gsci.ratio {mratios}R Documentation

Test version! Simultaneous confidence intervals for ratios of linear combinations of parameter estimates

Description

This function calculates simultaneous confidence intervals for ratios of user-defined linear combinations, given a parameter vector and a corresponding variance-covariance matrix. Beside unadjusted intervals, multiplicity adjustments are available using quantiles of a multivariate Normal- or t-distribution. The function provides a more general, but less user-friendly function to calculate ratios of mean parameters from linear (mixed models).

Usage

gsci.ratio(est, vcmat, Num.Contrast, Den.Contrast, degfree = NULL, conf.level = 0.95, alternative = "two.sided", adjusted = TRUE)

Arguments

est A numeric vector of parameter estimates, for example coefficients of a linear model
vcmat The corresponding variance-covariance matrix (Number of rows and columns should be the same as the length of the parameter vector)
Num.Contrast Numerator contrast matrix, where the number of columns must be the same as the length of the parameter vector, and each row represents one contrast
Den.Contrast Denominator contrast matrix, where the number of columns must be the same as the length of the parameter vector, and each row represents one contrast
degfree Degrees of freedom used for calculating quantiles of a (multivariate) t-distribution. If NULL, Normal approximations are used
conf.level Simultaneous confidence level in case of adjusted == TRUE, and comparisonwise confidence level in case of adjusted == FALSE
alternative a character string: "two.sided" for two-sided intervals, "less" for upper confidence limits, "greater" for lower confidence limits
adjusted If TRUE, the simultaneous confidence level is controlled, otherwise the comparisonwise confidence level is used

Details

THIS VERSION IS ONLY FOR TESTING!!!

Given a parameter vector and it's corresponding variance-covariance matrix, simultaneous confidence intervals for several ratios of linear combinations of these parameters are calculated. For simultaneous confidence intervals (adjusted=TRUE) the Plug-in method is used (plugging the maximum likelihood estimates of the ratios in the unknown correlation matrix, to calculate quantiles of a multivariate distribution).

Linear combinations can be defined by providing matrices for the nominator and the denominator; some pre-defined contrasts can be constructed by the function contrMatRatio. (These may be weighted for different sample sizes.)

Value

An object of class "sci.ratio" and "gsci.ratio", containing a list with elements:

estimate point estimates of the ratios
CorrMat.est estimate of the correlation matrix
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)

Daniel Gerhard, adapting code of Gemechis Dilba and Frank Schaarschmidt

References

The code is an adaptation of the methods described for the completely randomized one-way layout by 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.

When used in mixed models, the methods are only asymptically valid.

See Also

glht(multcomp) for simultaneous CI of differences of means, and function sci.ratio.gen(mratios)

Examples


library(mratios)

# 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)

lmfit <- lm(Weight~Dose-1, data=BW)
est <- coefficients(lmfit)
vc <- vcov(lmfit)
CMAT <- contrMatRatio(table(BW$Dose), type="Dunnett")

BWnoninf <- gsci.ratio(est, vc, CMAT$numC, CMAT$denC, alternative="greater", degfree=lmfit$df.residual)
BWnoninf
# the same:
sci.ratio(Weight~Dose, data=BW, type="Dunnett", alternative="greater")

# Plot
plot(BWnoninf, rho0=0.9)



#### Mixed Model Example
library(nlme)
data(Milk)
# maybe there are nicer models available
lmefit <- lme(protein ~ Diet-1, data=Milk, random=~Time|Cow, correlation=corAR1(form=~Time|Cow))
estm <- fixef(lmefit)
vcm <- vcov(lmefit)
# all-pair comparisons
CM <- rbind(c(1,0,0),
            c(1,0,0),
            c(0,1,0))
DM <- rbind(c(0,1,0),
            c(0,0,1),
            c(0,0,1))
rownames(CM) <- c("b/b+l", "b/l", "b+l/l")
gscimix <- gsci.ratio(estm, vcm, CM, DM, degfree=anova(lmefit)[,2])
plot(gscimix)

[Package mratios version 1.3.9 Index]