gmodels (version 2.18.1)

estimable: 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,,  show.beta0, ...)
# S3 method for default
estimable (obj, cm, beta0,, show.beta0, joint.test=FALSE, ...)

# S3 method for mlm
estimable(obj, cm, beta0,,  show.beta0, ...)



Regression (lm, glm, lme, mer, mlm) object.


Vector, List, or Matrix specifying estimable linear functions or contrasts. See below for details.


Vector of null hypothesis values

Confidence level. If provided, confidence intervals will be computed.


Logical value. If TRUE a 'joint' Wald test for the hypothesis \(L \beta=\beta_0\) is performed. Otherwise 'row-wise' tests are performed, i.e. \((L \beta)_i=\beta_{0i}\)


Logical value. If TRUE a column for beta0 will be included in the output table. Defaults to TRUE when beta0 is specified, FALSE otherwise.




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.


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.

See Also

fit.contrast, lm, lme, contrasts, contrast


Run this code
# 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
pm <- pmax(x2-0.5, 0) # knot at 0.5
reg2 <- lm(y ~ x + x2 + pm )

range <- seq(-2, 2, , 50)
tmp <- estimable(reg2,
                          'pm'=pmax(range-0.5, 0)
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.
lm1  <- lm (Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris)
glm1 <- glm(Sepal.Length ~ Sepal.Width + Species + Sepal.Width:Species, data=iris,

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)
# }

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