Confidence Intervals for Model Parameters

Description

Computes confidence intervals for one or more parameters in a fitted model. Package MASS adds methods for glm and nls fits.

Usage

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## S3 method for class 'glm'
confint(object, parm, level = 0.95, trace = FALSE, ...)

## S3 method for class 'nls'
confint(object, parm, level = 0.95, ...)

Arguments

object

a fitted model object. Methods currently exist for the classes "glm", "nls" and for profile objects from these classes.

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.

trace

logical. Should profiling be traced?

...

additional argument(s) for methods.

Details

confint is a generic function in package stats.

These confint methods call the appropriate profile method, then find the confidence intervals by interpolation in the profile traces. If the profile object is already available it should be used as the main argument rather than the fitted model object itself.

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1 - level)/2 and 1 - (1 - level)/2 in % (by default 2.5% and 97.5%).

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

confint (the generic and "lm" method), profile

Examples

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expn1 <- deriv(y ~ b0 + b1 * 2^(-x/th), c("b0", "b1", "th"),
               function(b0, b1, th, x) {})

wtloss.gr <- nls(Weight ~ expn1(b0, b1, th, Days),
   data = wtloss, start = c(b0=90, b1=95, th=120))

expn2 <- deriv(~b0 + b1*((w0 - b0)/b1)^(x/d0),
         c("b0","b1","d0"), function(b0, b1, d0, x, w0) {})

wtloss.init <- function(obj, w0) {
  p <- coef(obj)
  d0 <-  - log((w0 - p["b0"])/p["b1"])/log(2) * p["th"]
  c(p[c("b0", "b1")], d0 = as.vector(d0))
}

out <- NULL
w0s <- c(110, 100, 90)
for(w0 in w0s) {
    fm <- nls(Weight ~ expn2(b0, b1, d0, Days, w0),
              wtloss, start = wtloss.init(wtloss.gr, w0))
    out <- rbind(out, c(coef(fm)["d0"], confint(fm, "d0")))
  }
dimnames(out) <- list(paste(w0s, "kg:"),  c("d0", "low", "high"))
out

ldose <- rep(0:5, 2)
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- cbind(numdead, numalive = 20 - numdead)
budworm.lg0 <- glm(SF ~ sex + ldose - 1, family = binomial)
confint(budworm.lg0)
confint(budworm.lg0, "ldose")

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