Generates replicates of the MLEs of the parameters occuring in a regression-scale model using as reference distribution the conditional distribution of the MLEs given the value of the ancillary.
rsm.sample(data = stop("no data given"), R = 10000,
ran.gen = stop("candidate distribution is missing, with no default"),
trace = TRUE, step = 100, …)A special conditional sampling data object. This object must be a list with the following elements:
ancthe vector containing the values of the ancillary; usually the Pearson residuals. It has to be of the same length than the number of observations in the linear regression model.
Xthe model matrix. It may be obtained applying
model.matrix to the fitted rsm
object of interest. The number of observations has to be the
same than the dimension of the ancillary, and the number of
covariates must correspond to the number of regression
coefficients defined in the coef component.
coefthe vector of true values of the regression coefficients, that is, the values used in the simulation study.
dispthe true value of the scale parameter used in the simulation study.
familya family.rsm object characterizing the error
distribution of the linear regression model. The following
generator functions are available in the marg
package of the R package bundle hoa:
student (Student's t), extreme (Gumbel or extreme
value), logistic, logWeibull,
logExponential, logRayleigh and Huber
(Huber's least favourable). The demonstration file
margdemo.R that accompanies the marg package shows
how to create a new generator function.
fixeda logical value. If TRUE the scale parameter is known.
The make.sample.data function can be used
to create this data object from a fitted rsm model.
the number of replicates.
a function which describes how the candidate values used in the
Metropolis-Hastings algorithm should be generated. It must be
a function of at least two arguments. The first one is the data
object data, and the second argument is R, the
number of replicates required. Any other information needed may
be passed through the … argument. The returned value
should be a R times k matrix of simulated values.
For the value of k see the details section below.
a logical value; if TRUE, the iteration number is printed.
Defaults to TRUE.
a numercial value defining after how many iterations to print the iteration number. Default is 100.
absorbs additional arguments to ran.gen. These are passed
unchanged each time this function is called.
The returned value is an object of class cs containing the
following components:
a matrix with R rows each of which contains a sample from
the conditional distribution of the MLEs.
the acceptance probabilities at each Metropolis-Hastings step, that is, the probabilities with which the candidate values drawn from the candidate generation distribution are accepted.
the value of .Random.seed when rsm.sample was
called.
the data as passed to rsm.sample.
the value of R as passed to rsm.sample.
the original call to rsm.sample.
The function rsm.sample causes creation of the dataset
.Random.seed if it does not already exist,
otherwise its value is updated.
The file csamplingdemo.R contains code that can be used to
run a conditional simulation study similar to the one described
in Brazzale (2000, Section 7.3) using the data given in
Example 3 of DiCiccio, Field and Fraser (1990).
The rsm.sample function uses the Metropolis-Hastings
algorithm to generate an ergodic chain with equilibrium distribution
equal to the conditional distribution of the MLEs given
the ancillary. Because of the broad applicability of this
algorithm
the candidate generation density was not built in, but has to be
supplied by the user through the ran.gen argument. The
output of this function must be a R times k matrix,
where k = p + 1 or k = p + 2 depending
on whether the
scale parameter is fixed or not. The first p columns contain
the MLEs of the regression coefficients, the following the
MLEs of the scale parameter if unknown, and the last
column contains the probabilities of the candidate values drawn
from the candidate generation distribution. Note that these
probabilities need only be calculated up to a normalizing constant.
All information is supplied through the data argument. The
user has to keep to the structure described above. If a conditional
simulation is to be performed for a fitted rsm object, the
make.sample.data function can be used to
generate this special object. It is advisable to specify the
logical switch fixed in the conditional sampling object,
although it needs not (in which case the scale parameter is supposed
to be unknown).
The conditional simulation (cs) object generated by
rsm.sample contains all information necessary for further
investigation, such as the derivation of the conditional
distribution of test statistics, the calculation of conditional
coverage levels of confidence intervals and many more. As the
computation is somewhat tricky, an example is given in the
demonstration file csamplingdemo.R.
Brazzale, A. R. (2000) Practical Small-Sample Parametric Inference. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss Federal Institute of Technology Lausanne.
DiCiccio, T. J., Field, C. A. and Fraser, D. A. S. (1990) Approximations of marginal tail probabilities and inference for scalar parameters. Biometrika, 77, 77--95.