normalmixPMLE: normalmixPMLE

In hkasahar/normalregMix: normalregMix: An R Package for Normal Mixture Regression Models

Description

Estimates parameters of a finite mixture of univariate normals by penalized maximum log-likelhood functions.

Usage

normalmixPMLE(y, x = NULL, m = 2, z = NULL, vcov.method = c("Hessian",
  "OPG", "none"), ninits = 25, epsilon = 1e-08, maxit = 2000,
  epsilon.short = 0.01, maxit.short = 500, binit = NULL)

Arguments

y	n by 1 vector of data
x	n by q matrix of data for x (if exists)
m	The number of components in the mixture
z	n by p matrix of regressor associated with gamma
vcov.method	Method used to compute the variance-covariance matrix, one of "Hessian" and "OPG". The default option is "Hessian". When method = "Hessian", the variance-covarince matrix is estimated by the Hessian using the formula given in Boldea and Magnus (2009). When method = "OPG", the outer product of gradients is used.
ninits	The number of randomly drawn initial values.
epsilon	The convergence criterion. Convergence is declared when the penalized log-likelihood increases by less than epsilon.
maxit	The maximum number of iterations.
epsilon.short	The convergence criterion in short EM. Convergence is declared when the penalized log-likelihood increases by less than epsilon.short.
maxit.short	The maximum number of iterations in short EM.
binit	The initial value of parameter vector that is included as a candidate parameter vector

Value

A list of class normalMix with items:

coefficients	A vector of parameter estimates. Ordered as α_1,…,α_m,μ_1,…,μ_m,σ_1,…,σ_m,\gam.
parlist	The parameter estimates as a list containing alpha, mu, and sigma (and gam if z is included in the model).
vcov	The estimated variance-covariance matrix.
loglik	The maximized value of the log-likelihood.
penloglik	The maximized value of the penalized log-likelihood.
aic	Akaike Information Criterion of the fitted model.
bic	Bayesian Information Criterion of the fitted model.
postprobs	n by m matrix of posterior probabilities for observations
components	n by 1 vector of integers that indicates the indices of components each observation belongs to based on computed posterior probabilities
call	The matched call.
m	The number of components in the mixture.

Note

normalmixPMLE maximizes the penalized log-likelihood function using the EM algorithm with combining short and long runs of EM steps as in Biernacki et al. (2003). normalmixPMLE first runs the EM algorithm from ninits* 4m(1 + p) initial values with the convertence criterion epsilon.short and maxit.short. Then, normalmixPMLE uses ninits best initial values to run the EM algorithm with the convertence criterion epsilon and maxit.

References

Biernacki, C., Celeux, G. and Govaert, G. (2003) Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture Models, Computational Statistics and Data Analysis, 41, 561–575.

Boldea, O. and Magnus, J. R. (2009) Maximum Likelihood Estimation of the Multivariate Normal Mixture Model, Journal of the American Statistical Association, 104, 1539–1549.

Chen, J., Tan, X. and Zhang, R. (2008) Inference for Normal Mixtures in Mean and Variance, Statistica Sinica, 18, 443–465.

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

Examples

data(faithful)
attach(faithful)

normalmixPMLE(y = eruptions, m = 1)
normalmixPMLE(y = eruptions, m = 2)

out <- normalmixPMLE(y = eruptions, m = 2)
summary(out)

hkasahar/normalregMix documentation built on May 17, 2019, 4 p.m.