GaussianModel mixmodGaussianModel(family = "all", listModels = NULL,
free.proportions = TRUE, equal.proportions = TRUE)GaussianModel In general family, we can allow the volumes, the shapes and the orientations of clusters to vary or to be equal between clusters. Variations on assumptions on the parameters $\lambda_{k}, D_{k}$ and $A_{k}$ $(1 \leq k \leq K)$ lead to 8 general models of interest. For instance, we can assume different volumes and keep the shapes and orientations equal by requiring that $A_{k}=A$ ($A$ unknown) and $D_{k}=D$ ($D$ unknown) for $k=1,\ldots,K$. We denote this model $[\lambda_{k}DAD']$. With this convention, writing $[\lambda D_{k}AD'_{k}]$ means that we consider the mixture model with equal volumes, equal shapes and different orientations. In diagonal family, we assume that the variance matrices $\Sigma_{k}$ are diagonal. In the parameterization, it means that the orientation matrices $D_{k}$ are permutation matrices. We write $\Sigma_{k}=\lambda_{k}B_{k}$ where $B_{k}$ is a diagonal matrix with $| B_{k}|=1$. This particular parameterization gives rise to 4 models: $[\lambda B]$, $[\lambda_{k}B]$, $[\lambda B_{k}]$ and $[\lambda_{k}B_{k}]$.
In spherical family, we assume spherical shapes, namely $A_{k}=I$, $I$ denoting the identity matrix. In such a case, two parsimonious models are in competition: $[\lambda I]$ and $[\lambda_{k}I]$.
mixmodGaussianModel()
# all Gaussian models with equal proportions
mixmodGaussianModel(family="all",free.proportions=FALSE)
# Diagonal and Spherical Gaussian models
mixmodGaussianModel(family=c("diagonal","spherical"))
# Gaussian models with a pre-defined list
mixmodGaussianModel(listModels=c("Gaussian_p_L_C","Gaussian_p_L_Ck","Gaussian_pk_L_I"))Run the code above in your browser using DataLab