binomial_tls() and beta_binomial_tls() describe the count response
distribution for fit_tls(), and beta_tls() the continuous-proportion
response in (0, 1) (e.g. PSII operating efficiency or relative chlorophyll
fluorescence). All three model survival as a four-parameter logistic function
of log10 duration; the beta-binomial and beta families add a dispersion
parameter phi.
Value
A tls_family object: a list with family, family_code
(0 binomial, 1 beta-binomial, 2 beta), and links for the natural-scale
parameters.
Details
The phi convention for the beta-binomial family is the sum of the Beta
shape parameters: for fitted survival probability p, counts are
Beta-Binomial with shapes a = p * phi and b = (1 - p) * phi. Larger phi
means less overdispersion (the binomial is recovered as phi grows). This
matches the simulation convention in simulate_tls() and differs from the
precision/size parameterisations used by some other packages. The beta
family uses the same shapes for the continuous proportion, y ~ Beta(p * phi, (1 - p) * phi), so phi carries the identical meaning and a
larger phi again means a tighter response around the fitted curve.
Examples
binomial_tls()
#> $family
#> [1] "binomial"
#>
#> $family_code
#> [1] 0
#>
#> $links
#> low up k CTmax z
#> "logit" "logit" "log" "identity" "log"
#>
#> attr(,"class")
#> [1] "tls_family"
beta_binomial_tls()
#> $family
#> [1] "beta_binomial"
#>
#> $family_code
#> [1] 1
#>
#> $links
#> low up k CTmax z phi
#> "logit" "logit" "log" "identity" "log" "log"
#>
#> attr(,"class")
#> [1] "tls_family"
beta_tls()
#> $family
#> [1] "beta"
#>
#> $family_code
#> [1] 2
#>
#> $links
#> low up k CTmax z phi
#> "logit" "logit" "log" "identity" "log" "log"
#>
#> attr(,"class")
#> [1] "tls_family"