Multivariate mixture of regression Prior model description class

An S4 class to represent a multivariate mixture of regression model. The model follows [minka-linear](https://tminka.github.io/papers/minka-linear.pdf) . The model corresponds to the following generative model: $$ \pi \sim Dirichlet(\alpha)$$ $$ Z_i \sim \mathcal{M}(1,\pi)$$ $$ V_k \sim \mathcal{W}(\varepsilon^{-1},n_0)$$ $$ A_k \sim \mathcal{MN}(0,(V_k)^{-1},\tau X^{t}X)$$ $$ Y_{i.}|X_{i.}, A_k, Z_{ik}=1 \sim \mathcal{N}(A_k x_{i.},V_{k}^{-1})$$ with $\mathcal{W}(\epsilon^{-1},n_0)$ the Whishart 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 MixedModels-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)

Value

a MoRPrior-class object a MoR-class object

Functions

MoR-class: MoR class constructor
MoRPrior: MoRPrior class constructor
MoR: MoR class constructor

Slots

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

Examples

MoRPrior(y ~ x1 + x2)
#> An object of class "MoRPrior"
#> Slot "formula":
#> y ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.001
#> 
#> Slot "N0":
#> [1] NaN
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
MoRPrior(y ~ x1 + x2, N0 = 100)
#> An object of class "MoRPrior"
#> Slot "formula":
#> y ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.001
#> 
#> Slot "N0":
#> [1] 100
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
MoRPrior(cbind(y1, y2) ~ x1 + x2, N0 = 100)
#> An object of class "MoRPrior"
#> Slot "formula":
#> cbind(y1, y2) ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.001
#> 
#> Slot "N0":
#> [1] 100
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
MoR(y ~ x1 + x2)
#> An object of class "MoR"
#> Slot "formula":
#> y ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.1
#> 
#> Slot "N0":
#> [1] NaN
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
#> Slot "alpha":
#> [1] 1
#> 
MoR(y ~ x1 + x2, N0 = 100)
#> An object of class "MoR"
#> Slot "formula":
#> y ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.1
#> 
#> Slot "N0":
#> [1] 100
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
#> Slot "alpha":
#> [1] 1
#> 
MoR(cbind(y1, y2) ~ x1 + x2, N0 = 100)
#> An object of class "MoR"
#> Slot "formula":
#> cbind(y1, y2) ~ x1 + x2
#> <environment: 0x55d410fdf2a8>
#> 
#> Slot "tau":
#> [1] 0.1
#> 
#> Slot "N0":
#> [1] 100
#> 
#> Slot "epsilon":
#>      [,1]
#> [1,]  NaN
#> 
#> Slot "alpha":
#> [1] 1
#>