Log-Normal Family for Multiplicative Processes — ratiod

Two-process model where both numerator and denominator follow log-normal distributions. Appropriate when the underlying process is multiplicative and residuals are log-normally distributed.

Use cases:

Abundance indices (CPUE with continuous effort)
Economic ratios (costs, prices)
Body condition indices

Usage

ratiod_lognormal(link_num = "log", link_denom = "log", denom_fixed = FALSE)

Arguments

link_num: Link function for the numerator median: "log".
link_denom: Link function for the denominator median: "log".
denom_fixed: If TRUE, the denominator is a known exposure rather than a modelled response: the numerator's median is the exposure times exp(eta), and the ratio is exp(eta).

Value

A ratiod_family object

Details

The log-normal distribution arises when a variable is the product of many independent positive factors. If \(Y = e^X\) where \(X\) is normal, then \(Y\) is log-normal.

For ratios, if both numerator and denominator are log-normal, the ratio is also log-normal (difference of normals on log scale). This can simplify interpretation when working on the log scale.

Examples

# Create family object
fam <- ratiod_lognormal()
print(fam)
#> tulpaRatio family: lognormal_lognormal 
#> Log-normal numerator and denominator (multiplicative processes) 
#> 
#> Numerator:  lognormal(log)
#> Denominator: lognormal (log) 

# Simulate body condition data
set.seed(123)
n <- 60
df <- data.frame(
  weight = rlnorm(n, meanlog = 3, sdlog = 0.3),
  length_cubed = rlnorm(n, meanlog = 2, sdlog = 0.2),
  age = sample(1:5, n, replace = TRUE),
  sex = factor(rep(c("M", "F"), each = n/2)),
  cohort = factor(rep(1:6, each = n/6))
)

# \donttest{
# Fit model
fit <- tratio(
  weight | length_cubed ~ age + sex + (1 | cohort),
  data = df,
  family = ratiod_lognormal(),
  control = list(iter = 400, chains = 1, seed = 1)
)
#> Warning: 1 divergent transition(s) after warmup; raise `adapt_delta` or reparameterise.
summary(fit)
#> ratio model summary
#> ===================
#> 
#> Inference: Exact (Tier 1) via hmc
#> Family: lognormal_lognormal 
#> 
#> Fixed effects (numerator):
#>        parameter   mean    sd   2.5% 97.5%  rhat ess_bulk
#>  num:(Intercept)  3.151 0.122  2.876 3.410 1.035       58
#>          num:age -0.033 0.023 -0.075 0.010 1.011      121
#>         num:sexM -0.047 0.109 -0.235 0.176 1.019       39
#> 
#> Fixed effects (denominator):
#>          parameter   mean    sd   2.5% 97.5%  rhat ess_bulk
#>  denom:(Intercept)  1.992 0.093  1.827 2.152 0.999       43
#>          denom:age -0.003 0.015 -0.029 0.026 1.004       44
#>         denom:sexM  0.045 0.103 -0.119 0.335 1.041       38
#> 
#> Variance components:
#>    parameter  mean    sd  2.5% 97.5%  rhat ess_bulk
#>  sigma_denom 0.181 0.018 0.151 0.227 0.999       97
#>    sigma_num 0.282 0.032 0.226 0.346 0.996       78
#>     sigma_re 0.097 0.076 0.008 0.284 1.050       32
#> 
#> Diagnostics:
#>   Divergences: 1 
#>   Avg. acceptance: 0.82 
#>   Chains: 1 
#>   Iterations: 400 
#>   Warmup: 200 
#>   R-hat > 1.01 for 5 parameter(s), largest 1.050 (sigma_re).
#>   Bulk ESS < 100 for 8 parameter(s), smallest 32 (sigma_re).
#>   Run longer chains or reparameterise before using these estimates.
# }