likelihood_space {alien}

Calculate log-likelihood space for a given time series and data

Description

This function allows to calculate the log-likelihood values for a given set of parameter values. It can be used for diagnostics of the likelihood space and check - among others - for parameter contribution to log-likelihood. passing FALSE for the calculate argument allows to experiment with different parameter values sets before calculating their log-likelihoods. Please note: This functions may take a lot of time, depending on the number of parameters, and steps!

Usage

likelihood_space(
  y,
  mu = NULL,
  pi = NULL,
  data = NULL,
  growth = TRUE,
  type = "exponential",
  centers,
  ranges,
  steps_from_centers,
  calculate = TRUE
)

Arguments

y

either a vector describing the number of discovered alien and invasive species (IAS) over a given time period, or the name (quoted or unquoted) of the corresponding column in the provided data.

mu

a formula defining the predictors for \mu_t, the annual introduction rate. Formulas should be provided in the syntax ~ x1 + x2 + ... + xn. Use ~ 1 for an intercept only model.

pi

a formula defining the predictors for \Pi_{st}, the annual probability of detection. Formulas should be provided in the syntax ~ x1 + x2 + ... + xn. Use ~ 1 for an intercept only model.

data

a data frame containing the variables in the model(s).

growth

logical. Should the population growth parameter \gamma_2 be included in the model for \Pi_{st}?. Note that values for init, if provided, need to include an initial value for the growth parameter, when growth = TRUE.

type

Define whether the mu function should be on "linear" or "exponential" scale. Defaults to "exponential".

centers

the values used as the center-points for the parameter values. Usually the maximum likelihood estimation from a call to snc. Length should be either 1 or correspond to number of parameters (including the growth parameter).

ranges

the range of the parameter values in term of the center. The values will be withing center - (center * range) and center + (center * range). Length should be either 1 or correspond to number of parameters (including the growth parameter).

steps_from_centers

How many values in the range between center and center + (center * range) should be included in the set. Length should be either 1 or correspond to number of parameters (including the growth parameter).

calculate

Whether to calculate the log-likelihoods (TRUE) or just view the parameter values (FALSE).

Value

A data frame containing the parameter values, and if calculate = TRUE including the log-likelihood values for each parameter combination.

Examples

if (FALSE){ # this takes a while...
example_model <- snc(sfestuary)
estimates <- example_model$coefficients$Estimate

likelihood_space <- likelihood_space(y = sfestuary, centers = estimates,
                                     ranges = 1.5, steps_from_center = 10,
                                     calculate = TRUE)

# with specified formula:
example_buba <- snc(y = aliens, pi = ~ natives, data = medfish)
estimates <- example_buba$coefficients$Estimate

likelihood_space <- likelihood_space(y = aliens, pi = ~ natives,
                                     data = medfish, centers = estimates,
                                     ranges = 1.5, steps_from_center = 10,
                                     calculate = TRUE)
 }