tests/testthat/test_poisson_tests.R

In gmcmacran/MLTesteR: Likelihood Ratio Tests and Confidence Intervals

# The sum of a N iid poisson random variables
# is a poisson random variable with lambda of sum = N*lambda
exact_test <- function(x, lambda, alternative) {
  # sum of x
  lambda <- lambda * length(x)
  x <- sum(x)

  calc_two_sided_p_value <- function(x, lambda) {
    relErr <- 1 + 1e-07
    d <- dpois(x, lambda)
    m <- lambda
    if (x == m) {
      1
    } else if (x < m) {
      nearInf <- ceiling(m * 20)
      i <- seq.int(from = ceiling(m), to = nearInf)
      y <- sum(dpois(i, lambda) <= d * relErr)
      ppois(x, lambda) + ppois(pmax(nearInf - y, 0), lambda, lower.tail = FALSE)
    } else {
      i <- seq.int(from = 0, to = floor(m))
      y <- sum(dpois(i, lambda) <= d * relErr)
      ppois(y - 1, lambda) + ppois(x - 1, lambda, lower.tail = FALSE)
    }
  }


  calc_left_p_value <- function(x, lambda) {
    ppois(q = x, lambda = lambda, lower.tail = TRUE)
  }

  calc_right_p_value <- function(x, lambda) {
    ppois(q = x - 1, lambda = lambda, lower.tail = FALSE)
  }

  if (alternative == "two.sided") {
    p.value <- calc_two_sided_p_value(x, lambda)
  }
  if (alternative == "greater") {
    p.value <- calc_right_p_value(x, lambda)
  }
  if (alternative == "less") {
    p.value <- calc_left_p_value(x, lambda)
  }
  return(list(p.value = p.value))
}



###############################################
# Null True
###############################################
for (alt in c("two.sided", "greater", "less")) {
  set.seed(2)
  x <- rpois(200, 1)
  test <- poisson_lambda_one_sample(x, 1, alt)

  test_that("Check structure.", {
    expect_true(all(class(test) == c("one_sample_case_one", "lrtest")))
    expect_true(length(test) == 5)
    expect_true(all(names(test) == c("statistic", "p.value", "conf.int", "conf.level", "alternative")))
  })

  test_02 <- exact_test(x = x, lambda = 1, alternative = alt)
  test_that("Check contents", {
    expect_true(test$p.value > .05)
    expect_true(abs(test$p.value - test_02$p.value) < .03)
  })

  if (alt == "two.sided") {
    test_that("check contents", {
      expect_true(test$statistic >= 0)
    })
  }

  # .0499 instead of .05 b/c of floating point error associated with convergence.
  CI1 <- test$conf.int[1] + .Machine$double.eps # Avoid boundary
  CI2 <- test$conf.int[2] - .Machine$double.eps
  test_that("Check CI", {
    expect_true(ifelse(is.finite(CI1), poisson_lambda_one_sample(x, CI1, alt)$p.value, .05) >= .0499)
    expect_true(ifelse(is.finite(CI2), poisson_lambda_one_sample(x, CI2, alt)$p.value, .05) >= .0499)
  })
  rm(CI1, CI2)
}

###############################################
# Null False
###############################################
for (alt in c("two.sided", "greater")) {
  set.seed(1)
  x <- rpois(2000, 3)
  test <- poisson_lambda_one_sample(x, 1, alt)

  test_that("Check structure.", {
    expect_true(all(class(test) == c("one_sample_case_one", "lrtest")))
    expect_true(length(test) == 5)
    expect_true(all(names(test) == c("statistic", "p.value", "conf.int", "conf.level", "alternative")))
  })

  test_02 <- exact_test(x = x, lambda = 1, alternative = alt)
  test_that("Check contents", {
    expect_true(test$p.value <= .05)
    expect_true(abs(test$p.value - test_02$p.value) < .01)
  })

  if (alt == "two.sided") {
    test_that("check contents", {
      expect_true(test$statistic >= 0)
    })
  }

  CI1 <- test$conf.int[1] + .Machine$double.eps # Avoid boundary
  CI2 <- test$conf.int[2] - .Machine$double.eps
  pval <- pmin(
    ifelse(is.finite(CI1), poisson_lambda_one_sample(x, CI1, alt)$p.value, .05),
    ifelse(is.finite(CI2), poisson_lambda_one_sample(x, CI2, alt)$p.value, .05)
  )
  test_that("Check CI", {
    expect_true(pval <= .0500001)
  })
  rm(CI1, CI2, pval)
}

for (alt in c("two.sided", "less")) {
  set.seed(1)
  x <- rpois(200, 1)
  test <- poisson_lambda_one_sample(x, 3, alt)

  test_that("Check structure.", {
    expect_true(all(class(test) == c("one_sample_case_one", "lrtest")))
    expect_true(length(test) == 5)
    expect_true(all(names(test) == c("statistic", "p.value", "conf.int", "conf.level", "alternative")))
  })

  test_02 <- exact_test(x = x, lambda = 3, alternative = alt)
  test_that("Check contents", {
    expect_true(test$p.value <= .05)
    expect_true(abs(test$p.value - test_02$p.value) < .01)
  })

  if (alt == "two.sided") {
    test_that("check contents", {
      expect_true(test$statistic >= 0)
    })
  }

  CI1 <- test$conf.int[1] + .Machine$double.eps # Avoid boundary
  CI2 <- test$conf.int[2] - .Machine$double.eps
  pval <- pmin(
    ifelse(is.finite(CI1), poisson_lambda_one_sample(x, CI1, alt)$p.value, .05),
    ifelse(is.finite(CI2), poisson_lambda_one_sample(x, CI2, alt)$p.value, .05)
  )
  test_that("Check CI", {
    expect_true(pval <= .0500001)
  })
  rm(CI1, CI2, pval)
}

###############################################
# Input checking
###############################################
test_that("x input checking works", {
  expect_error(poisson_lambda_one_sample(c()), "Argument x should have at least 15 data points.")
  expect_error(poisson_lambda_one_sample(rep("foo", 15)), "Argument x should be numeric.")
})

set.seed(1)
x <- rpois(50, lambda = 1)
test_that("lambda input checking works", {
  expect_error(poisson_lambda_one_sample(x, c(1, 2)), "The tested parameter should have length one.")
  expect_error(poisson_lambda_one_sample(x, "foo"), "The tested parameter should be numeric.")
  expect_error(poisson_lambda_one_sample(x, 0), "The tested parameter should be above 0.")
})

test_that("alternative input checking works", {
  expect_error(poisson_lambda_one_sample(x, 1, c("two.sided", "less")), "Argument alternative should have length one.")
  expect_error(poisson_lambda_one_sample(x, 1, 1), "Argument alternative should be a character.")
  expect_error(poisson_lambda_one_sample(x, 1, "lesss"), "Argument alternative should be 'two.sided', 'less', or 'greater.")
})

test_that("conf.level input checking works", {
  expect_error(poisson_lambda_one_sample(x, 1, "less", c(.50, .75)), "conf.level should have length one.")
  expect_error(poisson_lambda_one_sample(x, 1, "less", "foo"), "conf.level should be numeric.")
  expect_error(poisson_lambda_one_sample(x, 1, "less", 0), "conf.level should between zero and one.")
  expect_error(poisson_lambda_one_sample(x, 1, "less", 1), "conf.level should between zero and one.")
})

###############################################
# Null True
###############################################
set.seed(1)
x <- rpois(150, 1)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
test <- poisson_lambda_one_way(x, fctr, .95)

test_that("Check structure.", {
  expect_true(all(class(test) == c("one_way_case_one", "lrtest")))
  expect_true(length(test) == 6)
  expect_true(all(names(test) == c("statistic", "p.value", "conf.ints", "overall.conf", "individ.conf", "alternative")))
})

dat <- data.frame(fctr = fctr, x = x)
model_00 <- glm(x ~ 1, data = dat, family = poisson(link = "identity"))
model_01 <- glm(x ~ fctr, data = dat, family = poisson(link = "identity"))

test_02 <- lmtest::lrtest(model_00, model_01)
test_that("Check contents", {
  expect_true(test$p.value > .05)
  expect_true(test$statistic >= 0)
  expect_equal(test$p.value, test_02[["Pr(>Chisq)"]][2])
})

# make sure CIs match
CI1 <- unname(test$conf.ints[[1]])
CI2 <- poisson_lambda_one_sample(x[which(fctr == 1)], 2, test$alternative, test$individ.conf)$conf.int
test_that("Check CI", {
  expect_equal(CI1, CI2)
})
rm(CI1, CI2, dat, model_00, model_01)

###############################################
# Null False
###############################################

set.seed(1)
x <- c(rpois(50, 1), rpois(50, 1.50), rpois(50, 2))
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
test <- poisson_lambda_one_way(x, fctr, .95)

test_that("Check structure.", {
  expect_true(all(class(test) == c("one_way_case_one", "lrtest")))
  expect_true(length(test) == 6)
  expect_true(all(names(test) == c("statistic", "p.value", "conf.ints", "overall.conf", "individ.conf", "alternative")))
})

dat <- data.frame(fctr = fctr, x = x)
model_00 <- glm(x ~ 1, data = dat, family = poisson(link = "identity"))
model_01 <- glm(x ~ fctr, data = dat, family = poisson(link = "identity"))

test_02 <- lmtest::lrtest(model_00, model_01)
test_that("Check contents", {
  expect_true(test$p.value <= .05)
  expect_true(test$statistic >= 0)
  expect_equal(test$p.value, test_02[["Pr(>Chisq)"]][2])
})

# make sure CIs match
CI1 <- unname(test$conf.ints[[1]])
CI2 <- poisson_lambda_one_sample(x[which(fctr == 1)], 2, test$alternative, test$individ.conf)$conf.int
test_that("Check CI", {
  expect_equal(CI1, CI2)
})
rm(CI1, CI2, dat, model_00, model_01)

###############################################
# Input checking
###############################################
test_that("x input checking works", {
  expect_error(poisson_lambda_one_way(c()), "Argument x should have at least 30 data points.")
  expect_error(poisson_lambda_one_way(rep("foo", 30)), "Argument x should be numeric.")
})

set.seed(1)
x <- rpois(100, 1)
fctr1 <- factor(rep(1, 100), levels = c("1", "2", "3"))
fctr2 <- factor(c(rep(1, 60), rep(2, 40)), levels = c("1", "2", "3"))
fctr3 <- factor(c(rep(1, 60), rep(2, 39), 3), levels = c("1", "2", "3"))
test_that("fctr input checking works", {
  expect_error(poisson_lambda_one_way(x, "foo"), "Argument fctr should have same length as x.")
  expect_error(poisson_lambda_one_way(x, rep("foo", 100)), "Argument fctr should be a factor.")
  expect_error(poisson_lambda_one_way(x, factor(rep("foo", 100))), "Argument fctr should have at least two unique values.")
  expect_error(poisson_lambda_one_way(x, fctr1), "Argument fctr should have at least two unique values.")
  expect_error(poisson_lambda_one_way(x, fctr2), "Each level in fctr needs to be present.")
  expect_error(poisson_lambda_one_way(x, fctr3), "Each groups needs to contain at least 15 data points for CIs to be accurate.")
})
rm(fctr1, fctr2, fctr3)

fctr <- c(rep(1, 50), rep(2, 50))
fctr <- factor(fctr, levels = c("1", "2"))
test_that("conf.level input checking works", {
  expect_error(poisson_lambda_one_way(x, fctr, c(.50, .75)), "conf.level should have length one.")
  expect_error(poisson_lambda_one_way(x, fctr, "foo"), "conf.level should be numeric.")
  expect_error(poisson_lambda_one_way(x, fctr, 0), "conf.level should between zero and one.")
  expect_error(poisson_lambda_one_way(x, fctr, 1), "conf.level should between zero and one.")
})