends on possibly nonnormal regressor variables. The expected values an
d covariance matrices of the mixture components are parameterized using con
ditional mean- and covariance-structures. We discuss the construction of th
e likelihood function, estimation of the mixture model with regressors usin
g three different EM algorithms, estimation of the asymptotic covariance ma
trix of parameters and testing for the number of mixture components. In add
ition to simulation studies, data on food preferences are analyzed.