ci.lin: Compute linear functions of parameters with standard errors...
In Epi: Statistical Analysis in Epidemiology
ci.lin R Documentation
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
obj
A model object (in general of class glm, but for
ci.lin and ci.exp it may also be of class
lm,
coxph,
survreg,
clogistic,
cch,
lme,
mer,
lmerMod,
glmerMod,
gls,
nls,
gnlm,
MIresult,
mipo,
polr,
or rq).
ctr.mat
Matrix, data frame or list (of two or four data frames).
If 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 obj, see argument
xvars and details.
xvars
Character vector. If quantitative variables in the model
are omitted from data frames supplied in a list to ctr.mat,
they should be listed here. Omitted factors need not be mentioned
here.
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 grep) to find the subset. Repeat
parameters may result from using a character vector. This is
considered a facility.
subint
Character. subset selection, but where each
element of the character vector is used to
select a subset of parameters and only the intersection
of these is returned.
diffs
If TRUE, all differences between parameters
in the subset are computed, and the subset argument is
required. The argument ctr.mat is ignored. If obj
inherits from lm, and subset is given as a string
subset is used to search among the factors in the model and
differences of all factor levels for the first match are shown.
If subset does not match any of the factors in the model, all
pairwise differences between parameters matching are returned.
fnam
Should the common part of the parameter names be included
with the annotation of contrasts? Ignored if diffs==T. If a
string is supplied this will be prefixed to the labels.
vcov
Should the covariance matrix of the set of parameters be
returned? If this is set, Exp is ignored. See details.
alpha
Significance level for the confidence intervals.
df
Integer. Number of degrees of freedom in the t-distribution used
to compute the quantiles used to construct the confidence intervals.
Exp
For ci.lin, if TRUE columns 5:6 are replaced
with exp( columns 1,5,6 ). For ci.exp, if FALSE, the
untransformed parameters are returned. For ci.pred it
indicates whether the predictions should be exponentiated - the
default (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 FALSE, the prediction on the link
scale is returned.
sample
Logical or numerical. If TRUE or numerical a
sample of size as.numeric(sample) is drawn from the
multivariate normal with mean equal to the (subset defined)
coefficients and variance equal to the estimated variance-covariance
of these. These are then transformed by ctr.mat and
returned.
pval
Logical. Should a column of P-values be included with the
estimates and confidence intervals output by ci.exp.
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.
...
Parameters passed on to ci.lin.
newdata
Data frame of covariates where prediction is made.
r1, r2
Estimates of rates in two independent groups, with
confidence limits. Can be either 3-column matrices or data frames
with estimates and confidence intervals or 2 two column structures
with confidence limits. Only the confidence limits
se1, se2
Standard errors of log-rates in the two groups. If
given, it is assumed that r1 and r2 represent
log-rates.
log.tr
Logical, if true, it is assumed that r1 and
r2 represent log-rates with confidence intervals.
Value
ci.lin returns a matrix with number of rows and row names as
ctr.mat. The columns are Estimate, Std.Err, z, P, 2.5% and
97.5% (or according to the value of alpha). If
vcov=TRUE a list of length 2 with components coef (a
vector), the desired functional of the parameters and vcov (a
square matrix), the variance covariance matrix of this, is returned
but not printed. If Exp==TRUE the confidence intervals for the
parameters are replaced with three columns: exp(estimate,c.i.).
ci.exp returns only the exponentiated parameter estimates with
confidence intervals. It is merely a wrapper for ci.lin,
fishing out the last 3 columns from ci.lin(...,Exp=TRUE). If
you just want the estimates and confidence limits, but not
exponentiated, use ci.exp(...,Exp=FALSE).
If ctr.mat is a data frame, the model matrix corresponding to
this is constructed and supplied. This is only supported for objects
of class lm, glm, gam and coxph.
So the default behaviour will be to produce the same as
ci.pred, apparently superfluous. The purpose of this is to
allow the use of the arguments vcov that produces the
variance-covariance matrix of the predictions, and 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 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
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 Ns(x,knots=kk) then the 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 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 (pr1-pr2) - (pr3-pr4) with obvious notation. Useful to
derive esoteric interaction effects.
Finally, only arguments Exp, vcov, alpha and
sample from ci.lin are honored when 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 ci.lin (really
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 xvars argument. Factors omitted need not be
listed in xvars, although no harm is done doing so.
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 H0. The selection of the subset of
parameters is the same as for ci.lin. Using the ctr.mat
argument makes it possible to do a Wald test for equality of
parameters. Wald returns a named numerical vector of length 3,
with names Chisq, d.f. and P.
ci.mat returns a 2 by 3 matrix with rows c(1,0,0) and
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 ci.lin and
ci.cum.
The 1.96 is replaced by the appropriate quantile from the normal or
t-distribution when arguments alpha and/or df are given.
ci.pred returns a 3-column matrix with estimates and upper and
lower confidence intervals as columns. This is just a convenience
wrapper for predict.glm(obj,se.fit=TRUE) which returns a rather
unhandy structure. The prediction with c.i. is made in the 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.
ci.ratio returns the rate-ratio of two independent set of
rates given with confidence intervals or s.e.s. If se1 and
se2 are given and log.tr=FALSE it is assumed that
r1 and r2 are rates and se1 and se2 are
standard errors of the log-rates.
Author(s)
Bendix Carstensen,
http://bendixcarstensen.com & Michael Hills
See Also
See ci.eta for a simple version only needing
coefficients and variance-covariance matrix. See also ci.cum
for a function computing cumulative sums of (functions of) parameter
estimates, and ci.surv for a function computing
confidence intervals for survival functions based on smoothed
rates. The example code for matshade has an application
of predicting a rate-ratio using a list of two prediction frames in the
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
## Not run:
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 ) )
## End(Not run)
# 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
# ---------------------------------------------------------
Epi documentation built on Oct. 1, 2024, 5:07 p.m.
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| ci.lin | R Documentation |
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
obj |
A model object (in general of class |
ctr.mat |
Matrix, data frame or list (of two or four data frames). If 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 |
xvars |
Character vector. If quantitative variables in the model
are omitted from data frames supplied in a list to |
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 |
subint |
Character. |
diffs |
If TRUE, all differences between parameters
in the subset are computed, and the |
fnam |
Should the common part of the parameter names be included
with the annotation of contrasts? Ignored if |
vcov |
Should the covariance matrix of the set of parameters be
returned? If this is set, |
alpha |
Significance level for the confidence intervals. |
df |
Integer. Number of degrees of freedom in the t-distribution used to compute the quantiles used to construct the confidence intervals. |
Exp |
For |
sample |
Logical or numerical. If |
pval |
Logical. Should a column of P-values be included with the
estimates and confidence intervals output by |
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. |
... |
Parameters passed on to |
newdata |
Data frame of covariates where prediction is made. |
r1, r2 |
Estimates of rates in two independent groups, with confidence limits. Can be either 3-column matrices or data frames with estimates and confidence intervals or 2 two column structures with confidence limits. Only the confidence limits |
se1, se2 |
Standard errors of log-rates in the two groups. If
given, it is assumed that |
log.tr |
Logical, if true, it is assumed that |
Value
ci.lin returns a matrix with number of rows and row names as
ctr.mat. The columns are Estimate, Std.Err, z, P, 2.5% and
97.5% (or according to the value of alpha). If
vcov=TRUE a list of length 2 with components coef (a
vector), the desired functional of the parameters and vcov (a
square matrix), the variance covariance matrix of this, is returned
but not printed. If Exp==TRUE the confidence intervals for the
parameters are replaced with three columns: exp(estimate,c.i.).
ci.exp returns only the exponentiated parameter estimates with
confidence intervals. It is merely a wrapper for ci.lin,
fishing out the last 3 columns from ci.lin(...,Exp=TRUE). If
you just want the estimates and confidence limits, but not
exponentiated, use ci.exp(...,Exp=FALSE).
If ctr.mat is a data frame, the model matrix corresponding to
this is constructed and supplied. This is only supported for objects
of class lm, glm, gam and coxph.
So the default behaviour will be to produce the same as
ci.pred, apparently superfluous. The purpose of this is to
allow the use of the arguments vcov that produces the
variance-covariance matrix of the predictions, and 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 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
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 Ns(x,knots=kk) then the 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 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 (pr1-pr2) - (pr3-pr4) with obvious notation. Useful to
derive esoteric interaction effects.
Finally, only arguments Exp, vcov, alpha and
sample from ci.lin are honored when 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 ci.lin (really
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 xvars argument. Factors omitted need not be
listed in xvars, although no harm is done doing so.
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 H0. The selection of the subset of
parameters is the same as for ci.lin. Using the ctr.mat
argument makes it possible to do a Wald test for equality of
parameters. Wald returns a named numerical vector of length 3,
with names Chisq, d.f. and P.
ci.mat returns a 2 by 3 matrix with rows c(1,0,0) and
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 ci.lin and
ci.cum.
The 1.96 is replaced by the appropriate quantile from the normal or
t-distribution when arguments alpha and/or df are given.
ci.pred returns a 3-column matrix with estimates and upper and
lower confidence intervals as columns. This is just a convenience
wrapper for predict.glm(obj,se.fit=TRUE) which returns a rather
unhandy structure. The prediction with c.i. is made in the 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.
ci.ratio returns the rate-ratio of two independent set of
rates given with confidence intervals or s.e.s. If se1 and
se2 are given and log.tr=FALSE it is assumed that
r1 and r2 are rates and se1 and se2 are
standard errors of the log-rates.
Author(s)
Bendix Carstensen, http://bendixcarstensen.com & Michael Hills
See Also
See ci.eta for a simple version only needing
coefficients and variance-covariance matrix. See also ci.cum
for a function computing cumulative sums of (functions of) parameter
estimates, and ci.surv for a function computing
confidence intervals for survival functions based on smoothed
rates. The example code for matshade has an application
of predicting a rate-ratio using a list of two prediction frames in the
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
## Not run:
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 ) )
## End(Not run)
# 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
# ---------------------------------------------------------
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