Performs approximate conditional inference on a scalar parameter of
interest in regression-scale models. The output is stored in an
object of class
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either the covariate occurring in the model formula whose
coefficient represents the parameter of interest or
a formula expression (only if no
argument only to be used if no
an optional data frame in which to interpret the variables
occurring in the formula (only if no
number of output points (minimum 10) that are calculated exactly; the default is 20.
approximate number of output points (minimum 50) produced by the
spline interpolation. The default is the maximum between 100 and
defines the range MLE +/-
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.
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.
a list of iteration and algorithmic constants that control the
additional arguments, such as
This function is a method for the generic function
rsm. It can be invoked by calling
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
cond.rsm implements several small sample
asymptotic methods for approximate conditional inference in
regression-scale models. Approximations for both the modified/marginal
log likelihood function and approximate conditional/marginal tail
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 two-level factor.
Approximate conditional (or equivalently marginal) inference is performed
by either updating a
fitted regression-scale model or defining the model formula and
family. All approximations are calculated exactly for
equally spaced points ranging from
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.
are stored in an object of class
marg. Method functions
plot can be used to examine the output or
represent it graphically. Components can be extracted using
Main references for the methods considered are the papers by Barndorff-Nielsen (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.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 non-convergence
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
to may then be used to limit the default range of
MLE +/- 3.5 * s.e. A further possibility is to
fine-tuning the constants (number of iterations, convergence
threshold) that control the
rsm fit through the
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.
Barndorff-Nielsen, 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 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.
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.
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## 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 18.62-year ## astronomical tidal cycle and 11-year 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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