Confidence intervals
This computes confidence intervals for given parameter(s), based either on parametric bootstrap or, for fixed-effect parameters, on the p_v-based approximation of the profile likelihood ratio for this parameter. The profiling is over all other fitted parameters, including fixed effects, as well as variances of random effects and spatial correlations if these were fitted. The bootstrap is performed if the parm argument is a function or a quoted expression or if the boot_args argument is a list. The profile confidence interval is computed if neither of these conditions is true; in that case parm must be the name(s) of some fixed-effect coefficient.
## S3 method for class 'HLfit'
confint(object, parm, level=0.95, verbose=TRUE,
boot_args=NULL, format="default", ...)object |
An object of class |
parm |
character vector, integer vector, or function, or a quoted expression. If character, the name(s) of parameter(s) to be fitted; if integer, their position in the |
level |
The coverage of the interval. |
verbose |
whether to print the interval or not. As the function returns its more extensive results invisibly, this printing is the only visible output. |
boot_args |
NULL or a list of arguments passed to functions |
format |
Only effective non-default value is |
... |
Additional arguments (maybe not used, but conforming to the generic definition of |
The format of the value varies, but in all cases distinguished below, one or more tables are included, as a table attribute, in the format of the stats::confint result, to facilitate consistent extraction of results. By default confint returns invisibly the full values described below, but if format="stats", only the table attribute is returned.
If a profile CI has been computed for a single parameter, a list is returned including the confidence interval as shown by verbose=TRUE, and the fits lowerfit and upperfit giving the profile fits at the confidence bounds. This list bears the table attribute.
If a profile CI has been computed for several parameters, a structured list, named according to the parameter names, of such single-parameter results is returned, and a single table attribute for all parameters is attached to the upper level of the list.
If a bootstrap was performed, for a single parameter the result of the boot.ci call is returned, to which a table attribute is added. This table is now a list of tables for the different bootstrap CI types (default being normal, percent, and basic), each such table in the format of the stats::confint results. For several parameters, a named list of boot.ci results is returned, its names being the parameter names, and the table attribute is attached to the upper level of the list.
The boot.ci return value for each parameter includes the call to boot.ci. This call is typically shown including a long t vector, which makes a bulky display. spaMM hacks the printing to abbreviate long ts.
data("wafers")
wfit <- HLfit(y ~X1+(1|batch),family=Gamma(log),data=wafers,method="ML")
confint(wfit,"X1") # profile CI
if (spaMM.getOption("example_maxtime")>30) {
# bootstrap CI induced by 'boot_args':
confint(wfit,names(fixef(wfit)), boot_args=list(nsim=99, seed=123))
# bootstrap CI induced by 'parm' being a function:
confint(wfit,parm=function(v) fixef(v),
boot_args=list(nb_cores=10, nsim=199, seed=123))
# Same effect if 'parm' is a quoted expression in terms of 'hlfit':
confint(wfit,parm=quote(fixef(hlfit)),
boot_args=list(nb_cores=10, nsim=199, seed=123))
# CI for the variance of the random effect:
( ci <- confint(wfit,parm=function(fit){VarCorr(fit)[1,"Variance"]},
boot_args=list(nb_cores=10, nsim=199, seed=123)) )
# The distribution of bootstrap replicates:
plot(ecdf(ci$call$t))
# We may be far from ideal condition for accuracy of bootstrap intervals;
# for variances, a log transformation may sometimes help, but not here.
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