vb_growth_mix {lhmixr}

Fit finite mixture von Bertalanffy growth model.

Description

vb_growth_mix fits sex-specific growth models where some of the animals are of unknown sex. Optimisation is via the Expectation-Maximisation algorithm. Equality constraints across sexes can be implemented for any combination of parameters using the binding argument.

Usage

vb_growth_mix(start.list, data, binding, maxiter.em = 1000, reltol = 1e-08,
  plot.fit = FALSE, verbose = TRUE, optim.method = "BFGS",
  estimate.mixprop = TRUE, distribution)

Arguments

start.list

A list with a list called par containing starting values for: "mixprop", "growth.par" (see Examples).

data

A data.frame with columns: "age", "length" and "obs.sex". "obs.sex" must have values "female", "male", "unclassified".

binding

A (4x2) parameter index matrix with rows named (in order): "lnlinf", "lnk", "lnnt0", "lnsigma" and the left column for the female parameter index and right column for male parameter index. Used to impose arbitrary equality constraints across the sexes (see Examples).

maxiter.em

Integer for maximum number of EM iterations (1e3 default).

reltol

Relative tolerance for EM observed data log likelihood convergence (1e-8 default).

plot.fit

Logical, if TRUE fit plotted per iteration. Red and blue circles are used for known females and males, respectively. Unclassified animals are plotted as triangle with the colour indicating the expected probability of being female or male (FALSE default).

verbose

Logical, if TRUE iteration and observed data log-likelihood printed.

optim.method

Character, complete data optimisation method to use in optim.

estimate.mixprop

Logical, if TRUE the mixing proportion is estimated, otherwise fixed at the starting value.

distribution

Character with options: "normal" or "lognormal".

Value

List containing the components:

logLik.vec

Observed data log-likelihood at each iteration.

logLik

Observed data log-likelihood on the last EM iteration.

complete_data

Data frame of the data (re-ordered) with component probabilities (tau).

coefficients

Parameter estimates (on the real line) and associated standard errors on the real line.

vcov

Estimated variance covariance matrix of the parameters estimated on the real line. Can be used to obtain parameter standard errors on the natural scale.

convergence

Binary with a "0" denoting convergence of the EM algorithm.

Source

Minto, C., Hinde, J. and Coelho, R. (2017). Including unsexed individuals in sex-specific growth models. Canadian Journal of Fisheries and Aquatic Sciences. DOI: 10.1139/cjfas-2016-0450.

Examples

set.seed(1010)
sim.dat <- sim_vb_data(nfemale = 50, nmale = 50, mean_ageF = 4, mean_ageM = 4,
                      growth_parF = c(linf = 30, k = 0.5, t0 = -1, sigma = 0.1),
                      growth_parM = c(linf = 25, k = 0.5, t0 = -1, sigma = 0.1),
                      mat_parF = c(A50 = 5, MR = 2), mat_parM = c(A50 = 3, MR = 2),
                      distribution = "lognormal")

## Model fit with contrained Brody's growth coefficient
## Set up the constraint
binding <- matrix(c(1:2, rep(3, 2), 4:7), ncol = 2, byrow = TRUE)
rownames(binding) <- c("lnlinf", "lnk", "lnnt0", "lnsigma")
colnames(binding) <- c("female", "male")
## note: lnnt0 is the natural logarithm of the negative of t0 (t0 < 0)
## starting values 
start.par <- c(c(log(30), log(25)), rep(log(0.3), 1), rep(log(1), 2), rep(log(.1), 2))
start.list <- list(par = list(mixprop = 0.5, growth.par = start.par))
vb.bind.fit <- vb_growth_mix(data = sim.dat, start.list = start.list,
                             binding = binding, distribution = "lognormal",
                             reltol = 1e-6)