rchisqmix | R Documentation |
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.
rchisqmix(n, s, q) dchisqmix(x, s, q) qchisqmix(p, s, q) pchisqmix(quant, s, q, lower.tail = TRUE)
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.
pval_simu
library(graphics) library(stats) sample_mixt <- rchisqmix(n=1000, s=3, q=3) plot(density(sample_mixt))
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