hormone: Hormone Data

Description

A data set described in Carroll and Ruppert (1988) concerning hormone assay.

Usage

data(hormone)

Arguments

Details

The data is described in Carroll and Ruppert (1988).

References

Carroll, R. J. and Ruppert, D. (1988) Transformation and Weighting in Regression. New York, USA: Chapman & Hall.

Yee, T. W. (2012) Two-parameter reduced-rank vector generalized linear models. In preparation.

Examples

Run this code

data(hormone)
summary(hormone)

modelI <-rrvglm(Y ~ 1 + X, data = hormone, trace = TRUE,
                normal1(zero = NULL, lsd = "identity", imethod = 2))

# Alternative way to fit modelI
modelI.other <- vglm(Y ~ 1 + X, data = hormone, trace = TRUE,
                     normal1(zero = NULL, lsd = "identity"))

# Inferior to modelI
modelII <- vglm(Y ~ 1 + X, data = hormone, trace = TRUE,
                family = normal1(zero = NULL))

logLik(modelI)
logLik(modelII) # Less than logLik(modelI)


# Reproduce Equations (1)--(3) on p.65 of Carroll and Ruppert (1988)

# Equation (1)
hormone <- transform(hormone, rX = 1 / X)
clist <- list("(Intercept)" = diag(2), X = diag(2), rX = rbind(0, 1))
fit1 <- vglm(Y ~ 1 + X + rX, family = normal1(zero = NULL),
             constraints = clist, data = hormone, trace = TRUE)
coef(fit1, matrix = TRUE)
summary(fit1) # Actually, the intercepts do not seem significant
plot(Y ~ X, hormone, col = "blue")
lines(fitted(fit1) ~ X, hormone, col = "orange")

# Equation (2)
fit2 <- rrvglm(Y ~ 1 + X, normal1(zero = NULL), hormone, trace = TRUE)
coef(fit2, matrix = TRUE)
plot(Y ~ X, hormone, col = "blue")
lines(fitted(fit2) ~ X, hormone, col = "red")
# Add +- 2 SEs
lines(fitted(fit2) + 2 * exp(predict(fit2)[, "log(sd)"]) ~ X,
      hormone, col = "orange")
lines(fitted(fit2) - 2 * exp(predict(fit2)[, "log(sd)"]) ~ X,
      hormone, col = "orange")

# Equation (3)
# Does not fit well because the loge link for the mean is not good.
fit3 <- rrvglm(Y ~ 1 + X, maxit = 300, data = hormone, trace = TRUE,
               normal1(lmean = "loge", zero = NULL))
coef(fit3, matrix = TRUE)
plot(Y ~ X, hormone, col = "blue") # Does not look okay.
lines(exp(predict(fit3)[, 1]) ~ X, hormone, col = "red")
# Add +- 2 SEs
lines(fitted(fit3) + 2 * exp(predict(fit3)[, "log(sd)"]) ~ X,
      hormone, col = "orange")
lines(fitted(fit3) - 2 * exp(predict(fit3)[, "log(sd)"]) ~ X,
      hormone, col = "orange")