mixtools (version 1.0.1)

boot.comp: Performs Parametric Bootstrap for Sequentially Testing the Number of Components in Various Mixture Models

Description

Performs a parametric bootstrap by producing B bootstrap realizations of the likelihood ratio statistic for testing the null hypothesis of a k-component fit versus the alternative hypothesis of a (k+1)-component fit to various mixture models. This is performed for up to a specified number of maximum components, k. A p-value is calculated for each test and once the p-value is above a specified significance level, the testing terminates. An optional histogram showing the distribution of the likelihood ratio statistic along with the observed statistic can also be produced.

Usage

boot.comp(y, x = NULL, N = NULL, max.comp = 2, B = 100,
          sig = 0.05, arbmean = TRUE, arbvar = TRUE,
          mix.type = c("logisregmix", "multmix", "mvnormalmix",
          "normalmix", "poisregmix", "regmix", "regmix.mixed", 
          "repnormmix"), hist = TRUE, ...)

Arguments

y

The raw data for multmix, mvnormalmix, normalmix, and repnormmix and the response values for logisregmix, poisregmix, and regmix. See the documentation c

x

The predictor values required only for the regression mixtures logisregmix, poisregmix, and regmix. A column of 1s for the intercept term must not be included! See the documentation concerning their respecti

N

An n-vector of number of trials for the logistic regression type logisregmix. If NULL, then N is an n-vector of 1s for binary logistic regression.

max.comp

The maximum number of components to test for. The default is 2. This function will perform a test of k-components versus (k+1)-components sequentially until we fail to reject the null hypothesis. This decision rule is governed by the calculat

B

The number of bootstrap realizations of the likelihood ratio statistic to produce. The default is 100, but ideally, values of 1000 or more would be more acceptable.

sig

The significance level for which to compare the p-value against when performing the test of k-components versus (k+1)-components.

arbmean

If FALSE, then a scale mixture analysis can be performed for mvnormalmix, normalmix, regmix, or repnormmix. The default is TRUE.

arbvar

If FALSE, then a location mixture analysis can be performed for mvnormalmix, normalmix, regmix, or repnormmix. The default is TRUE.

mix.type

The type of mixture analysis you wish to perform. The data inputted for y and x depend on which type of mixture is selected. logisregmix corresponds to a mixture of logistic regressions. multmix c

hist

An argument to provide a matrix plot of histograms for the boostrapped likelihood ratio statistic.

...

Additional arguments passed to the various EM algorithms for the mixture of interest.

Value

• boot.comp returns a list with items:
• p.values
  The p-values for each test of k-components versus (k+1)-components.
• log.lik
  The B bootstrap realizations of the likelihood ratio statistic.
• obs.log.lik
  The observed likelihood ratio statistic for each test which is used in determining the p-values.

References

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

See Also

logisregmixEM, multmixEM, mvnormalmixEM, normalmixEM, poisregmixEM, regmixEM, regmixEM.mixed, repnormmixEM

Examples

## Bootstrapping to test the number of components on the RTdata.

data(RTdata)
set.seed(100)
x <- as.matrix(RTdata[, 1:3])
y <- makemultdata(x, cuts = quantile(x, (1:9)/10))$y
a <- boot.comp(y = y, max.comp = 1, B = 5, mix.type = "multmix", 
               epsilon = 1e-3)
a$p.values