tram (version 1.4-5)

perm_test: Permutation Transformation Tests

Description

P-values for a parameter in a linear transformation model and corresponding confidence intervals obtained from by the permutation principle

Usage

perm_test(object, ...)
# S3 method for tram
perm_test(object, parm = names(coef(object)), 
    statistic = c("Score", "Likelihood", "Wald"),
    alternative = c("two.sided", "less", "greater"), 
    nullvalue = 0, confint = TRUE, level = .95, 
    Taylor = FALSE, block_permutation = TRUE, maxsteps = 25, ...)

Value

An object of class htest or a list thereof. See Coxph

for an example.

Arguments

object

an object of class tram

parm

a vector of names of parameters to be tested. These parameters must be present in object.

statistic

a character string specifying the statistic to be permuted. The default Score is the classical permutation test for the esiduals of a model excluding the parameter parm. Only available for nullvalue = 0, confidence intervals are not available. Permuting the likelihood or the model coefficients under the nullvalue is highly expermimental as are the corresponding confidence intervals.

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".

nullvalue

a number specifying an optional parameter used to form the null hypothesis.

confint

a logical indicating whether a confidence interval should be computed. Score confidence intervals are computed by default. A 1st order Taylor approximation to the Score statistc is used with Taylor = TRUE (in case numerical inversion of the score statistic fails, Wald-type confidence intervals relying from this approximation are returned) . For the remaining likelihood and Wald statistics, confidence intervals are highly experimental (and probably not worth looking at).

level

the confidence level.

block_permutation

a logical indicating wheather stratifying variables shall be interpreted as blocks defining admissible permutations.

Taylor

a logical requesting the use of a 1st order Taylor approximation when inverting the score statistic.

maxsteps

number of function evaluations when inverting the score statistic for computing confidence intervals.

...

additional arguments to independence_test.

Details

Permutation test for one single parameters in the linear predictor of object is computed. This parameters must be present in object. This is somewhat experimental and not recommended for serious practical use (yet!).

Examples

  ## Tritiated Water Diffusion Across Human Chorioamnion
  ## Hollander and Wolfe (1999, p. 110, Tab. 4.1)
  diffusion <- data.frame(
      pd = c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46,
             1.15, 0.88, 0.90, 0.74, 1.21),
      age = factor(rep(c("At term", "12-26 Weeks"), c(10, 5)))
  )

  ### plot the two quantile functions
  boxplot(pd ~ age, data = diffusion)

  ### the Wilcoxon rank sum test, with a confidence interval
  ### for a median shift
  wilcox.test(pd ~ age, data = diffusion, conf.int = TRUE, exact = TRUE)

  ### a corresponding parametric transformation model with a log-odds ratio
  ### difference parameter, ie a difference on the log-odds scale
  md <- Colr(pd ~ age, data = diffusion)

  ### assess model fit by plotting estimated distribution fcts
  agef <- sort(unique(diffusion$age))
  col <- c("black", "darkred")
  plot(as.mlt(md), newdata = data.frame(age = agef),
       type = "distribution", col = col)
  legend("bottomright", col = col, lty = 1, legend = levels(agef), 
         bty = "n", pch = 19)
  ## compare with ECDFs: not too bad (but not good, either)
  npfit <- with(diffusion, tapply(pd, age, ecdf))
  lines(npfit[[1]], col = col[1])
  lines(npfit[[2]], col = col[2])

  ### Wald confidence interval
  confint(md)

  ### Likelihood confidence interval
  confint(profile(md))

  ### Score confidence interval
  confint(score_test(md))
  confint(score_test(md, Taylor = TRUE))	### returns Wald with N(0, 1) quantiles
  confint(md)					### also Wald with N(0, 1) quantiles

  ### exact permutation score test
  (pt <- perm_test(md, confint = TRUE, distribution = "exact"))
  (pt <- perm_test(md, confint = TRUE, distribution = "exact", 
                   Taylor = TRUE))		### uses asymptotic normal
                                                ### permutation quantiles
                                                ### for Wald-like interval

  if (require("coin")) {
     ### Note that perm_test can't compute confidence
     ### intervals for K samples. For computing p-values, one
     ### only needs to fit the null model and the scores
     aq <- airquality[complete.cases(airquality[, c("Ozone", "Month")]),]
     aq$Month <- factor(aq$Month)
     pKW <- kruskal.test(Ozone ~ Month, data = aq)$p.value
     aq$O <- ordered(aq$Ozone)
     ### scores = residuals wrt constant intercept term are
     ### linear function of rank(aq$Ozone) when method = "logistic"
     aq$r <- resid(Polr(O ~ 1, data = aq, method = "logistic")) 
     ### permutation test against proportional odds alternatives
     all.equal(pKW, 
               c(pvalue(independence_test(r ~ Month, data = aq, 
                                          teststat = "quad"))))
     ### Savage scores against proportional hazards alternatives
     aq$r <- resid(Polr(O ~ 1, data = aq, method = "cloglog")) 
     ### van der Waerden normal scores
     aq$r <- resid(Polr(O ~ 1, data = aq, method = "probit")) 
  }

  ### compare with probabilistic indices obtained from asht::wmwTest
  if (require("asht", warn.conflicts = FALSE)) {
      print(wt2 <- wmwTest(pd ~ I(relevel(age, "At term")), 
                      data = diffusion, method = "exact.ce"))
      ### as log-odds ratios
      print(PI(prob = wt2$conf.int))
      print(PI(prob = wt2$estimate))
  }