predict_adjust {api2lm}

Adjust prediction intervals for multiple comparisons

Description

A function to produce adjusted confidence/prediction intervals for predicted mean/new responses 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 predict.lm function.

Usage

predict_adjust(
  object,
  newdata,
  se.fit = FALSE,
  scale = NULL,
  df = Inf,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  type = c("response", "terms"),
  method = "none",
  terms = NULL,
  na.action = stats::na.pass,
  pred.var = res.var/weights,
  weights = 1,
  ...
)

Arguments

object

Object of class inheriting from "lm"

newdata

An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

se.fit

A switch indicating if standard errors are required.

scale

Scale parameter for std.err. calculation.

df

Degrees of freedom for scale.

interval

Type of interval calculation. Can be abbreviated.

level

Tolerance/confidence level.

type

Type of prediction (response or model term). Can be abbreviated.

method

A character string indicating the type of adjustment to make. The default choice is "none". The other available options are "bonferroni", "wh" (Working-Hotelling), and "scheffe".

terms

If type = "terms", which terms (default is all terms), a character vector.

na.action

function determining what should be done with missing values in newdata. The default is to predict NA.

pred.var

the variance(s) for future observations to be assumed for prediction intervals. See ‘Details’.

weights

variance weights for prediction. This can be a numeric vector or a one-sided model formula. In the latter case, it is interpreted as an expression evaluated in newdata.

...

further arguments passed to or from other methods.

Details

Let a = 1 - level. All intervals are computed using the formula prediction +/- m * epesd, where m is a multiplier and epesd is the estimated standard deviation of the prediction error of the estimate.

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

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

The Working-Hotelling and Scheffe adjustments are distinct; the Working-Hotelling typically is related to a multiple comparisons adjustment for confidence intervals of the response mean while the Scheffe adjustment is typically related to a multiple comparisons adjustment for prediction intervals for a new response. However, references often uses these names interchangeably, so we use them equivalently in this function.

method = "wh" (Working-Hotelling) or method = "scheffe" and interval = "confidence" produces Working-Hotelling-adjusted intervals that use the multiplier m = sqrt(p * stats::qf(level, df1 = p, df2 = object$df.residual)), where p is the number of estimated coefficients in the model.

method = "wh" (Working-Hotelling) or method = "scheffe" and interval = "prediction" produces Scheffe-adjusted intervals that use the multiplier m = sqrt(k * stats::qf(level, df1 = k, df2 = object$df.residual)), where k is the number of intervals being produced.

Value

predict_adjust produces:

A vector of predictions if interval = "none".

A matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. For type = "terms" this is a matrix with a column per term and may have an attribute "constant".

If se.fit is TRUE, a list with the following components is returned:

• fit: vector or matrix as above

• se.fit: standard error of predicted means

• residual.scale: residual standard deviations

• df: degrees of freedom for residual

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.

See Also

predict.lm

Examples

fit <- lm(100/mpg ~ disp + hp + wt + am, data = mtcars)
newdata <- as.data.frame(rbind(
               apply(mtcars, 2, mean),
               apply(mtcars, 2, median)))
predict_adjust(fit, newdata = newdata,
               interval = "confidence",
               method = "none")
predict_adjust(fit, newdata = newdata,
               interval = "confidence",
               method = "bonferroni")
predict_adjust(fit, newdata = newdata,
               interval = "confidence",
               method = "wh")
predict_adjust(fit, newdata = newdata,
               interval = "prediction",
               method = "scheffe")