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R version 3.2.3 (2015-12-10) -- "Wooden Christmas-Tree"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
>
> library("multcomp")
Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS
Attaching package: 'TH.data'
The following object is masked from 'package:MASS':
geyser
>
> ###<FIXME> compare results of mmod and glht.mlf </FIXME>
>
> ### code by Christian Ritz
> "mmod" <- function(modelList, varName, seType = "san")
+ {
+ require(multcomp, quietly = TRUE)
+ require(sandwich, quietly = TRUE)
+
+ if (length(seType) == 1) {seType <- rep(seType, length(modelList))}
+ if (length(varName) == 1) {varName <- rep(varName, length(modelList))}
+
+ ## Extracting score contributions from the individual model fits
+ makeIIDdecomp <- function(modelObject, varName)
+ {
+ numObsUsed <- ifelse(inherits(modelObject, "coxph"), modelObject$n, nrow(modelObject$model))
+ iidVec0 <- bread(modelObject)[varName, , drop = FALSE] %*% t(estfun(modelObject))
+ moNAac <- modelObject$na.action
+ numObs <- numObsUsed + length(moNAac)
+ iidVec <- rep(0, numObs)
+ if (!is.null(moNAac))
+ {
+ iidVec[-moNAac] <- sqrt(numObs/numObsUsed) * iidVec0
+ }
+ else {
+ iidVec <- iidVec0
+ }
+ list(iidVec = iidVec, numObsUsed = numObsUsed, numObs = numObs)
+ }
+ numModels <- length(modelList)
+ if (identical(length(varName), 1))
+ {
+ varName <- rep(varName, numModels)
+ }
+ iidList <- mapply(makeIIDdecomp, modelList, varName, SIMPLIFY = FALSE)
+ iidresp <- matrix(as.vector(unlist(lapply(iidList, function(listElt) {listElt[[1]]}))), nrow = numModels, byrow = TRUE)
+ pickFct <- function(modelObject, varName, matchStrings)
+ {
+ as.vector(na.omit((coef(summary(modelObject))[varName, ])[matchStrings]))
+ }
+
+ ## Retrieving parameter estimates from the individual fits
+ estVec <- as.vector(unlist(mapply(pickFct, modelList, varName, MoreArgs = list(matchStrings = c("Estimate", "coef")))))
+ # "Estimate" or "coef" used in glm(), lm() and coxph() summary output, respectively
+
+ ## Calculating the estimated variance-covariance matrix of the parameter estimates
+ numObs <- iidList[[1]]$numObs
+ covar <- (iidresp %*% t(iidresp)) / numObs
+ vcMat <- covar / numObs # Defining the finite-sample variance-covariance matrix
+
+ ## Replacing sandwich estimates by model-based standard errors
+ modbas <- seType == "mod"
+ if (any(modbas))
+ {
+ corMat <- cov2cor(vcMat)
+ ## Retrieving standard errors for the specified estimate from the individual fits
+ modSE <- as.vector(unlist(mapply(pickFct, modelList, varName, MoreArgs = list(matchStrings = c("Std. Error", "se(coef)")))))
+
+ sanSE <- sqrt(diag(vcMat))
+ sanSE[modbas] <- modSE[modbas]
+ vcMat <- diag(sanSE) %*% corMat %*% diag(sanSE)
+ }
+
+ ## Naming the parameter vector (easier way to extract the names of the model fits provided as a list in the first argument?)
+ names1 <- sub("list", "", deparse(substitute(modelList)), fixed = TRUE)
+ names2 <- sub("(", "", names1, fixed = TRUE)
+ names3 <- sub(")", "", names2, fixed = TRUE)
+ names4 <- sub(" ", "", names3, fixed = TRUE)
+ names(estVec) <- unlist(strsplit(names4, ","))
+
+ return(parm(coef = estVec, vcov = vcMat, df = 0))
+ }
>
>
>
>
>
> set.seed(29)
> ## Combining linear regression and logistic regression
> y1 <- rnorm(100)
> y2 <- factor(y1 + rnorm(100, sd = .1) > 0)
> x1 <- gl(4, 25)
> x2 <- runif(100, 0, 10)
>
> m1 <- lm(y1 ~ x1 + x2)
> m2 <- glm(y2 ~ x1 + x2, family = binomial())
> ## Note that the same explanatory variables are considered in both models
> ## but the resulting parameter estimates are on 2 different scales (original and log-odds scales)
>
> ## Simultaneous inference for the same parameter in the 2 model fits
> simult.x12 <- mmod(list(m1, m2), c("x12", "x12"))
> summary(glht(simult.x12))
Simultaneous Tests for General Linear Hypotheses
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
m1 == 0 -0.3537 0.2808 -1.260 0.312
m2 == 0 -0.6409 0.5681 -1.128 0.382
(Adjusted p values reported -- single-step method)
>
> ## Simultaneous inference for different parameters in the 2 model fits
> simult.x12.x13 <- mmod(list(m1, m2), c("x12", "x13"))
> summary(glht(simult.x12.x13))
Simultaneous Tests for General Linear Hypotheses
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
m1 == 0 -0.3537 0.2808 -1.260 0.351
m2 == 0 -0.8264 0.5874 -1.407 0.276
(Adjusted p values reported -- single-step method)
>
> ## Simultaneous inference for different and identical parameters in the 2 model fits
> simult.x12x2.x13 <- mmod(list(m1, m1, m2), c("x12", "x13", "x13"))
> summary(glht(simult.x12x2.x13))
Simultaneous Tests for General Linear Hypotheses
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
m1 == 0 -0.3537 0.2808 -1.260 0.407
m1 == 0 -0.4220 0.2801 -1.507 0.274
m2 == 0 -0.8264 0.5874 -1.407 0.323
(Adjusted p values reported -- single-step method)
> confint(glht(simult.x12x2.x13))
Simultaneous Confidence Intervals
Fit: NULL
Quantile = 2.3087
95% family-wise confidence level
Linear Hypotheses:
Estimate lwr upr
m1 == 0 -0.3537 -1.0019 0.2945
m1 == 0 -0.4220 -1.0687 0.2247
m2 == 0 -0.8264 -2.1825 0.5297
>
>
> ## Examples for binomial data
>
> ## Two independent outcomes
> y1.1 <- rbinom(100, 1, 0.5)
> y1.2 <- rbinom(100, 1, 0.5)
> group <- factor(rep(c("A", "B"), 50))
>
> modely1.1 <- glm(y1.1 ~ group, family = binomial)
> modely1.2 <- glm(y1.2 ~ group, family = binomial)
>
> mmObj.y1 <- mmod(list(modely1.1, modely1.2), "groupB")
> simult.y1 <- glht(mmObj.y1)
> summary(simult.y1)
Simultaneous Tests for General Linear Hypotheses
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
modely1.1 == 0 0.8473 0.4186 2.024 0.084 .
modely1.2 == 0 0.2404 0.4008 0.600 0.796
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Adjusted p values reported -- single-step method)
>
> ## Two perfectly correlated outcomes
> y2.1 <- rbinom(100, 1, 0.5)
> y2.2 <- y2.1
> group <- factor(rep(c("A", "B"), 50))
>
> modely2.1 <- glm(y2.1 ~ group, family = binomial)
> modely2.2 <- glm(y2.2 ~ group, family = binomial)
>
> mmObj.y2 <- mmod(list(modely2.1, modely2.2), "groupB")
> simult.y2 <- glht(mmObj.y2)
> summary(simult.y2)
Simultaneous Tests for General Linear Hypotheses
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
modely2.1 == 0 0.2412 0.4015 0.601 0.548
modely2.2 == 0 0.2412 0.4015 0.601 0.548
(Adjusted p values reported -- single-step method)
>
>
> proc.time()
user system elapsed
0.352 0.012 0.359
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