modelSelect {poolABC}

Perform model selection with Approximate Bayesian Computation

Description

Estimates posterior model probabilities using Approximate Bayesian Computation (ABC).

Usage

modelSelect(target, index, sumstats, tol, method, warning = TRUE)

Arguments

target

is a vector with the target summary statistics. These are usually computed from observed data.

index

is a vector of model indices. This can be a a character vector of model names, repeated as many times as there are simulations for each model. This vector will be coerced to factor and it must have the same length as nrow(sumstats) to indicate which row of the sumstats matrix belongs to which model.

sumstats

is a vector or matrix containing the simulated summary statistics for all the models. Each row or vector entry should be a different simulation and each column of a matrix should be a different statistic. The order must be the same as the order of the models in the index vector.

tol

is a numerical value, indicating the required proportion of points nearest the target values (tolerance).

method

a character string, either "rejection" or "regression", indicating which algorithm should be used for model selection.

warning

logical, if TRUE (default) warnings produced while running this function, mainly related with accepting simulations for just one of the models, will be displayed.

Details

Prior to using this function, simulations must have been performed under, at least, two different models. When method is "rejection", the posterior posterior probability of a given model is approximated by the proportion of accepted simulations of that particular model. Note that this approximation is only valid if all models where, a priori, equally likely and if the number of simulations performed is the same for all models. When the method is set to "regression", a multinomial logistic regression is used to estimate the posterior model probabilities. This multinomial regression is implemented in the multinom function.

Value

a list with the following elements:

method

the method used for model selection.

indices

a vector of model indices in the accepted region. In other words, this vector contains the name of the accepted model for each accepted point.

pred

a vector of model probabilities.

ss

the summary statistics in the accepted region.

weights

vector of regression weights when method is regression.

nmodels

the number of a priori simulations performed for each model.

Examples

# load the matrix with simulated parameter values
data(sumstats)

# select a random simulation to act as target just to test the function
target <- sumstats[10 ,]

# create a "fake" vector of model indices
# this assumes that half the simulations were from one model and the other half from other model
# this is not true but serves as an example of how to use this function
index <- c(rep("model1", nrow(sumstats)/2), rep("model2", nrow(sumstats)/2))

# perform model selection with ABC
modelSelect(target = target, index = index, sumstats = sumstats, tol = 0.01, method = "regression")