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```
# The following tests are for calibration with simple linear regression models.
context("Inverse estimation in the SLR model")
test_that("output matches answers to Graybill and Iyer (1996, chap. 6)", {
# Thermostat example from Graybill and Iyer (1996, p. 431)
thermom <- data.frame(temp = seq(from = 96, to = 110, by = 2),
read = c(95.71, 98.16, 99.52, 102.09, 103.79, 106.18,
108.14, 110.21))
thermom.cal1 <- calibrate(thermom, y0 = 104)
thermom.cal2 <- calibrate(thermom, y0 = 100, level = 0.9)
expect_that(round(thermom.cal1$estimate, 3), equals(103.995))
expect_that(round(thermom.cal1$lower, 1), equals(103.4))
expect_that(round(thermom.cal1$upper, 1), equals(104.6))
expect_that(round(thermom.cal2$estimate, 1), equals(100.1))
expect_that(round(thermom.cal2$lower, 2), equals(99.63))
expect_that(round(thermom.cal2$upper, 2), equals(100.59))
# Reaction chamber example from Graybill and Iyer (1996, p. 433)
chamber <- data.frame(dial = seq(from = 0, to = 100, by = 10),
temp = c(206.36, 225.52, 252.18, 289.33, 318.11, 349.49,
383.03, 410.70, 444.40, 469.14, 501.16))
chamber.reg <- calibrate(chamber, y0 = 400, mean.response = TRUE,
level = 0.99)
# Expectations for regulation
expect_that(round(chamber.reg$estimate, 1), equals(66.5))
expect_that(round(chamber.reg$lower, 2), equals(65.07))
expect_that(round(chamber.reg$upper, 2), equals(68.03))
# Crystal weight example from Graybill and Iyer (1996, p. 434)
crystal.lm <- lm(weight ~ time, data = crystal)
crystal.reg <- calibrate(crystal.lm, y0 = 5, mean.response = TRUE,
level = 0.9)
# Expectations for calibration
expect_equal(round(crystal.reg$estimate, 2), 9.93)
expect_equal(round(crystal.reg$lower, 2), 8.65)
expect_equal(round(crystal.reg$upper, 2), 11.05)
})
test_that("errors are handled appropriately", {
# Simulated data
set.seed(101)
x <- rep(seq(from = 0, to = 10, length = 10), 2)
y <- 3 + 0.01*x + rnorm(length(x), sd = 0.5)
d1 <- data.frame(x, y)
d2 <- list(x = 1:11, y = 1:10 + rnorm(10, sd = 1))
# Expectations
expect_that(calibrate(d1, y0 = 3), gives_warning())
expect_that(calibrate(d1, y0 = 3, mean.response = TRUE), gives_warning())
expect_that(calibrate(d1, y0 = 2), throws_error())
expect_that(calibrate(d1, y0 = 2.5, mean.response = TRUE), throws_error())
expect_that(calibrate(d2, y0 = 2.5), throws_error())
expect_that(calibrate(y ~ x + I(x^2), y0 = 2.5), throws_error())
})
test_that("approximate standard error is correct", {
# Crystal weight example from Graybill and Iyer (1996, p. 434)
crystal.lm <- lm(weight ~ time, data = crystal)
crystal.cal <- calibrate(crystal.lm, y0 = 5, interval = "Wald")
crystal.reg <- calibrate(crystal.lm, y0 = 5, interval = "Wald",
mean.response = TRUE)
# Calculate and compare standard error using invest and car::deltaMethod
# covmat.cal <- diag(3)
# covmat.cal[1:2, 1:2] <- vcov(crystal.lm)
# covmat.cal[3, 3] <- summary(crystal.lm)$sigma^2
# coefs <- unname(coef(crystal.lm))
# params <- c(b0 = coefs[1], b1 = coefs[2], y0 = 5)
se.cal <- 2.211698 #car::deltaMethod(params, g = "(y0-b0)/b1", vcov. = covmat.cal)$SE
se.reg <- 0.6658998 #car::deltaMethod(crystal.lm, g = "(5-b0)/b1",
#parameterNames = c("b0", "b1"))$SE
# Expectations
expect_that(crystal.cal$se, equals(se.cal, tol = 1e-04)) # small diff
expect_that(crystal.reg$se, equals(se.reg, tol = 1e-04))
})
test_that("all methods produce equivalent results", {
# Generate some data
set.seed(101)
x <- rep(1:10, each = 3)
y <- 2 + 3 * x + rnorm(length(x), sd = 1)
d <- data.frame(x = x, y = y)
# Matrix method - inversion interval
cal1 <- calibrate(cbind(x, y), y0 = 15, mean.response = FALSE)
# data.frame method - inversion interval
cal2 <- calibrate(data.frame(x, y), y0 = 15, mean.response = FALSE)
# list method - inversion interval
cal3 <- calibrate(list(x, y), y0 = 15, mean.response = FALSE)
# formula method - inversion interval
cal4 <- calibrate(y ~ x, y0 = 15, mean.response = FALSE)
# formula method w/ data - inversion interval
cal5 <- calibrate(y ~ x, data = d, y0 = 15, mean.response = FALSE)
# lm method - inversion interval
cal6 <- calibrate(lm(y ~ x), y0 = 15, mean.response = FALSE)
# formula method w/ transformations - inversion interval
cal7 <- calibrate(exp(log(y)) ~ sqrt(x^2), y0 = 15, mean.response = FALSE)
# Matrix method - Wald interval
cal8 <- calibrate(cbind(x, y), y0 = 15, mean.response = FALSE,
interval = "Wald")
# Matrix method - Wald interval
cal9 <- calibrate(data.frame(x, y), y0 = 15, mean.response = FALSE,
interval = "Wald")
# data.frame method - Wald interval
cal10 <- calibrate(list(x, y), y0 = 15, mean.response = FALSE,
interval = "Wald")
# formula method - Wald interval
cal11 <- calibrate(y ~ x, y0 = 15, mean.response = FALSE, interval = "Wald")
# formula method w/ data - Wald interval
cal12 <- calibrate(y ~ x, data = d, y0 = 15, mean.response = FALSE,
interval = "Wald")
# lm method - Wald interval
cal13 <- calibrate(lm(y ~ x), y0 = 15, mean.response = FALSE,
interval = "Wald")
# formula method method w/transformations - Wald interval
cal14 <- calibrate(exp(log(y)) ~ sqrt(x^2), y0 = 15, mean.response = FALSE,
interval = "Wald")
# These should all be identical
expect_identical(cal1, cal2)
expect_identical(cal1, cal3)
expect_identical(cal1, cal4)
expect_identical(cal1, cal5)
expect_identical(cal1, cal6)
expect_equal(cal1, cal7) # Why are these two not identical?
# These should all be identical
expect_identical(cal8, cal9)
expect_identical(cal8, cal10)
expect_identical(cal8, cal11)
expect_identical(cal8, cal12)
expect_identical(cal8, cal13)
expect_equal(cal8, cal14) # Why are these two not identical?
})
test_that("errors get handled apprropriately", {
# Nonlinear least squares fit
nls.fit <- nls(weight ~ theta1/(1 + exp(theta2 + theta3 * log(conc))),
start = list(theta1 = 1000, theta2 = -1, theta3 = 1),
data = nasturtium)
# Multiple linear regression
mlr.fit1 <- lm(weight ~ time + I(time ^ 2), data = crystal)
mlr.fit2 <- lm(cbind(weight, weight ^ 2) ~ time, data = crystal)
# Expectations
expect_error(calibrate(nls.fit, y0 = c(309, 296, 419)))
expect_error(calibrate(mlr.fit1, y0 = c(309, 296, 419)))
expect_error(calibrate(mlr.fit1, y0 = c(309, 296, 419)))
})
test_that("multiple inference procedures work", {
# Crystal weight example from Graybill and Iyer (1996, p. 434)
crystal.lm <- lm(weight ~ time, data = crystal)
crystal.cal <- calibrate(crystal.lm, y0 = 5, interval = "Wald")
crystal.cal.multi <- calibrate(crystal.lm, y0 = 5, interval = "Wald",
adjust = "Scheffe", k = 1)
# Expectations
expect_equal(crystal.cal, crystal.cal.multi)
})
```

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