# anova.lmm: Multivariate Tests For Linear Mixed Model In LMMstar: Repeated Measurement Models for Discrete Times

 anova.lmm R Documentation

## Multivariate Tests For Linear Mixed Model

### Description

Simultaneous tests of linear combinations of the model paramaters using Wald tests or Likelihood Ratio Test (LRT).

### Usage

``````## S3 method for class 'lmm'
anova(
object,
effects = NULL,
robust = FALSE,
rhs = NULL,
df = !is.null(object\$df),
ci = TRUE,
transform.sigma = NULL,
transform.k = NULL,
transform.rho = NULL,
transform.names = TRUE,
...
)
``````

### Arguments

 `object` a `lmm` object. Only relevant for the anova function. `effects` [character or numeric matrix] Should the Wald test be computed for all variables (`"all"`), or only variables relative to the mean (`"mean"` or `"fixed"`), or only variables relative to the variance structure (`"variance"`), or only variables relative to the correlation structure (`"correlation"`). Can also be use to specify linear combinations of coefficients or a contrast matrix, similarly to the `linfct` argument of the `multcomp::glht` function. `robust` [logical] Should robust standard errors (aka sandwich estimator) be output instead of the model-based standard errors. `rhs` [numeric vector] the right hand side of the hypothesis. Only used when the argument effects is a matrix. `df` [logical] Should a F-distribution be used to model the distribution of the Wald statistic. Otherwise a chi-squared distribution is used. `ci` [logical] Should an estimate, standard error, confidence interval, and p-value be output for each hypothesis? `transform.sigma, transform.k, transform.rho, transform.names` are passed to the `vcov` method. See details section in `coef.lmm`. `...` Not used. For compatibility with the generic method.

### Details

By default adjustment of confidence intervals and p-values for multiple comparisons is based on the distribution of the maximum-statistic. This is refered to as a single-step Dunnett multiple testing procedures in table II of Dmitrienko et al. (2013). It is performed using the multcomp package with the option `test = adjusted("single-step")` with equal degrees of freedom or by simulation using a Student's t copula with unequal degrees of freedom (more in the note of the details section of `confint.Wald_lmm`).

### Value

A data.frame (LRT) or a list of containing the following elements (Wald):

• `multivariate`: data.frame containing the multivariate Wald test. The column `df.num` refers to the degrees of freedom for the numerator (i.e. number of hypotheses) wherease the column `df.denum` refers to the degrees of freedom for the denominator (i.e. Satterthwaite approximation).

• `univariate`: data.frame containing each univariate Wald test.

• `glht`: used internally to call functions from the multcomp package.

• `object`: list containing key information about the linear mixed model.

• `vcov`: variance-covariance matrix associated to each parameter of interest (i.e. hypothesis).

• `iid`: matrix containing the influence function relative to each parameter of interest (i.e. hypothesis).

• `args`: list containing argument values from the function call.

### References

Dmitrienko, A. and D'Agostino, R., Sr (2013), Traditional multiplicity adjustment methods in clinical trials. Statist. Med., 32: 5172-5218. https://doi.org/10.1002/sim.5990.

`summary.Wald_lmm` or `confint.Wald_lmm` for a summary of the results.
`autoplot.Wald_lmm` for a graphical display of the results.
`rbind.Wald_lmm` for combining result across models and adjust for multiple comparisons.

### Examples

``````#### simulate data in the long format ####
set.seed(10)
dL <- sampleRem(100, n.times = 3, format = "long")

#### fit Linear Mixed Model ####
eUN.lmm <- lmm(Y ~ visit + X1 + X2 + X5,
repetition = ~visit|id, structure = "UN", data = dL)

#### Multivariate Wald test ####
## F-tests
anova(eUN.lmm)
anova(eUN.lmm, effects = "all")
anova(eUN.lmm, robust = TRUE, df = FALSE)
summary(anova(eUN.lmm))

## user defined F-test
summary(anova(eUN.lmm, effects = c("X1=0","X2+X5=10")))
print(anova(eUN.lmm, effects = "mean_visit"), columns = add("null"))

## chi2-tests
anova(eUN.lmm, df = FALSE)

## with standard contrast
if(require(multcomp)){
amod <- lmm(breaks ~ tension, data = warpbreaks)
e.amod <- anova(amod, effect = mcp(tension = "Tukey"))
summary(e.amod)
}

#### Likelihood ratio test ####
eUN0.lmm <- lmm(Y ~ X1 + X2, repetition = ~visit|id, structure = "UN", data = dL)
anova(eUN.lmm, eUN0.lmm)

eCS.lmm <- lmm(Y ~ X1 + X2 + X5, repetition = ~visit|id, structure = "CS", data = dL)
anova(eUN.lmm, eCS.lmm)
``````

LMMstar documentation built on Nov. 9, 2023, 1:06 a.m.