# lrt.stat: Likelihood ratio type statistic (global) In jelsema/CLME: Constrained Inference for Linear Mixed Effects Models

## Description

Calculates the likeihood ratio type test statistic (under Normality assumption) for a constrained linear mixed effects model. This is the default test statistic for CLME.

## Usage

 `1` ```lrt.stat(theta, theta.null, cov.theta, ...) ```

## Arguments

 `theta` estimated coefficients. `theta.null` coefficients estimated under the null hypothesis. `cov.theta` covariance matrix of the (unconstrained) coefficients. `...` additional arguments, to enable custom test statistic functions.

## Value

Output is a numeric value.

## Note

This is an internal function, unlikely to be useful outside of CLME-package. To define custom functions, the arguments available are:

`theta`, `theta.null`, `cov.theta`, `B`, `A`, `Y`, `X1`, `X2`, `U`, `tsq`, `ssq`, `Nks`, and `Qs`.

Of the additional arguments, `B` and `A` are identical to those produced by `create.constraints`. The rest, `Y`, `X1`, `X2`, `U`, `tsq`, , `ssq`, `Nks`, and `Qs`, are equivalent to arguments to `clme_em`.

Custom functions must produce numeric output. Output may have length greater than 1, which corresponds to testing multiple global hypotheses.

`clme_em`, `w.stat`
 ```1 2 3 4 5 6 7 8``` ```data( rat.blood ) cons <- list(order = "simple", decreasing = FALSE, node = 1 ) clme.out <- clme(mcv ~ time + temp + sex + (1|id), data = rat.blood , constraints = cons, seed = 42, nsim = 0) # Individually compute lrt statistic lrt.stat(clme.out\$theta, clme.out\$theta.null, clme.out\$cov.theta ) ```