TcGSA (version 0.12.10)

rchisqmix: Chi-Squared Mixtures Distribution

Description

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.

Usage

rchisqmix(n, s, q)
dchisqmix(x, s, q)
qchisqmix(p, s, q)
pchisqmix(quant, s, q, lower.tail = TRUE)

Arguments

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 TRUE (default), probabilities are \(P[X \le x]\); otherwise, \(P[X > x]\).

Value

A vector of random independent observations of the \(\chi^2\) mixture identified by the values of s and q.

Details

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 \(\chi^2\) 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: $$LRT_{H_0}\sim\sum_{k=q}^{q+r}{{r}\choose{k-q}}2^{-r}\chi^2_{(k)}$$

References

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.

See Also

pval_simu

Examples

# NOT RUN {
library(graphics)
library(stats)

sample_mixt <- rchisqmix(n=1000, s=3, q=3)
plot(density(sample_mixt))


# }