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

## Description

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

## Usage

 1 2 3 4 fmrHP(y, X, m, intercept = FALSE, lambda, equal.var = FALSE, 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 ic.type the information criterion to be used; currently supporting "AIC", "BIC", and "GIC". B initial values for the rescaled coefficients with first column being the common effect, and the rest m columns being the heterogeneity for corresponding 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.eps: Convergence threshold for Bregman coordinate descent algorithm. Defaults value is 1E-6.

• inner.maxit: Maximum number of iteration for Bregman coordinate descent algorithm. 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 + 1 \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

  1 2 3 4 5 6 7 8 9 10 11 12 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))) fmrHP(y, X, m = m, lambda = 0.01, control = list(n.ini = 10)) 

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