VGAM (version 1.1-9)

hormone: Hormone Assay Data

Description

A hormone assay data set from Carroll and Ruppert (1988).

Usage

data(hormone)

Format

A data frame with 85 observations on the following 2 variables.

X

a numeric vector, suitable as the x-axis in a scatter plot. The reference method.

Y

a numeric vector, suitable as the y-axis in a scatter plot. The test method.

Details

The data is given in Table 2.4 of Carroll and Ruppert (1988), and was downloaded from http://www.stat.tamu.edu/~carroll prior to 2019. The book describes the data as follows. The data are the results of two assay methods for hormone data; the scale of the data as presented is not particularly meaningful, and the original source of the data refused permission to divulge further information. As in a similar example of Leurgans (1980), the old or reference method is being used to predict the new or test method. The overall goal is to see whether we can reproduce the test-method measurements with the reference-method measurements. Thus calibration might be of interest for the data.

References

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

Leurgans, S. (1980). Evaluating laboratory measurement techniques. Biostatistics Casebook. Eds.: Miller, R. G. Jr., and Efron, B. and Brown, B. W. Jr., and Moses, L. New York, USA: Wiley.

Yee, T. W. (2014). Reduced-rank vector generalized linear models with two linear predictors. Computational Statistics and Data Analysis, 71, 889--902.

See Also

uninormal, rrvglm.

Examples

if (FALSE) {
data(hormone)
summary(hormone)

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

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

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

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


# Reproduce the top 3 equations on p.65 of Carroll and Ruppert (1988).
# They are called Equations (1)--(3) here.

# 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 = uninormal(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, uninormal(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)[, "loglink(sd)"]) ~ X,
      hormone, col = "orange")
lines(fitted(fit2) - 2 * exp(predict(fit2)[, "loglink(sd)"]) ~ X,
      hormone, col = "orange")

# Equation (3)
# Does not fit well because the loglink link for the mean is not good.
fit3 <- rrvglm(Y ~ 1 + X, maxit = 300, data = hormone, trace = TRUE,
               uninormal(lmean = "loglink", 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)[, "loglink(sd)"]) ~ X,
      hormone, col = "orange")
lines(fitted(fit3) - 2 * exp(predict(fit3)[, "loglink(sd)"]) ~ X,
      hormone, col = "orange")
}