path.fmrReg: Finite Mixture Model with lasso and adaptive penalty
In fmerPack: Tools of Heterogeneity Pursuit via Finite Mixture Effects Model

Description Usage Arguments Details Value Examples

View source: R/fmrReg.R

Produce solution paths 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.

1
2
3

path.fmrReg(y, X, m, equal.var = FALSE,
            ic.type = "ALL", B = NULL, prob = NULL, rho = NULL, 
            control = list(), modstr = list(), report = FALSE)

`y`	a vector of response (n \times 1)
`X`	a matrix of covariate (n \times p)
`m`	number of components
`equal.var`	indicating whether variances of different components are equal
`ic.type`	the information criterion to be used; currently supporting "ALL", "AIC", "BIC", and "GIC".
`B`	initial values for the rescaled coefficients with columns being the columns being the coefficient 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
`control`	a list of parameters for controlling the fitting process
`modstr`	a list of model parameters controlling the model fitting
`report`	indicating whether printing the value of objective function during EM algorithm for validation checking of initial value.

Model parameters can be specified through argument modstr. The available include

lambda: A vector of user-specified lambda values with default NULL.
lambda.min.ratio: Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value.
nlambda: The number of lambda values.
w: Weight matrix for penalty function. Default option is NULL, which means lasso penailty is used for model fitting.
intercept: Should intercept(s) be fitted (default=TRUE) or set to zero (FALSE).
no.penalty: A vector of user-specified indicators of the variables with no penalty.
common.var: A vector of user-specified indicators of the variables with common effect among different components.
select.ratio: A user-specified ratio indicating the ratio of variables to be selected.

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.

A list consisting of

`lambda`	vector of lambda used in model fitting
`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)
`IC`	values of information criteria

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(1, 1, 1), 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)))
## lasso
fit1 <- path.fmrReg(y, X, m = m, modstr = list(nlambda = 10), control = list(n.ini = 1))
## adaptive lasso
fit2 <- path.fmrReg(y, X, m = m, 
                   modstr = list(w = abs(select.tuning(fit1)$B + 1e-6)^2))