# 40_lmt: Likelihood Mixture Tests In EMCluster: EM Algorithm for Model-Based Clustering of Finite Mixture Gaussian Distribution

 Likelihood Mixture Tests R Documentation

## Likelihood Mixture Tests

### Description

This function test two mixture Gaussian models with unstructured covariance matrix and different numbers of clusters.

### Usage

```lmt(emobj.0, emobj.a, x, tau = 0.5, n.mc.E.delta = 1000,
n.mc.E.chi2, verbose = FALSE)
```

### Arguments

 `emobj.0` a `emret` object for the null hypothesis. `emobj.a` a `emret` object for the alternative hypothesis. `x` the data matrix, dimension n * p. `tau` proportion of null and alternative hypotheses. `n.mc.E.delta` number of Monte Carlo simulations for expectation of delta (difference of logL). `n.mc.E.chi2` number of Monte Carlo simulations for expectation of chisquare statistics. `verbose` if verbose.

### Details

This function calls several subroutines to compute information, likelihood ratio statistics, degrees of freedom, non-centrality of chi-squared distributions ... etc. Based on Monte Carlo methods to estimate parameters of likelihood mixture tests, this function return a p-value for testing H0: `emobj.0` v.s. Ha: `emobj.a`.

### Value

A list of class `lmt` are returned.

### Author(s)

Wei-Chen Chen wccsnow@gmail.com and Ranjan Maitra.

### See Also

`init.EM`.

### Examples

```## Not run:
library(EMCluster, quietly = TRUE)
set.seed(1234)

x <- as.matrix(iris[, 1:4])
p <- ncol(x)
min.n <- p * (p + 1) / 2
.EMC\$short.iter <- 200

ret.2 <- init.EM(x, nclass = 2, min.n = min.n, method = "Rnd.EM")
ret.3 <- init.EM(x, nclass = 3, min.n = min.n, method = "Rnd.EM")
ret.4 <- init.EM(x, nclass = 4, min.n = min.n, method = "Rnd.EM")

(lmt.23 <- lmt(ret.2, ret.3, x))
(lmt.34 <- lmt(ret.3, ret.4, x))
(lmt.24 <- lmt(ret.2, ret.4, x))

## End(Not run)
```

EMCluster documentation built on Aug. 20, 2022, 5:05 p.m.