Contrasts and estimable linear functions of model coefficients
Compute and test contrasts and other estimable linear functions of model coefficients for for lm, glm, lme, mer, and geese objects
estimable(obj, cm, beta0, conf.int=NULL, show.beta0, ...) ## Default S3 method: estimable(obj, cm, beta0, conf.int=NULL, show.beta0, joint.test=FALSE, ...) ## S3 method for class 'mlm' estimable(obj, cm, beta0, conf.int=NULL, show.beta0, ...)
obj |
Regression (lm, glm, lme, mer, mlm) object. |
cm |
Vector, List, or Matrix specifying estimable linear functions or contrasts. See below for details. |
beta0 |
Vector of null hypothesis values |
conf.int |
Confidence level. If provided, confidence intervals will be computed. |
joint.test |
Logical value. If TRUE a 'joint' Wald test for the hypothesis L %*% beta=beta0 is performed. Otherwise 'row-wise' tests are performed, i.e. (L %*% beta)[i]=beta0[i] |
show.beta0 |
Logical value. If TRUE a column for beta0 will be included in the output table. Defaults to TRUE when beta0 is specified, FALSE otherwise. |
... |
ignored |
estimable computes an estimate, test statitic, significance
test, and (optional) confidence interval for each linear functions of
the model coefficients specified by cm.
The estimable function(s) may be specified via a vector, list, or
matrix. If cm is a vector, it should contained named elements
each of which gives the coefficient to be applied to the
corresponding parameter. These coefficients will be used to construct
the contrast matrix, with unspecified model parameters assigned zero
coefficients. If cm is a list, it should contain one or more
coefficient vectors, which will be used to construct rows of the
contrast matrix. If cm is a matrix, column names must match (a
subset of) the model parameters, and each row should contain the
corresponding coefficient to be applied. Model parameters which are
not present in the set of column names of cm will be set to zero.
The estimates and their variances are obtained by applying the
contrast matrix (generated from) cm to the model estimates
variance-covariance matrix. Degrees of freedom are obtained from the
appropriate model terms.
The user is responsible for ensuring that the specified linear functions are meaningful.
For computing contrasts among levels of a single factor,
fit.contrast may be more convenient. For computing contrasts
between two specific combinations of model parameters, the
contrast function in Frank Harrell's 'rms' library
(formerly 'Design') may be more convenient.
Returns a matrix with one row per linear function. Columns contain
the beta0 value (optional, see show.beta0 above), estimated
coefficients, standard errors, t values, degrees of freedom, two-sided
p-values, and the lower and upper endpoints of the
1-alpha confidence intervals.
The estimated fixed effect parameters of lme objects may have
different degrees of freedom. If a specified contrast includes
nonzero coefficients for parameters with differing degrees of freedom,
the smallest number of degrees of freedom is used and a warning
message is issued.
BXC (Bendix Carstensen) bxc\@novonordisk.com, Gregory R. Warnes greg@warnes.net, Soren Hojsgaard sorenh@agrsci.dk, and Randall C Johnson rjohnson@ncifcrf.gov
# setup example data
y <- rnorm(100)
x <- cut(rnorm(100, mean=y, sd=0.25),c(-4,-1.5,0,1.5,4))
levels(x) <- c("A","B","C","D")
x2 <- rnorm(100, mean=y, sd=0.5)
# simple contrast and confidence interval
reg <- lm(y ~ x)
estimable(reg, c( 0, 1, 0, -1) ) # full coefficient vector
estimable(reg, c("xB"=1,"xD"=-1) ) # just the nonzero terms
# Fit a spline with a single knot at 0.5 and plot the *pointwise*
# confidence intervals
library(gplots)
pm <- pmax(x2-0.5, 0) # knot at 0.5
reg2 <- lm(y ~ x + x2 + pm )
range <- seq(-2, 2, , 50)
tmp <- estimable(reg2,
cm=cbind(
'(Intercept)'=1,
'xC'=1,
'x2'=range,
'pm'=pmax(range-0.5, 0)
),
conf.int=0.95)
plotCI(x=range, y=tmp[, 1], li=tmp[, 6], ui=tmp[, 7])
# Fit both linear and quasi-Poisson models to iris data, then compute
# joint confidence intervals on contrasts for the Species and
# Sepal.Width by Species interaction terms.
data(iris)
lm1 <- lm (Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris)
glm1 <- glm(Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris,
family=quasipoisson("identity"))
cm <- rbind(
'Setosa vs. Versicolor' = c(0, 0, 1, 0, 1, 0),
'Setosa vs. Virginica' = c(0, 0, 0, 1, 0, 1),
'Versicolor vs. Virginica'= c(0, 0, 1,-1, 1,-1)
)
estimable(lm1, cm)
estimable(glm1, cm)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.