Description Usage Arguments Details Value Note References See Also Examples
Performs approximate conditional inference on a scalar parameter of
interest in regressionscale models. The output is stored in an
object of class marg
.
1 2 3 4 5 
object 
a 
offset 
either the covariate occurring in the model formula whose
coefficient represents the parameter of interest or 
formula 
a formula expression (only if no 
family 
a 
dispersion 
argument only to be used if no 
data 
an optional data frame in which to interpret the variables
occurring in the formula (only if no 
pts 
number of output points (minimum 10) that are calculated exactly; the default is 20. 
n 
approximate number of output points (minimum 50) produced by the
spline interpolation. The default is the maximum between 100 and
twice 
tms 
defines the range MLE +/ 
from 
starting value of the sequence that contains the values of the parameter of interest for which output points are calculated exactly. The default is MLE  3.5 * s.e. 
to 
ending value of the sequence that contains the values of the parameter of interest for which output points are calculated exactly. The default is MLE + 3.5 * s.e. 
control 
a list of iteration and algorithmic constants that control the

trace 
if 
... 
additional arguments, such as 
This function is a method for the generic function cond
for class rsm
. It can be invoked by calling cond
for
an object of the appropriate class, or directly by calling
cond.rsm
regardless of the class of the object.
cond.rsm
has also to be used if the rsm
object is not
provided throught the object
argument but specified by
formula
and family
.
The function cond.rsm
implements several small sample
asymptotic methods for approximate conditional inference in
regressionscale models. Approximations for both the modified/marginal
log likelihood function and approximate conditional/marginal tail
probabilities are
available (see marg.object
for details). Attention is
restricted to a scalar parameter of interest, either a regression
coefficient or the scale parameter. In the first case, the
associated covariate may be either numerical or a twolevel factor.
Approximate conditional (or equivalently marginal) inference is performed
by either updating a
fitted regressionscale model or defining the model formula and
family. All approximations are calculated exactly for pts
equally spaced points ranging from from
to to
. A
spline interpolation is used to extend them over the whole interval
of interest, except for the range of values defined by MLE
+/ tms
* s.e. where the spline interpolation is
replaced by a higher order polynomial interpolation. This is done
in order to avoid numerical instabilities which are likely to occur
for values of the parameter of interest close to the MLE.
Results
are stored in an object of class marg
. Method functions
like print
, summary
and
plot
can be used to examine the output or
represent it graphically. Components can be extracted using
coef
, formula
and
family
.
Main references for the methods considered are the papers by BarndorffNielsen (1991), DiCiccio, Field and Fraser (1990) and DiCiccio and Field (1991). The theory and statistics used are summarized in Brazzale (2000, Chapters 2 and 3). More details of the implementation are given in Brazzale (1999; 2000, Section 6.3.1).
The returned value is an object of class marg
; see
marg.object
for details.
If the parameter of interest is the scale parameter, all calculations are performed on the logarithmic scale, though most results are reported on the original scale.
In rare occasions, cond.rsm
dumps because of nonconvergence
of the function rsm
which is used to refit the model
for a fixed value of the parameter of interest. This happens for
instance if this value is too extreme. The arguments from
and to
may then be used to limit the default range of
MLE +/ 3.5 * s.e. A further possibility is to
finetuning the constants (number of iterations, convergence
threshold) that control the rsm
fit through the
control
argument.
cond.rsm
may also dump if the estimate of the parameter of
interest is large (tipically > 400) in absolute value. This may be
avoided by reparametrizing the model.
BarndorffNielsen, O. E. (1991) Modified signed log likelihood ratio. Biometrika, 78, 557–564.
Brazzale, A. R. (1999) Approximate conditional inference for logistic and loglinear models. J. Comput. Graph. Statist., 8, 653–661.
Brazzale, A. R. (2000) Practical SmallSample 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.
DiCiccio, T. J. and Field, C. A. (1991) An accurate method for approximate conditional and Bayesian inference about linear regression models from censored data. Biometrika, 78, 903–910.
marg.object
, summary.marg
,
plot.marg
, rsm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  ## Sea Level Data
data(venice)
attach(venice)
Year < 1:51/51
c11 < cos(2*pi*1:51/11) ; s11 < sin(2*pi*1:51/11)
c19 < cos(2*pi*1:51/18.62) ; s19 < sin(2*pi*1:51/18.62)
##
## quadratic model fitted to the sea level, includes 18.62year
## astronomical tidal cycle and 11year sunspot cycle
venice.rsm < rsm(sea ~ Year + I(Year^2) + c11 + s11 + c19 + s19,
family = extreme)
names(coef(venice.rsm))
## "(Intercept)" "Year" "I(Year^2)" "c11" "s11" "c19" "s19"
##
## variable of interest: quadratic term
venice.marg < cond(venice.rsm, I(Year^2))
##
detach()
## House Price Data
data(houses)
houses.rsm < rsm(price ~ ., family = student(5), data = houses)
##
## parameter of interest: scale parameter
houses.marg < cond(houses.rsm, scale)

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