# R/poTest.R In car: Companion to Applied Regression

#### Documented in poTestpoTest.polrprint.poTest

```# added by J. Fox on 2017-10-14

poTest <- function(model, ...){
UseMethod("poTest")
}

poTest.polr <- function(model, ...){
if (model\$method != "logistic") stop("test for proportional odds is only for the logistic model")
X <- model.matrix(model)
y <- model.frame(model)[, 1]
levels <- levels(y)
k <- length(levels)
p <- ncol(X) - 1
y <- as.numeric(y)
models <- vector(k - 1, mode="list")
for (j in 1:(k - 1)){
models[[j]] <- glm(y > j ~ X - 1, family=binomial)
}
vcov <- matrix(0, (k - 1)*p, (k - 1)*p)
for (el in 1:(k - 1)){
for (j in 1:el){
W.j.el <- fitted(models[[el]]) - fitted(models[[j]])*fitted(models[[el]])
W.el.el <- fitted(models[[el]]) - fitted(models[[el]])^2
W.j.j <- fitted(models[[j]]) - fitted(models[[j]])^2
V <- solve(t(X * W.j.j) %*% X) %*% (t(X * W.j.el) %*% X) %*% solve(t(X * W.el.el) %*% X)
subs.j <- (j - 1)*p + 1:p
subs.el <- (el - 1)*p + 1:p
vcov[subs.j, subs.el] <- vcov[subs.el, subs.j] <- V[-1, -1]
}
}
beta <- unlist(lapply(models, function(m) coef(m)[-1]))
D <- matrix(0, (k - 2)*p, (k - 1)*p)
I <- diag(p)
for (j in 1:(k - 2)){
subs.j <- (j - 1)*p + 1:p
subs.el <- j*p + 1:p
D[subs.j, 1:p] <- I
D[subs.j, subs.el] <- -I
}
chisq <- t(D %*% beta) %*% solve(D %*% vcov %*% t(D)) %*% (D %*% beta)
df <- (k - 2)*p
chisq.p <- numeric(p)
zeros <- matrix(0, k - 2, (k - 1)*p)
D.p <- vector(p, mode="list")
for (i in 1:p){
DD <- zeros
j <- 1:(k - 2)
DD[j, i] <- 1
DD[cbind(j, j*p + i)] <- -1
chisq.p[i] <- t(DD %*% beta) %*% solve(DD %*% vcov %*% t(DD)) %*% (DD %*% beta)
D.p[[i]] <- DD
}
b <- coef(model)
coef.names <- names(b)
b <- cbind(b, matrix(beta, ncol = k - 1))
colnames(b) <- c("b[polr]", paste0("b[>", levels[1:(k - 1)], "]"))
result <- list(call=model\$call, coef.names=coef.names, b=b,
vcov=vcov, D=D, chisq=as.vector(chisq), df=df,
D.p=D.p, chisq.p=chisq.p, df.p = k - 2)
class(result) <- "poTest"
result
}

print.poTest <- function(x, digits=3, ...){
cat("\nTests for Proportional Odds\n")
print(x\$call)
cat("\n")
names <- c("Overall", x\$coef.names)
chisq <- c(x\$chisq, x\$chisq.p)
df <- c(x\$df, rep(x\$df.p, length(x\$chisq.p)))
pval <- pchisq(chisq, df, lower.tail=FALSE)
table <- cbind(chisq, df, pval)
colnames(table) <- c("Chisquare", "df", "Pr(>Chisq)")
b <- x\$b
b <- rbind(rep(NA, ncol(b)), b)
table <- cbind(b, table)
rownames(table) <- names
printCoefmat(table, P.values=TRUE, has.Pvalue=TRUE, tst.ind = ncol(b) + 1,
na.print="", digits=digits)
invisible(x)
}
```

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car documentation built on Oct. 20, 2022, 1:05 a.m.