Description Usage Arguments Details Value Author(s) References See Also Examples

Density, distribution function, quantile function and random generation for mixtures of chi-squared distributions that corresponds to the null distribution of the Likelihood Ratio between 2 nested mixed models.

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`n` |
number of observations. |

`s` |
number of fixed effects to be tested. |

`q` |
number of random effects to be tested. |

`x, quant` |
a quantile. |

`p` |
a probability. |

`lower.tail` |
logical; if |

The approximate null distribution of a likelihood ratio for 2 nested mixed
models, where both fixed and random effects are tested simultaneously, is a
very specific mixture of *chi-square* distributions [Self & Liang
(1987), Stram & Lee (1994) and Stram & Lee (1995)]. It depends on both the
number of random effects and the number of fixed effects to be tested
simultaneously:

*LRT_H0~∑ k=q..q+r combination(r,k-q) 2^(-r) χ^2 (k)*

A vector of random independent observations of the *chi-square* mixture
identified by the values of `s`

and `q`

.

Boris P. Hejblum

Self, S. G. and Liang, K., 1987, Asymptotic properties of maximum
likelihood estimators and likelihood ratio tests under nonstandard
conditions, *Journal of the American Statistical Association* 82:
605–610.

Stram, D. O. and Lee, J. W., 1994, Variance components testing in the
longitudinal mixed effects model, *Biometrics* 50: 1171–1177.

Stram, D. O. and Lee, J. W., 1995, Corrections to "Variance components
testing in the longitudinal mixed effects model" by Stram, D. O. and Lee, J.
W.; 50: 1171–1177 (1994), *Biometrics* 51: 1196.

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