apollo_outOfSample {apollo}

Cross-validation of fit (LL)

Description

Randomly generates estimation and validation samples, estimates the model on the first and calculates the likelihood for the second, then repeats.

Usage

apollo_outOfSample(
  apollo_beta,
  apollo_fixed,
  apollo_probabilities,
  apollo_inputs,
  estimate_settings = list(estimationRoutine = "bgw", maxIterations = 200, writeIter =
    FALSE, hessianRoutine = "none", printLevel = 3L, silent = TRUE),
  outOfSample_settings = list(nRep = 10, validationSize = 0.1, samples = NA, rmse = NULL)
)

Arguments

apollo_beta

Named numeric vector. Names and values for parameters.

apollo_fixed

Character vector. Names (as defined in apollo_beta) of parameters whose value should not change during estimation.

apollo_probabilities

Function. Returns probabilities of the model to be estimated. Must receive three arguments:

• apollo_beta: Named numeric vector. Names and values of model parameters.

• apollo_inputs: List containing options of the model. See apollo_validateInputs.

• functionality: Character. Can be either "components", "conditionals", "estimate" (default), "gradient", "output", "prediction", "preprocess", "raw", "report", "shares_LL", "validate" or "zero_LL".

apollo_inputs

List grouping most common inputs. Created by function apollo_validateInputs.

estimate_settings

List. Options controlling the estimation process. See apollo_estimate.

outOfSample_settings

List. Contains settings for this function. User input is required for all settings except those with a default or marked as optional.

nRep

Numeric scalar. Number of times a different pair of estimation and validation sets are to be extracted from the full database. Default is 30.

samples

Numeric matrix or data.frame. Optional argument. Must have as many rows as observations in the database, and as many columns as number of repetitions wanted. Each column represents a re-sample, and each element must be a 0 if the observation should be assigned to the estimation sample, or 1 if the observation should be assigned to the prediction sample. If this argument is provided, then nRep and validationSize are ignored. Note that this allows sampling at the observation rather than the individual level.

validationSize

Numeric scalar. Size of the validation sample. Can be a percentage of the sample (0-1) or the number of individuals in the validation sample (>1). Default is 0.1.

rmse

Character matrix with two columns. Used to calculate Root Mean Squared Error (RMSE) of prediction. The first column must contain the names of observed outcomes in the database. The second column must contain the names of the predicted outcomes as returned by apollo_prediction. If omitted or NULL, no RMSE is calculated. This only works for models with a single component.

Details

A common way to test for overfitting of a model is to measure its fit on a sample not used during estimation that is, measuring its out-of-sample fit. A simple way to do this is splitting the complete available dataset in two parts: an estimation sample, and a validation sample. The model of interest is estimated using only the estimation sample, and then those estimated parameters are used to measure the fit of the model (e.g. the log-likelihood of the model) on the validation sample. Doing this with only one validation sample, however, may lead to biased results, as a particular validation sample need not be representative of the population. One way to minimise this issue is to randomly draw several pairs of estimation and validation samples from the complete dataset, and apply the procedure to each pair.

The splitting of the database into estimation and validation samples is done at the individual level, not at the observation level. If the sampling wants to be done at the individual level (not recommended on panel data), then the optional outOfSample_settings$samples argument should be provided.

This function writes two different files to the working/output directory:

• modelName_outOfSample_params.csv: Records the estimated parameters, final log-likelihood, and number of observations on each repetition.

• modelName_outOfSample_samples.csv: Records the sample composition of each repetition.

The first two files are updated throughout the run of this function, while the last one is only written once the function finishes.

When run, this function will look for the two files above in the working/output directory. If they are found, the function will attempt to pick up re-sampling from where those files left off. This is useful in cases where the original bootstrapping was interrupted, or when additional re-sampling wants to be performed.

Value

A matrix with the average log-likelihood per observation for both the estimation and validation samples, for each repetition. Two additional files with further details are written to the working/output directory.