Description Usage Arguments Details Value References See Also Examples

Perform the likelihood ratio test (LRT) for assessing the number of mixture components in a specific finite mixture model parameterisation. The observed significance is approximated by using the (parametric) bootstrap for the likelihood ratio test statistic (LRTS).

1 2 3 4 5 6 7 8 9 | ```
mclustBootstrapLRT(data, modelName = NULL, nboot = 999, level = 0.05, maxG = NULL,
verbose = interactive(), ...)
## S3 method for class 'mclustBootstrapLRT'
print(x, ...)
## S3 method for class 'mclustBootstrapLRT'
plot(x, G = 1, hist.col = "grey", hist.border = "lightgrey", breaks = "Scott",
col = "forestgreen", lwd = 2, lty = 3, main = NULL, ...)
``` |

`data` |
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables. |

`modelName` |
A character string indicating the mixture model to be fitted.
The help file for |

`nboot` |
The number of bootstrap replications to use (by default 999). |

`level` |
The significance level to be used to terminate the sequential bootstrap procedure. |

`maxG` |
The maximum number of mixture components |

`verbose` |
A logical controlling if a text progress bar is displayed during the bootstrap procedure. By default is |

`...` |
Further arguments passed to or from other methods. In particular, see the optional arguments in |

`x` |
An |

`G` |
A value specifying the number of components for which to plot the bootstrap distribution. |

`hist.col` |
The colour to be used to fill the bars of the histogram. |

`hist.border` |
The color of the border around the bars of the histogram. |

`breaks` |
See the argument in function |

`col, lwd, lty` |
The color, line width and line type to be used to represent the observed LRT statistic. |

`main` |
The title for the graph. |

The implemented algorithm for computing the LRT observed significance using the bootstrap is the following.
Let *G_0* be the number of mixture components under the null hypothesis versus *G_1 = G_0+1* under the alternative. Bootstrap samples are drawn by simulating data under the null hypothesis. Then, the p-value may be approximated using eq. (13) on McLachlan and Rathnayake (2014). Equivalently, using the notation of Davison and Hinkley (1997) it may be computed as

*
p-value = (1 + #{LRTS*_b ≥ LRT_obs}) / (B+1)*

where

*B* = number of bootstrap samples

*LRT_obs* = LRTS computed on the observed data

*LRT*_b* = LRTS computed on the *b*th bootstrap sample.

An object of class `'mclustBootstrapLRT'`

with the following components:

`G` |
A vector of number of components tested under the null hypothesis. |

`modelName` |
A character string specifying the mixture model as provided in the function call (see above). |

`obs` |
The observed values of the LRTS. |

`boot` |
A matrix of dimension |

`p.value` |
A vector of p-values. |

Davison, A. and Hinkley, D. (1997) *Bootstrap Methods and Their Applications*. Cambridge University Press.

McLachlan G.J. (1987) On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. *Applied Statistics*, 36, 318-324.

McLachlan, G.J. and Peel, D. (2000) *Finite Mixture Models*. Wiley.

McLachlan, G.J. and Rathnayake, S. (2014) On the number of components in a Gaussian mixture model. *Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery*, 4(5), pp. 341-355.

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