LMEgradient {lme4} | R Documentation

## The gradient and Hessian in lme optimization-method

### Description

The LMEgradient and LMEhessian generic functions return the gradient and the Hessian of the log-likelihood or log-restricted-likelihood in an lme model with respect to the parameters of the object represented by `x`.

### Usage

    LMEgradient(x, A, nlev)
    LMEhessian(x, A, H, nlev)

### Arguments

`x` | a parameterized component of an lme model, usually the precision matrix of an `lmeLevel`. Such precision matrices inherit from the `pdMat` class.
`A` | an upper triangular matrix with the same number of columns as the matrix represented by `x`
`H` | an array of four dimensions with each dimension same as the number of columns of the matrix represented by `x`
`nlev` | integer: the number of levels of the grouping factor corresponding to the random-effects structure

### Value

LMEgradient returns a numeric vector of length `length(coef(x))`.
LMEhessian returns a symmetric matrix with number of columns `length(coef(x))`.

### Author(s)

Douglas Bates bates@stat.wisc.edu and Saikat DebRoy saikat@stat.wisc.edu

### See Also

`pdMat-class`, `lmeLevel-class`

### Examples

    library(lme4)
    data(Oxboys)
    m3 <- pdLogChol(~ age)
    as(m3, 'pdmatrix') <- crossprod(model.matrix(formula(m3), as(Oxboys, "data.frame")))
    LMEgradient(m3, diag(2), 19)

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