# Finite Mixture Effects Model with Heterogeneity Pursuit 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. ```r 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 ($1 / \sigma$), 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. ## Returns 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 ## 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. ## Examples ```r 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)) ```

fmrHP function