Likelihood for composition vectors

Returns the log-likelihood for composition data, e.g., length, age, or stock composition, with various statistical distributions supported.

Usage

like_comp(
  obs,
  pred,
  type = c("multinomial", "dirmult1", "dirmult2", "lognormal"),
  N = sum(obs),
  theta,
  stdev
)

Arguments

obs

A vector of observed values. Internally converted to proportions.

pred

A vector of predicted values. Same length as obs. Internally converted to proportions.

type

Character for the desired distribution

N

Numeric, the sample size corresponding to obs for multinomial or Dirichlet multinomial distributions.

theta

Numeric, the linear (type = "dirmult1") or saturating (type = "dirmult2") Dirichlet-multinomial parameter, respectively. See Thorson et al. (2017)

stdev

Numeric or vectorized for obs, the likelihood standard deviation for lognormal distribution.

Value

Numeric representing the log-likelihood.

Details

Observed and predicted vectors are internally converted to proportions.

For type = "lognormal", zero observations are removed from the likelihood calculation.

References

Thorson et al. 2017. Model-based estimates of effective sample size in stock assessment models using the Dirichlet-multinomial distribution. Fish. Res. 192:84-93. doi:10.1016/j.fishres.2016.06.005

Examples

M <- 0.1
age <- seq(1:10)
pred <- exp(-M * age)
obs <- pred * rlnorm(10, sd = 0.05)
like_comp(obs, pred, N = 10, type = "multinomial")
#> [1] -8.330521
like_comp(obs, pred, N = 100, type = "multinomial")
#> [1] -17.57996
like_comp(obs, pred, N = 10, type = "dirmult1", theta = 1)
#> [1] -11.33651
like_comp(obs, pred, N = 10, type = "dirmult1", theta = 20)
#> [1] -8.015671