`pseudo.rlr.test`

tests whether certain variance components are zeros
using pseudo restricted likelihood ratio test,
assuming the variance components of interest are equal.
This function is a wrapper of the `RLRTSim`

function
in the `RLRsim`

package.

1 | ```
pseudo.rlr.test(Y, X, Z, Sigma, m0, nsim = 5000L, seed = 130623L)
``` |

`Y` |
response vector of length |

`X` |
fixed effects design matrix of dimension |

`Z` |
a list of random effects design matrices.
Each matrix should have |

`Sigma` |
a list of random effects correlation structures. Each matrix should be symmetric and positive definite, and match the dimension of the corresponding random effects design matrix. |

`m0` |
an integer indicating the number of nuisance variance components.
Should be between |

`nsim` |
number of simulations from the null distribution. If zero, REML estimates are computed but tests are not performed. |

`seed` |
a seed to be set before simulating from the null distribution. |

A vector of the test statistic and the p-value of pseudo restricted likelihood ratio test.

Yichi Zhang

Greven, S., Crainiceanu, C. M., Kuchenhoff, H., and Peters, A. (2008).
Restricted likelihood ratio testing for zero variance components in
linear mixed models.
*Journal of Computational and Graphical Statistics*, 17(4):870–891.

`rlr.test`

, `score.test`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
# two-way random effects ANOVA
n1 <- 5L
n2 <- 6L
n0 <- 4L
n <- n1 * n2 * n0
X <- cbind(rep(1, n))
A <- gl(n1, n2 * n0)
Z1 <- model.matrix(~ -1 + A, contrasts.arg = contr.treatment)
B <- rep(gl(n2, n0), n1)
Z2 <- model.matrix(~ -1 + B, contrasts.arg = contr.treatment)
Z3 <- model.matrix(~ -1 + B : A, contrasts.arg = contr.treatment)
set.seed(1L)
Y <- (X %*% 1
+ Z1 %*% rnorm(ncol(Z1), 0, 0.7)
+ Z2 %*% rnorm(ncol(Z2), 0, 0.3)
+ Z3 %*% rnorm(ncol(Z3), 0, 0.5)
+ rnorm(n, 0, 1))
Z <- list(Z1, Z2, Z3)
Sigma <- lapply(Z, function(z) diag(ncol(z)))
# tests interaction effects
pseudo.rlr.test(Y, X, Z, Sigma, 2L, 2000L, 2L)
# tests overall effects
pseudo.rlr.test(Y, X, Z, Sigma, 1L, 2000L, 3L)
``` |

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