MoR function

Multivariate mixture of regression Prior model description class

An S4 class to represent a multivariate mixture of regression model. The model follows minka-linear . The model corresponds to the following generative model: [REMOVE_ME]$\pi \sim Dirichlet(\alpha) [REMOVE_ME_2]$

[REMOVE_ME]$Z_i \sim \mathcal{M}(1,\pi) [REMOVE_ME_2]$

[REMOVE_ME]$V_k \sim \mathcal{W}(\varepsilon^{-1},n_0) [REMOVE_ME_2]$

[REMOVE_ME]$A_k \sim \mathcal{MN}(0,(V_k)^{-1},\tau XX^\top) [REMOVE_ME_2]$

[REMOVE_ME]$Y_{i.}|X_{i.}, A_k, Z_{ik}=1 \sim \mathcal{N}(A_k x_{i.},V_{k}^{-1}) [REMOVE_ME_2]$

with $\mathcal{W}(\epsilon^{-1},n_0)$ the Wishart distribution and $\mathcal{MN}$ the matrix-normal distribution. The MoR-class must be used when fitting a simple Mixture of Regression whereas the MoRPrior-class must be used when fitting a CombinedModels-class. class

MoRPrior(formula, tau = 0.001, N0 = NaN, epsilon = as.matrix(NaN))

MoR(formula, alpha = 1, tau = 0.1, N0 = NaN, epsilon = as.matrix(NaN))

Arguments

• formula: a formula that describe the linear model to use
• tau: Prior parameter (inverse variance) default 0.001
• N0: Prior parameter (default to NaN, in this case N0 will be fixed equal to the number of columns of Y.)
• epsilon: Covariance matrix prior parameter (default to NaN, in this case epsilon will be fixed to a diagonal variance matrix equal to 0.1 time the variance of the regression residuals with only one cluster.)
• alpha: Dirichlet prior parameter over the cluster proportions (default to 1)

Returns

a MoRPrior-class object

a MoR-class object

Description

An S4 class to represent a multivariate mixture of regression model. The model follows minka-linear . The model corresponds to the following generative model:

with $\mathcal{W}(\epsilon^{-1},n_0)$ the Wishart distribution and $\mathcal{MN}$ the matrix-normal distribution. The MoR-class must be used when fitting a simple Mixture of Regression whereas the MoRPrior-class must be used when fitting a CombinedModels-class.

Examples

MoRPrior(y ~ x1 + x2)
MoRPrior(y ~ x1 + x2, N0 = 100)
MoRPrior(cbind(y1, y2) ~ x1 + x2, N0 = 100)
MoR(y ~ x1 + x2)
MoR(y ~ x1 + x2, N0 = 100)
MoR(cbind(y1, y2) ~ x1 + x2, N0 = 100)

See Also

MoRFit-class, MoRPath-class

Other DlvmModels: CombinedModels, DcLbm, DcSbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MultSbm, Sbm, greed()