logisregmixEM: EM Algorithm for Mixtures of Logistic Regressions

Description

Returns EM algorithm output for mixtures of logistic regressions with arbitrarily many components.

Usage

logisregmixEM(y, x, N = NULL, lambda = NULL, beta = NULL, k = 2,
              addintercept = TRUE, epsilon = 1e-08, 
              maxit = 10000, verb = FALSE)

Value

logisregmixEM returns a list of class mixEM with items:

x: The predictor values.
y: The response values.
lambda: The final mixing proportions.
beta: The final logistic regression coefficients.
loglik: The final log-likelihood.
posterior: An nxk matrix of posterior probabilities for observations.
all.loglik: A vector of each iteration's log-likelihood.
restarts: The number of times the algorithm restarted due to unacceptable choice of initial values.
ft: A character vector giving the name of the function.

Arguments

y: An n-vector of successes out of N trials.
x: An nxp matrix of predictors. See addintercept below.
N: An n-vector of number of trials for the logistic regression. If NULL, then N is an n-vector of 1s for binary logistic regression.
lambda: Initial value of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by beta.
beta: Initial value of beta parameters. Should be a pxk matrix, where p is the number of columns of x and k is number of components. If NULL, then beta is generated by binning the data into k bins and using glm on the values in each of the bins. If both lambda and beta are NULL, then number of components is determined by k.
k: Number of components. Ignored unless lambda and beta are both NULL.
addintercept: If TRUE, a column of ones is appended to the x matrix before the value of p is calculated.
epsilon: The convergence criterion.
maxit: The maximum number of iterations.
verb: If TRUE, then various updates are printed during each iteration of the algorithm.

References

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley and Sons, Inc.

Examples

Run this code

## EM output for data generated from a 2-component logistic regression model.

set.seed(100)
beta <- matrix(c(1, .5, 2, -.8), 2, 2)
x <- runif(50, 0, 10)
x1 <- cbind(1, x)
xbeta <- x1%*%beta
N <- ceiling(runif(50, 50, 75))
w <- rbinom(50, 1, .3)
y <- w*rbinom(50, size = N, prob = (1/(1+exp(-xbeta[, 1]))))+
              (1-w)*rbinom(50, size = N, prob = 
              (1/(1+exp(-xbeta[, 2]))))
out.1 <- logisregmixEM(y, x, N, verb = TRUE, epsilon = 1e-01)
out.1

## EM output for data generated from a 2-component binary logistic regression model.

beta <- matrix(c(-10, .1, 20, -.1), 2, 2)
x <- runif(500, 50, 250)
x1 <- cbind(1, x)
xbeta <- x1%*%beta
w <- rbinom(500, 1, .3)
y <- w*rbinom(500, size = 1, prob = (1/(1+exp(-xbeta[, 1]))))+
              (1-w)*rbinom(500, size = 1, prob = 
              (1/(1+exp(-xbeta[, 2]))))
out.2 <- logisregmixEM(y, x, beta = beta, lambda = c(.3, .7), 
                       verb = TRUE, epsilon = 1e-01)
out.2