# minque: MINQUE Algorithm In CLME: Constrained Inference for Linear Mixed Effects Models

## Description

Algorithm to obtain MINQUE estimates of variance components of a linear mixed effects model.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```minque( Y, X1, X2 = NULL, U = NULL, Nks = dim(X1), Qs = dim(U), mq.eps = 1e-04, mq.iter = 500, verbose = FALSE, ... ) ```

## Arguments

 `Y` Nx1 vector of response data. `X1` Nxp1 design matrix. `X2` optional Nxp2 matrix of covariates. `U` optional Nxc matrix of random effects. `Nks` optional Kx1 vector of group sizes. `Qs` optional Qx1 vector of group sizes for random effects. `mq.eps` criterion for convergence for the MINQUE algorithm. `mq.iter` maximum number of iterations permitted for the MINQUE algorithm. `verbose` if `TRUE`, function prints messages on progress of the MINQUE algorithm. `...` space for additional arguments.

## Details

By default, the model assumes homogeneity of variances for both the residuals and the random effects (if included). See the Details in `clme_em` for more information on how to use the arguments `Nks` and `Qs` to permit heterogeneous variances.

## Value

The function returns a vector of the form (tau1^2, tau2^2, …, tauq^2, sigma1^2,sigma2^2,…, sigmak^2)'. If there are no random effects, then the output is just (sigma1^2,sigma2^2,…, sigmak^2)'.

## Note

This function is called by several other function in CLME to obtain estimates of the random effect variances. If there are no random effects, they will not call `minque`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```data( rat.blood ) model_mats <- model_terms_clme( mcv ~ time + temp + sex + (1|id) , data = rat.blood ) Y <- model_mats\$Y X1 <- model_mats\$X1 X2 <- model_mats\$X2 U <- model_mats\$U # No covariates or random effects minque(Y = Y, X1 = X1 ) # Include covariates and random effects minque(Y = Y, X1 = X1, X2 = X2, U = U ) ```

CLME documentation built on July 8, 2020, 5:49 p.m.