confint_adjust {api2lm}

Adjust confidence intervals for multiple comparisons

Description

A function to produce adjusted confidence intervals with a family-wise confidence level of at least level for lm objects (not applicable if no adjustment is used). Internally, the function is a slight revision of the code used in the confint.lm function.

Usage

confint_adjust(object, parm, level = 0.95, method = "none")

Arguments

object

a fitted model object.

parm

a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

the confidence level required.

method

A character string indicating the type of adjustment to make. The default choice is "none". The other option is "bonferroni".

Details

Let a = 1 - level. Let p be the number of estimated coefficients in the fitted model. All intervals are computed using the formula estimate +/- m * ese, where m is a multiplier and ese is the estimated standard error of the estimate.

method = "none" (no correction) produces the standard t-based confidence intervals with multiplier qt(1 - a/2, df = object$df.residual).

method = "bonferroni" produces Bonferroni-adjusted intervals that use the multiplier m = qt(1 - a/(2 * k), df = object$df.residual), where k is the number of intervals being produced.

method = "wh" produces Working-Hotelling-adjusted intervals that are valid for all linear combinations of the regression coefficients, which uses the multiplier m = sqrt(p * qf(level, df1 = p, df2 = object$df.residual)).

Value

A confint_adjust object, which is simply a a data.frame with columns term, lwr (the lower confidence limit), and upr (the upper confidence limit).

References

Bonferroni, C. (1936). Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commericiali di Firenze, 8, 3-62.

Working, H., & Hotelling, H. (1929). Applications of the theory of error to the interpretation of trends. Journal of the American Statistical Association, 24(165A), 73-85. doi:10.1080/01621459.1929.10506274

Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied Linear Statistical Models, 5th edition. New York: McGraw-Hill/Irwin. (p. 230)

See Also

confint.lm

Examples

## an extension of the documentation for confint.lm
fit <- lm(100/mpg ~ disp + hp + wt + am, data = mtcars)
# standard intervals
confint_adjust(fit)
# bonferroni-adjusted intervals
(cib <- confint_adjust(fit, method = "b"))
# plot results
plot(cib)
plot(cib, parm = c("hp", "disp"))
if (require(ggplot2)) {
  autoplot(cib)
  autoplot(cib, parm = c("hp", "disp"))
}
#' working-hotelling-adjusted intervals
(ciwh <- confint_adjust(fit, method = "wh"))