## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 4,
  dpi = 96
)

## ----setup--------------------------------------------------------------------
library(freqTLS)

## ----ctmax-z-properties-------------------------------------------------------
set.seed(1)
dat <- simulate_tls(family = "binomial", CTmax = 36, z = 4, seed = 1)
fit <- fit_tls(dat, y = survived, n = total, time = duration, temp = temp,
               family = "binomial", tref = 1)
ct <- get_ctmax(fit)$estimate
zz <- get_z(fit)$estimate

# (1) midpoint at temp = CTmax equals log10(tref) = log10(1) = 0
predict(fit, data.frame(temp = ct, duration = 1), type = "midpoint")

# (2) midpoint slope in temperature is -1/z
mids <- predict(fit, data.frame(temp = c(ct, ct + 1), duration = 1), type = "midpoint")
c(slope = diff(mids), minus_one_over_z = -1 / zz)

## ----derive-lt----------------------------------------------------------------
# LT50 (relative midpoint) at three temperatures, in hours
derive_lt(fit, p = 0.5, temp = c(35, 36, 37))

## ----bridge-check-------------------------------------------------------------
Tbar <- mean(c(35, 37))               # any centring temperature works
mids <- predict(fit, data.frame(temp = c(35, 37), duration = 1), type = "midpoint")
beta1 <- diff(mids) / 2               # slope in T  (= -1/z)
beta0 <- mids[1] - beta1 * (35 - Tbar) # intercept at T = Tbar

z_recovered     <- -1 / beta1
ctmax_recovered <- Tbar + (log10(1) - beta0) / beta1

rbind(
  fitted    = c(CTmax = ct, z = zz),
  recovered = c(CTmax = ctmax_recovered, z = z_recovered)
)