R: Simultaneous confidence intervals for ratios of linear...
sci.ratio
R Documentation
Simultaneous confidence intervals for ratios of linear combinations of means
Description
This function constructs simultaneous confidence intervals for ratios of linear combinations of normal means in a one-way ANOVA model.
Different methods are available for multiplicity adjustment.
Usage
sci.ratio(formula, data, type = "Dunnett", base = 1,
method = "Plug", Num.Contrast = NULL, Den.Contrast = NULL,
alternative = "two.sided", conf.level = 0.95, names=TRUE)
Arguments
formula
A formula specifying a numerical response and a grouping factor as e.g. response ~ treatment
data
A dataframe containing the response and group variable
type
type of contrast, with the following options:
"Dunnett": many-to-one comparisons, with the control group in the denominator
"Tukey": all-pair comparisons
"Sequen": comparison of consecutive groups, where the group with lower order is the denominator
"AVE": comparison of each group with average of all others, where the average is taken as denominator
"GrandMean": comparison of each group with grand mean of all groups, where the grand mean is taken as denominator
"Changepoint": ratio of averages of groups of higher order divided by averages of groups of lower order
"Marcus": Marcus contrasts as ratios
"McDermott": McDermott contrasts as ratios
"Williams": Williams contrasts as ratios
"UmbrellaWilliams": Umbrella-protected Williams contrasts as ratios
Note: type is ignored, if Num.Contrast and Den.Contrast are specified by the user (See below).
base
a single integer specifying the control (i.e. denominator) group for the Dunnett contrasts, ignored otherwise
method
character string specifying the method to be used for confidence interval construction:
"Plug": Plug-in of ratio estimates in the correlation matrix of the multivariate t distribution. This method is the default.
"Bonf": Simple Bonferroni-adjustment of Fieller confidence intervals for the ratios
"MtI": Sidak or Slepian- adjustment for two-sided and one-sided confidence intervals, respectively
"Unadj": Unadjusted Fieller confidence intervals for the ratios (i.e. with comparisonwise confidence level = conf.level)
Num.Contrast
Numerator contrast matrix, where columns correspond to groups and rows correspond to contrasts
Den.Contrast
Denominator contrast matrix, where columns correspond to groups and rows correspond to contrasts
alternative
a character string: "two.sided" for two-sided intervals, "less" for upper confidence limits, "greater" for lower confidence limits
conf.level
simultaneous confidence level in case of method="Plug","Bonf", or "MtI", and comparisonwise confidence level in case of method="Unadj"
names
logical, indicating whether rownames of the contrast matrices shall be retained in the output
Details
Given a one-way ANOVA model, the interest is in simultaneous confidence intervals
for several ratios of linear combinations of the treatment means. It is assumed that the
responses are normally distributed with homogeneous variances. Unlike in multiple testing
for ratios, the joint distribution of the likelihood ratio statistics has a multivariate t-distribution
the correlation matrix of which depends on the unknown ratios. This means that the critical
point needed for CI calculations also depends on the ratios. There are various methods
of dealing with this problem (for example, see Dilba et al., 2006). The methods include (i) the unadjusted
intervals (Fieller confidence intervals without multiplicity adjustments), (ii) Bonferroni (Fieller
intervals with simple Bonferroni adjustments), (iii) MtI (a method based on Sidak and Slepian
inequalities for two- and one-sided confidence intervals, respectively), and (iv) plug-in (plugging
the maximum likelihood estimates of the ratios in the unknown correlation matrix). The latter
method is known to have good simultaneous coverage probabilities. The MtI method consists
of replacing the unknown correlation matrix of the multivariate t by an identity matrix of the
same dimension.
See the examples for the usage of Numerator and Denominator contrasts.
Note that the argument names Num.Contrast and Den.Contrast need to be specified. If numerator and denominator contrasts are plugged in without
their argument names, they will not be recognized.
Value
An object of class "sci.ratio", containing a list with elements:
estimate
point estimates of the ratios
CorrMat.est
estimate of the correlation matrix (for the plug-in approach)
Num.Contrast
matrix of contrasts used for the numerator of ratios
Den.Contrast
matrix of contrasts used for the denominator of ratios
conf.int
confidence interval estimates of the ratios
And some further elements to be passed to print and summary functions.
Author(s)
Gemechis Dilba Djira
References
Dilba, G., Bretz, F., and Guiard, V. (2006): Simultaneous confidence sets and confidence intervals for multiple ratios. Journal of Statistical Planning and Inference 136, 2640-2658.
See Also
glht(multcomp) for simultaneous CI of differences of means,
plot.sci.ratio for a plotting function of the intervals
Examples
# # #
# Antibiotic activity of 8 different strains of a micro organisms.
# (Horn and Vollandt, 1995):
data(Penicillin)
boxplot(diameter~strain, data=Penicillin)
allpairs<-sci.ratio(diameter~strain, data=Penicillin, type="Tukey")
plot(allpairs)
summary(allpairs)
# Comparison to the grand mean of all strains:
CGM<-sci.ratio(diameter~strain, data=Penicillin, type="GrandMean")
plot(CGM)
summary(CGM)
# # #
# A 90-days chronic toxicity assay:
# Which of the doses (groups 2,3,4) do not show a decrease in
# bodyweight more pronounced than 90 percent of the bodyweight
# in the control group?
data(BW)
boxplot(Weight~Dose,data=BW)
BWnoninf <- sci.ratio(Weight~Dose, data=BW, type="Dunnett",
alternative="greater")
plot(BWnoninf, rho0=0.9)