Epi (version 2.26)

ci.lin: Compute linear functions of parameters with standard errors and confidence limits

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,
      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, gls, nls, gnlm, MIresult, mipo, polr, or rq).

ctr.mat

Contrast matrix to be multiplied to the parameter vector, i.e. the desired linear function of the parameters. Can also be a list of two data frames (see below), in which case all other arguments than Exp are ignored - see details.

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. 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 sting 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 of 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 intervals.

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 list of two data frames, the difference of the predictions (on the linear predictor scale) from using the first versus the last as newdata arguments to predict is computed. Columns that are identical in the two data frames can be omitted (see example). 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.

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.

See Also

See also ci.cum for a function computing cumulative sums of (functions of) parameter estimates.

Examples

# NOT RUN {
# 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]) )

# 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
ci.ratio( cbind(10,8,12.5), cbind(5,4,6.25) )
ci.ratio( cbind(8,12.5), cbind(4,6.25) )
# }