fmrReg: Finite Mixture Model with lasso and adaptive penalty

In fmerPack: Tools of Heterogeneity Pursuit via Finite Mixture Effects Model

Description

Produce solution for specific lambda of regularized finite mixture model with lasso or adaptive lasso penalty; compute the degrees of freeom, likelihood and information criteria (AIC, BIC and GIC) of the estimators. Model fitting is conducted by EM algorithm and coordinate descent.

Usage

fmrReg(y, X, m, intercept = FALSE, lambda, equal.var = FALSE, common.var = NULL,
       ic.type = c("ALL", "BIC", "AIC", "GIC"), 
       B = NULL, prob = NULL, rho = NULL, w = NULL, 
       control = list(), report = FALSE)

Arguments

y	a vector of response (n \times 1)
X	a matrix of covariate (n \times p)
m	number of components
intercept	indicating whether intercept should be included
lambda	value of tuning parameter
equal.var	indicating whether variances of different components are equal
common.var	indicating whether the effects over different components are the same for specific covariates
ic.type	the information criterion to be used; currently supporting "AIC", "BIC", and "GIC".
B	initial values for the rescaled coefficients with columns being the coefficients for different components
prob	initial values for prior probabilitis for different components
rho	initial values for rho vector (1 / σ), the reciprocal of standard deviation
w	weight matrix for penalty function. Default option is NULL
control	a list of parameters for controlling the fitting process
report	indicating whether printing the value of objective function during EM algorithm for validation checking of initial value.

Details

The available elements for argument control include

• epsilon: Convergence threshold for generalized EM algorithm. Defaults value is 1E-6.

• maxit: Maximum number of passes over the data for all lambda values. Default is 1000.

• inner.maxit: Maximum number of iteration for flexmix package to compute initial values. Defaults value is 200.

• n.ini: Number of initial values for EM algorithm. Default is 10. In EM algorithm, it is preferable to start from several different initial values.

Value

A list consisting of

y	vector of response
X	matrix of covariates
m	number of components
B.hat	estimated rescaled coefficient (p \times m \times nlambda)
pi.hat	estimated prior probabilities (m \times nlambda)
rho.hat	estimated rho values (m \times nlambda)
lambda	lambda used in model fitting
plik	value of penalized log-likelihood
loglik	value of log-likelihood
conv	indicator of convergence of EM algorithm
IC	values of information criteria
df	degree of freedom

Examples

library(fmerPack)
## problem settings
n <- 100; m <- 3; p <- 5;
sigma2 <- c(0.1, 0.1, 0.4); rho <- 1 / sqrt(sigma2)
phi <- rbind(c(1, 1, 1), c(1, 1, 1), c(0, -3, 3), c(-3, 3, 0), c(3, 0, -3))
beta <- t(t(phi) / rho)
## generate response and covariates
z <- rmultinom(n, 1, prob= rep(1 / m, m))
X <- matrix(rnorm(n * p), nrow = n, ncol = p)
y <- MASS::mvrnorm(1, mu = rowSums(t(z) * X[, 1:(nrow(beta))] %*% beta), 
                   Sigma = diag(colSums(z * sigma2)))
fmrReg(y, X, m = m, lambda = 0.01, control = list(n.ini = 10))

fmerPack documentation built on Feb. 1, 2021, 9:06 a.m.