ci.lin.Rd
\name{ci.lin}
\alias{ci.lin}
\alias{ci.mat}
\alias{ci.exp}
\alias{ci.pred}
\alias{ci.ratio}
\alias{Wald}
\title{
Compute linear functions of parameters with standard errors and
confidence limits, optionally transforming to a different scale.
}
\description{
For a given model object the function computes a linear function of
the parameters and the corresponding standard errors, p-values and
confidence intervals.
}
\usage{
ci.lin( obj,
ctr.mat = NULL,
subset = NULL,
subint = NULL,
xvars = NULL,
diffs = FALSE,
fnam = !diffs,
vcov = FALSE,
alpha = 0.05,
df = Inf,
Exp = FALSE,
sample = FALSE )
ci.exp( ..., Exp = TRUE, pval = FALSE )
Wald( obj, H0=0, ... )
ci.mat( alpha = 0.05, df = Inf )
ci.pred( obj, newdata,
Exp = NULL,
alpha = 0.05 )
ci.ratio( r1, r2,
se1 = NULL,
se2 = NULL,
log.tr = !is.null(se1) & !is.null(se2),
alpha = 0.05,
pval = FALSE )
}
\arguments{
\item{obj}{A model object (in general of class \code{glm}, but for
\code{ci.lin} and \code{ci.exp} it may also be of class
\code{lm},
\code{coxph},
\code{survreg},
\code{clogistic},
\code{cch},
\code{lme},
\code{mer},
\code{lmerMod},
\code{gls},
\code{nls},
\code{gnlm},
\code{MIresult},
\code{mipo},
\code{polr},
or \code{rq}).
}
\item{ctr.mat}{Matrix, data frame or list (of two or four data frames).
If \code{ctr.mat} is a matrix, it should be a contrast matrix to be
multiplied to the parameter vector, i.e. the desired linear function
of the parameters.
If it is a data frame it should have columns corresponding to a
prediction frame, see details.
If it is a list, it must contain two or four data frames that are
(possibly partial) prediction frames for \code{obj}, see argument
\code{xvars} and details.}
\item{xvars}{Character vector. If quantitative variables in the model are omitted
from data frames supplied in a list to \code{ctr.mat}, they should
be listed here. Omitted factors need not be mentioned here.}
\item{subset}{The subset of the parameters to be used. If given as a
character vector, the elements are in turn matched against the
parameter names (using \code{grep}) to find the subset. Repeat
parameters may result from using a character vector. This is
considered a facility.}
\item{subint}{Character. \code{sub}set selection, but where each
element of the character vector is used to
select a subset of parameters and only the \code{int}ersection
of these is returned.}
\item{diffs}{If TRUE, all differences between parameters
in the subset are computed, and the \code{subset} argumnt is
required. The argument \code{ctr.mat} is ignored. If \code{obj}
inherits from \code{lm}, and \code{subset} is given as a string
\code{subset} is used to search among the factors in the model and
differences of all factor levels for the first match are shown.
If \code{subset} does not match any of the factors in the model, all
pairwise differences between parameters matching are returned.}
\item{fnam}{Should the common part of the parameter names be included
with the annotation of contrasts? Ignored if \code{diffs==T}. If a
string is supplied this will be prefixed to the labels.}
\item{vcov}{Should the covariance matrix of the set of parameters be
returned? If this is set, \code{Exp} is ignored. See details.}
\item{alpha}{Significance level for the confidence intervals.}
\item{df}{Integer. Number of degrees of freedom in the t-distribution used
to compute the quantiles used to construct the confidence intervals.}
\item{Exp}{For \code{ci.lin}, if \code{TRUE} columns 5:6 are replaced
with exp( columns 1,5,6 ). For \code{ci.exp}, if \code{FALSE}, the
untransformed parameters are returned. For \code{ci.pred} it
indicates whether the predictions should be exponentiated - the
default (\code{Exp=NULL}) is to make a prediction with a Wald CI on
the scale of the linear predictor and back-transform it by the
inverse link function; if \code{FALSE}, the prediction on the link
scale is returned.}
\item{sample}{Logical or numerical. If \code{TRUE} or numerical a
sample of size \code{as.numeric(sample)} is drawn from the
multivariate normal with mean equal to the (\code{subset} defined)
coefficients and variance equal to the estimated variance-covariance
of these. These are then transformed by \code{ctr.mat} and
returned.}
\item{pval}{Logical. Should a column of P-values be included with the
estimates and confidence intervals output by \code{ci.exp}.}
\item{H0}{Numeric. The null values for the selected/transformed parameters to
be tested by a Wald test. Must have the same length as the selected
parameter vector.}
\item{\ldots}{Parameters passed on to \code{ci.lin}.}
\item{newdata}{Data frame of covariates where prediction is made.}
\item{r1,r2}{Estimates of rates in two independent groups, with
confidence intervals.}
\item{se1,se2}{Standard errors of log-rates in the two groups. If
given, it is assumed that \code{r1} and \code{r2} represent
log-rates.}
\item{log.tr}{Logical, if true, it is assumed that \code{r1} and
\code{r2} represent log-rates with confidence intervals.}
}
\value{
\code{ci.lin} returns a matrix with number of rows and row names as
\code{ctr.mat}. The columns are Estimate, Std.Err, z, P, 2.5\% and
97.5\% (or according to the value of \code{alpha}). If
\code{vcov=TRUE} a list of length 2 with components \code{coef} (a
vector), the desired functional of the parameters and \code{vcov} (a
square matrix), the variance covariance matrix of this, is returned
but not printed. If \code{Exp==TRUE} the confidence intervals for the
parameters are replaced with three columns: exp(estimate,c.i.).
\code{ci.exp} returns only the exponentiated parameter estimates with
confidence intervals. It is merely a wrapper for \code{ci.lin},
fishing out the last 3 columns from \code{ci.lin(...,Exp=TRUE)}. If
you just want the estimates and confidence limits, but not
exponentiated, use \code{ci.exp(...,Exp=FALSE)}.
If \code{ctr.mat} is a data frame, the model matrix corresponding to
this is constructed and supplied. This is only supported for objects
of class \code{lm}, \code{glm}, \code{gam} and \code{coxph}.
So the default behaviour will be to produce the same as
\code{ci.pred}, apparently superfluous. The purpose of this is to
allow the use of the arguments \code{vcov} that produces the
variance-covariance matrix of the predictions, and \code{sample} that
produces a sample of predictions using sampling from the multivariate
normal with mean equal to parameters and variance equal to the
hessian.
If \code{ctr.mat} is a list of two data frames, the difference of the
predictions from using the first versus the last as newdata arguments
to predict is computed. Columns that would be identical in the two
data frames can be omitted (see below), but names of numerical
variables omitted must be supplied in a character vector
\code{xvars}. Factors omitted need not be named.
If the second data frame has only one row, this is replicated to match
the number of rows in the first. This facility is primarily aimed at
teasing out RRs that are non-linear functions of a quantitative
variable without setting up contrast matrices using the same code as
in the model. Note however if splines are used with computed knots
stored in a vector such as \code{Ns(x,knots=kk)} then the \code{kk}
must be available in the (global) environment; it will not be found
inside the model object. In practical terms it means that if you save
model objects for later prediction you should save the knots used in
the spline setups too.
If \code{ctr.mat} is a list of four data frames, the difference of the
difference of predictions from using the first and second versus
difference of predictions from using the third and fourth is computed.
Simply \code{(pr1-pr2) - (pr3-pr4)} with obvious notation. Useful to
derive esoteric interaction effects.
Finally, only arguments \code{Exp}, \code{vcov}, \code{alpha} and
\code{sample} from \code{ci.lin} are honored when \code{ctr.mat} is a
data frame or a list of two data frames.
You can leave out variables (columns) from the two data frames that
would be identical, basically variables not relevant for the
calculation of the contrast. In many cases \code{ci.lin} (really
\code{Epi:::ci.dfr}) can figure out the names of the omitted columns,
but occasionally you will have to supply the names of the omitted
variables in the \code{xvars} argument. Factors omitted need not be
listed in \code{xvars}, although no harm is done doing so.
\code{Wald} computes a Wald test for a subset of (possibly linear
combinations of) parameters being equal to the vector of null
values as given by \code{H0}. The selection of the subset of
parameters is the same as for \code{ci.lin}. Using the \code{ctr.mat}
argument makes it possible to do a Wald test for equality of
parameters. \code{Wald} returns a named numerical vector of length 3,
with names \code{Chisq}, \code{d.f.} and \code{P}.
\code{ci.mat} returns a 2 by 3 matrix with rows \code{c(1,0,0)} and
\code{c(0,-1,1)*1.96}, devised to post-multiply to a p by 2 matrix with
columns of estimates and standard errors, so as to produce a p by 3 matrix
of estimates and confidence limits. Used internally in \code{ci.lin} and
\code{ci.cum}.
The 1.96 is replaced by the appropriate quantile from the normal or
t-distribution when arguments \code{alpha} and/or \code{df} are given.
\code{ci.pred} returns a 3-column matrix with estimates and upper and
lower confidence intervals as columns. This is just a convenience
wrapper for \code{predict.glm(obj,se.fit=TRUE)} which returns a rather
unhandy structure. The prediction with c.i. is made in the \code{link}
scale, and by default transformed by the inverse link, since the most
common use for this is for multiplicative Poisson or binomial models
with either log or logit link.
\code{ci.ratio} returns the rate-ratio of two independent set of
rates given with confidence intervals or s.e.s. If \code{se1} and
\code{se2} are given and \code{log.tr=FALSE} it is assumed that
\code{r1} and \code{r2} are rates and \code{se1} and \code{se2} are
standard errors of the log-rates.
}
\author{
Bendix Carstensen,
\url{http://BendixCarstensen.com} & Michael Hills
}
\seealso{See also \code{\link{ci.cum}} for a function computing
cumulative sums of (functions of) parameter estimates, and
\code{\link{ci.surv}} for a function computing confidence intervals
for survival functions based on smoothed rates. The example code for
\code{\link{matshade}} has an application of predicting a rate-ratio
using a list of two prediction frame in the \code{ctr.mat} argument.}
\examples{
# Bogus data:
f <- factor( sample( letters[1:5], 200, replace=TRUE ) )
g <- factor( sample( letters[1:3], 200, replace=TRUE ) )
x <- rnorm( 200 )
y <- 7 + as.integer( f ) * 3 + 2 * x + 1.7 * rnorm( 200 )
# Fit a simple model:
mm <- lm( y ~ x + f + g )
ci.lin( mm )
ci.lin( mm, subset=3:6, diff=TRUE, fnam=FALSE )
ci.lin( mm, subset=3:6, diff=TRUE, fnam=TRUE )
ci.lin( mm, subset="f", diff=TRUE, fnam="f levels:" )
print( ci.lin( mm, subset="g", diff=TRUE, fnam="gee!:", vcov=TRUE ) )
# Use character defined subset to get ALL contrasts:
ci.lin( mm, subset="f", diff=TRUE )
# Suppose the x-effect differs across levels of g:
mi <- update( mm, . ~ . + g:x )
ci.lin( mi )
# RR a vs. b by x:
nda <- data.frame( x=-3:3, g="a", f="b" )
ndb <- data.frame( x=-3:3, g="b", f="b" )
#
ci.lin( mi, list(nda,ndb) )
# Same result if f column is omitted because "f" columns are identical
ci.lin( mi, list(nda[,-3],ndb[,-3]) )
# However, crashes if knots in spline is supplied, and non-factor omitted
xk <- -1:1
xi <- c(-0.5,0.5)
ww <- rnorm(200)
mi <- update( mm, . ~ . -x + ww + Ns(x,knots=xk) + g:Ns(x,knots=xi) )
# Will crash
try( cbind( nda$x, ci.lin( mi, list(nda,ndb) ) ) )
# Must specify num vars (not factors) omitted from nda, ndb
cbind( nda$x, ci.lin( mi, list(nda,ndb), xvars="ww" ) )
# A Wald test of whether the g-parameters are 0
Wald( mm, subset="g" )
# Wald test of whether the three first f-parameters are equal:
( CM <- rbind( c(1,-1,0,0), c(1,0,-1,0)) )
Wald( mm, subset="f", ctr.mat=CM )
# or alternatively
( CM <- rbind( c(1,-1,0,0), c(0,1,-1,0)) )
Wald( mm, subset="f", ctr.mat=CM )
# Confidence intervals for ratio of rates
# Rates and ci supplied, but only the range (lower and upper ci) is used
ci.ratio( cbind(10,8,12.5), cbind(5,4,6.25) )
ci.ratio( cbind(8,12.5), cbind(4,6.25) )
# Beware of the offset when making predictions with ci.pred and ci.exp
\dontrun{
library( mgcv )
data( mortDK )
m.arg <- glm( dt ~ age , offset=log(risk) , family=poisson, data=mortDK )
m.form <- glm( dt ~ age + offset(log(risk)), family=poisson, data=mortDK )
a.arg <- gam( dt ~ age , offset=log(risk) , family=poisson, data=mortDK )
a.form <- gam( dt ~ age + offset(log(risk)), family=poisson, data=mortDK )
nd <- data.frame( age=60:65, risk=100 )
round( ci.pred( m.arg , nd ), 4 )
round( ci.pred( m.form, nd ), 4 )
round( ci.exp ( m.arg , nd ), 4 )
round( ci.exp ( m.form, nd ), 4 )
round( ci.pred( a.arg , nd ), 4 )
round( ci.pred( a.form, nd ), 4 )
round( ci.exp ( a.arg , nd ), 4 )
round( ci.exp ( a.form, nd ), 4 )
nd <- data.frame( age=60:65 )
try( ci.pred( m.arg , nd ) )
try( ci.pred( m.form, nd ) )
try( ci.exp ( m.arg , nd ) )
try( ci.exp ( m.form, nd ) )
try( ci.pred( a.arg , nd ) )
try( ci.pred( a.form, nd ) )
try( ci.exp ( a.arg , nd ) )
try( ci.exp ( a.form, nd ) )
}
# The offset may be given as an argument (offset=log(risk))
# or as a term (+offset(log)), and depending on whether we are using a
# glm or a gam Poisson model and whether we use ci.pred or ci.exp to
# predict rates the offset is either used or ignored and either
# required or not; the state of affairs can be summarized as:
#
# offset
# -------------------------------------
# usage required?
# ------------------ ---------------
# function model argument term argument term
# ---------------------------------------------------------
# ci.pred glm used used yes yes
# gam ignored used no yes
#
# ci.exp glm ignored ignored no yes
# gam ignored ignored no yes
# ---------------------------------------------------------
}
\keyword{models}
\keyword{regression}
