Fits a binomial regression with probit link function for estimating the length at which 50% of individuals are expected to transition from embryo to free-swimming status (b50). The model is implemented in Stan via precompiled models using the instantiate package.
The probit link is chosen based on a threshold-crossing interpretation where latent developmental readiness (influenced by maternal size, condition, temperature, etc.) is assumed normally distributed. This contrasts with the logit link which assumes log-odds, which are less interpretable in this biological context.
Usage
fit_bayesian_birth(
embryo_lts,
free_swimming_lts,
mean_b50 = NULL,
cv_b50 = 0.3,
mean_slope = 0,
sd_slope = 1,
parallel = TRUE,
chains = 4,
iter_warmup = 1000,
iter_sampling = 1000,
refresh = 500,
seed = 1234,
...
)Arguments
- embryo_lts
Numeric vector of embryo lengths (internally coded as status = 0).
- free_swimming_lts
Numeric vector of free-swimming lengths (internally coded as status = 1).
- mean_b50
Numeric. Prior mean for b50. If
NULL(default), computed as the midpoint between min(free_swimming_lts) and max(embryo_lts).- cv_b50
Numeric. Coefficient of variation for b50 prior. Default 0.3.
- mean_slope
Numeric. Prior mean for slope on log scale. Default 0.
- sd_slope
Numeric. Prior SD for slope on log scale. Default 1.
- parallel
Logical. Run chains in parallel? Default
TRUE.- chains
Integer. Number of MCMC chains. Default 4.
- iter_warmup
Integer. Warmup iterations per chain. Default 1000.
- iter_sampling
Integer. Sampling iterations per chain. Default 1000.
- refresh
Integer. Progress update frequency. Set to 0 for no output. Default 500.
- seed
Integer. Random seed for reproducibility. Default 1234.
- ...
Additional arguments passed to
$sample().
Value
A CmdStanMCMC object containing:
- b50
Length at 50% birth probability
- slope
Transition steepness (probit scale)
- b05, b95
Lengths at 5% and 95% birth probability
- transition_width
Width of transition zone (b95 - b05)
- log_lik
Log-likelihood values for LOO-CV
- p_pred
Predicted probabilities
- status_rep
Posterior predictive replications
- mean_p_embryo, mean_p_freeswim
Mean predicted probabilities by group
- prop_correct_rep
Classification accuracy in replications
Details
The linear predictor is parameterized directly in terms of b50: $$\eta_i = \text{slope} \times (\text{length}_i - b_{50})$$
Parameters are estimated using lognormal priors to ensure positivity.
Prior Specification
Priors are constructed using a coefficient of variation approach. The prior mean
for b50 is automatically computed as the midpoint between the maximum embryo
length and minimum free-swimming length (the transition zone). The prior SD
is then mean_b50 * cv_b50.
Initialization
Initial values are set to the data-derived midpoint estimate for b50 and a reasonable default for slope, ensuring chains start near the high-probability region of the posterior.
See also
vignette("fit_bayesian_birth") for usage examples with gulper shark data.
vignette("complete_workflow") for the full three-stage analysis pipeline.
Statistical Methods: Birth Size Estimation for the mathematical derivation.
Statistical Methods: Probit Link for justification of the probit over logit link.
fit_bayesian_maturity, fit_bayesian_growth for
downstream models that use birth estimates as priors.
Examples
if (FALSE) { # \dontrun{
# Fit birth model with data-derived priors
birth_fit <- fit_bayesian_birth(
embryo_lts = sharks[embryo == TRUE, length],
free_swimming_lts = sharks[embryo == FALSE, length]
)
# View summary
birth_fit$summary(c("b50", "slope", "transition_width"))
# Use b50 posterior as L0 prior for growth model
growth_fit <- fit_bayesian_growth(
...,
birth_stanfit = birth_fit
)
} # }