ci.lin {Epi}

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. 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 frame 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
# ---------------------------------------------------------