quickle {aster} | R Documentation |

Evaluates the objective function for approximate maximum likelihood for an aster model with random effects. Uses Laplace approximation to integrate out the random effects analytically. The “quasi” in the title is a misnomer in the context of aster models but the acronym PQL for this procedure is well-established in the generalized linear mixed models literature.

quickle(alphanu, bee, fixed, random, obj, y, origin, zwz, deriv = 0)

`alphanu` |
the parameter vector value where the function is evaluated, a numeric vector, see details. |

`bee` |
the random effects vector that is used as the starting point
for the inner optimization, which maximizes the penalized log likelihood
to find the optimal random effects vector matching |

`fixed` |
the model matrix for fixed effects. The number of rows
is |

`random` |
the model matrix or matrices for random effects.
The number of rows is |

`obj` |
aster model object, the result of a call to |

`y` |
response vector. May be omitted, in which case |

`origin` |
origin of aster model. May be omitted, in which case
default origin (see |

`zwz` |
A possible value of |

`deriv` |
Number of derivatives wanted, zero, one, or two. |

Define

*p(alpha, b, nu) = m(a + M alpha + Z b) + t(b) D^(- 1) b / 2 + log det[t(Z) W Z D + I] / 2*

where *m* is minus the log likelihood function of a saturated aster model,
where *a* is a known vector (the *offset vector* in the terminology
of `glm`

but the *origin* in the terminology
of `aster`

),
where *M* is a known matrix, the model matrix for fixed effects
(the argument `fixed`

of this function),
where *Z* is a known matrix, the model matrix for random effects
(either the argument `random`

of this function if it is a matrix or
`Reduce(cbind, random)`

if `random`

is a list of matrices),
where *D* is a diagonal matrix whose diagonal is the vector
`rep(nu, times = nrand)`

where `nrand`

is `sapply(random, ncol)`

when `random`

is a list of
matrices and `ncol(random)`

when `random`

is a matrix,
where *W* is an arbitrary symmetric positive semidefinite matrix
(*t(Z) W Z* is the argument `zwz`

of this function),
and where *I* is the identity matrix.
Note that *D* is a function of *nu*
although the notation does not explicitly indicate this.

The argument `alphanu`

of this function is the concatenation
of the parameter vectors *alpha* and *ν*.
The argument `bee`

of this function is a possible value of *b*.
The length of *alpha* is the column dimension of *M*.
The length of *b* is the column dimension of *Z*.
The length of *ν* is the length of the argument `random`

of this function if it is a list and is one otherwise.

Let *bstar* denote the minimizer
of *p(alpha, b, nu)* considered as a function of
*b* for fixed *alpha* and *nu*, so *bstar*
is a function of *alpha* and *nu*.
This function evaluates

*q(alpha, nu) = p(alpha, bstar, nu)*

and its gradient vector and Hessian matrix (if requested).
Note that *bstar* is a function of *alpha*
and *nu* although the notation does not explicitly indicate this.

a list with some of the following components: `value`

, `gradient`

,
`hessian`

, `alpha`

, `bee`

, `nu`

. The first three are
the requested derivatives. The second three are the corresponding parameter
values: `alpha`

and `nu`

are the corresponding parts of the
argument `alphanu`

, the value of `bee`

is the result of the inner
optimization (*bstar* in the notation in details),
not the argument `bee`

of this function.

Not intended for use by naive users. Use `summary.reaster`

,
which calls it.

data(radish) pred <- c(0,1,2) fam <- c(1,3,2) rout <- reaster(resp ~ varb + fit : (Site * Region), list(block = ~ 0 + fit : Block, pop = ~ 0 + fit : Pop), pred, fam, varb, id, root, data = radish) alpha.mle <- rout$alpha bee.mle <- rout$b nu.mle <- rout$sigma^2 zwz.mle <- rout$zwz obj <- rout$obj fixed <- rout$fixed random <- rout$random alphanu.mle <- c(alpha.mle, nu.mle) qout <- quickle(alphanu.mle, bee.mle, fixed, random, obj, zwz = zwz.mle, deriv = 2)

[Package *aster* version 1.1-2 Index]