context("Confidence intervals and p-values")

test_that("The confint method 'quadratic' is consistent with the summary", {
  expect_equivalent(
    confint(f_SFO_lin_mkin_ML, method = "quadratic"),
    summary(f_SFO_lin_mkin_ML)$bpar[, c("Lower", "Upper")])

  expect_equivalent(
    confint(f_SFO_lin_mkin_ML, method = "quadratic", backtransform = FALSE),
    summary(f_SFO_lin_mkin_ML)$par[, c("Lower", "Upper")])

  f_notrans <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE, transform_rates = FALSE)
  expect_equivalent(
    confint(f_notrans, method = "quadratic", transformed = FALSE),
    summary(f_notrans)$par[, c("Lower", "Upper")])

  expect_equivalent(
    confint(f_notrans, method = "quadratic", transformed = FALSE),
    summary(f_notrans)$bpar[, c("Lower", "Upper")])

})

test_that("Quadratic confidence intervals for rate constants are comparable to confint.nls", {

  SFO_trans <- function(t, parent_0, log_k_parent_sink) {
    parent_0 * exp(- exp(log_k_parent_sink) * t)
  }
  SFO_notrans <- function(t, parent_0, k_parent_sink) {
    parent_0 * exp(- k_parent_sink * t)
  }
  f_1_nls_trans <- nls(value ~ SFO_trans(time, parent_0, log_k_parent_sink),
    data = FOCUS_2006_A,
    start = list(parent_0 = 100, log_k_parent_sink = log(0.1)))
  f_1_nls_notrans <- nls(value ~ SFO_notrans(time, parent_0, k_parent_sink),
    data = FOCUS_2006_A,
    start = list(parent_0 = 100, k_parent_sink = 0.1))

  f_1_mkin_OLS <- mkinfit("SFO", FOCUS_2006_A, quiet = TRUE)
  f_1_mkin_OLS_notrans <- mkinfit("SFO", FOCUS_2006_A, quiet = TRUE,
    transform_rates = FALSE)

  # Check fitted parameter values
  expect_equivalent(
    (f_1_mkin_OLS$bparms.optim -coef(f_1_nls_notrans))/f_1_mkin_OLS$bparms.optim,
    rep(0, 2), tolerance = 1e-6)
  expect_equivalent(
    (f_1_mkin_OLS$par[1:2] - coef(f_1_nls_trans))/f_1_mkin_OLS$par[1:2],
    rep(0, 2), tolerance = 1e-6)

  # Check the standard error for the transformed parameters
  se_nls <- summary(f_1_nls_trans)$coefficients[, "Std. Error"]
  # This is of similar magnitude as the standard error obtained with the mkin
  se_mkin <- summary(f_1_mkin_OLS)$par[1:2, "Std. Error"]

  se_nls_notrans <- summary(f_1_nls_notrans)$coefficients[, "Std. Error"]
  # This is also of similar magnitude as the standard error obtained with the mkin
  se_mkin_notrans <- summary(f_1_mkin_OLS_notrans)$par[1:2, "Std. Error"]

  # The difference can partly be explained by the ratio between
  # the maximum likelihood estimate of the standard error sqrt(rss/n)
  # and the estimate used in nls sqrt(rss/rdf), i.e. by the factor
  # sqrt(n/rdf).
  # In the case of mkin, the residual degrees of freedom are only taken into
  # account in the subsequent step of generating the confidence intervals for
  # the parameters (including sigma)

  # Strangely, this only works for the rate constant to less than 1%, but
  # not for the initial estimate
  expect_equivalent(se_nls[2] / se_mkin[2], sqrt(8/5), tolerance = 0.01)
  expect_equivalent(se_nls_notrans[2] / se_mkin_notrans[2], sqrt(8/5), tolerance = 0.01)

  # Another case:
  f_2_mkin <- mkinfit("DFOP", FOCUS_2006_C, quiet = TRUE)
  f_2_nls <- nls(value ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = FOCUS_2006_C)
  se_mkin_2 <- summary(f_2_mkin)$par[1:4, "Std. Error"]
  se_nls_2 <- summary(f_2_nls)$coefficients[, "Std. Error"]
  # Here we the ratio of standard errors can be explained by the same
  # principle up to about 3%
  expect_equivalent(
    se_nls_2[c("lrc1", "lrc2")] / se_mkin_2[c("log_k1", "log_k2")],
    rep(sqrt(nrow(FOCUS_2006_C) / (nrow(FOCUS_2006_C) - 4)), 2),
    tolerance = 0.03)
})

#test_that("Likelihood profile based confidence intervals work", {

#   f <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE)
#   f <- fits[["SFO", "FOCUS_C"]]
#   f_notrans <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE, transform_rates = FALSE)
#   pf <- parms(f)
#   f_nll <- function(parent_0, k_parent_sink, sigma) {
#     - f$ll(c(parent_0 = as.numeric(parent_0),
#         k_parent_sink = as.numeric(k_parent_sink),
#         sigma = as.numeric(sigma)))
#   }
#   f_nll(parent_0 = 100, k_parent_sink = 0.3, sigma = 4.7)
#   f_nll(pf[1], pf[2], pf[3])
#   f_mle <- stats4::mle(f_nll, start = as.list(parms(f)), nobs = nrow(FOCUS_2006_C))
#   f_mle <- stats4::mle(f_nll, start = as.list(parms(f)), nobs = 17L)
#   logLik(f_mle)
#   stats4::confint(f_mle, nobs = nrow(FOCUS_2006_C))
# 
#     ci_mkin_1 <- confint(f,
#       method = "quadratic", backtransform = FALSE,
#       transformed = TRUE)
#     ci_maxLik_1 <- maxLik::confint.maxLik(f_maxLik)
# 
#     f_tc_2_maxLik <- maxLik::maxLik(f_tc_2$ll,
#       start = f_tc_2$par)
#     ci_tc_2 <- confint(f_tc_2, method = "quadratic",
#         backtransform = FALSE, transformed = TRUE,
#         distribution = "normal")
#     ci_tc_2_maxLik <- confint(f_tc_2_maxLik)
#     rel_diff_ci_tc_2 <- (ci_tc_2 - ci_tc_2_maxLik)/ci_tc_2_maxLik
#     # The ilr transformed variable appear to misbehave in the numeric differentiation
#     expect_equivalent(
#       rel_diff_ci_tc_2[c(2, 3, 4, 6, 7, 9, 10), ], rep(0, 14),
#       tolerance = 0.05)
# 
#     ci_tc_2[, 1]
#       ci_tc_2_maxLik[, 1]

#})