EM Algorithm for Mixtures of Regressions with Local Lambda Estimates

Returns output for one step of an EM algorithm output for mixtures of multiple regressions where the mixing proportions are estimated locally.

Usage

regmixEM.lambda(y, x, lambda = NULL, beta = NULL, sigma = NULL, 
                k = 2, addintercept = TRUE, arbmean = TRUE,
                arbvar = TRUE, epsilon = 1e-8, maxit = 10000,
                verb = FALSE)

Arguments

y

An n-vector of response values.

x

An nxp matrix of predictors. See addintercept below.

lambda

An nxk matrix of initial local values of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is simply one over the number of components.

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 has uniform standard normal entries. If both lambda and beta are NULL, then number of components is determined by sigma.

sigma

k-vector of initial global values of standard deviations. If NULL, then \(1/\code{sigma}^2\) has random standard exponential entries. If lambda, beta, and sigma are NULL, then number of components is determined by k.

k

The number of components. Ignored unless all of lambda, beta, and sigma are NULL.

addintercept

If TRUE, a column of ones is appended to the x matrix before the value of p is calculated.

arbmean

If TRUE, each mixture component is assumed to have a different set of regression coefficients (i.e., the betas).

arbvar

If TRUE, each mixture component is assumed to have a different sigma.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

regmixEM.lambda returns a list of class mixEM with items:

x

The set of predictors (which includes a column of 1's if addintercept = TRUE).

y

The response values.

lambda

The inputted mixing proportions.

beta

The final regression coefficients.

sigma

The final standard deviations. If arbmean = FALSE, then only the smallest standard deviation is returned. See scale below.

scale

If arbmean = FALSE, then the scale factor for the component standard deviations is returned. Otherwise, this is omitted from the output.

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.

Details

Primarily used within regmixEM.loc.

See also

regmixEM.loc

Examples

## Compare a 2-component and 3-component fit to NOdata.

data(NOdata)
attach(NOdata)
#> The following objects are masked from NOdata (pos = 3):
#> 
#>     Equivalence, NO
#> The following objects are masked from NOdata (pos = 5):
#> 
#>     Equivalence, NO
#> The following objects are masked from NOdata (pos = 9):
#> 
#>     Equivalence, NO
#> The following objects are masked from NOdata (pos = 10):
#> 
#>     Equivalence, NO
set.seed(100)
out1 <- regmixEM.lambda(Equivalence, NO)
out2 <- regmixEM.lambda(Equivalence, NO, k = 3)
c(out1$loglik, out2$loglik)
#> [1] 120.6423 123.5396