apollo_nl {apollo}

Calculates Nested Logit probabilities

Description

Calculates the probabilities of a Nested Logit model and can also perform other operations based on the value of the functionality argument.

Usage

apollo_nl(nl_settings, functionality)

Arguments

nl_settings

List of inputs of the NL model. It should contain the following.

• alternatives: Named numeric vector. Names of alternatives and their corresponding value in choiceVar.

• avail: Named list of numeric vectors or scalars. Availabilities of alternatives, one element per alternative. Names of elements must match those in alternatives. Values can be 0 or 1. These can be scalars or vectors (of length equal to rows in the database). A user can also specify avail=1 to indicate universal availability, or omit the setting completely.

• choiceVar: Numeric vector. Contains choices for all observations. It will usually be a column from the database. Values are defined in alternatives.

• componentName: Character. Name given to model component. If not provided by the user, Apollo will set the name automatically according to the element in P to which the function output is directed.

• nlNests: List of numeric scalars or vectors. Lambda parameters for each nest. Elements must be named with the nest name. The lambda at the root is automatically fixed to 1 if not provided by the user.

• nlStructure: Named list of character vectors. As many elements as nests, it must include the "root". Each element contains the names of the nests or alternatives that belong to it. Element names must match those in nlNests.

• utilities: Named list of deterministic utilities . Utilities of the alternatives. Names of elements must match those in alternatives.

• rows: Boolean vector. Consideration of which rows to include. Length equal to the number of observations (nObs), with entries equal to TRUE for rows to include, and FALSE for rows to exclude. Default is "all", equivalent to rep(TRUE, nObs).

functionality

Character. Setting instructing Apollo what processing to apply to the likelihood function. This is in general controlled by the functions that call apollo_probabilities, though the user can also call apollo_probabilities manually with a given functionality for testing/debugging. Possible values are:

• "components": For further processing/debugging, produces likelihood for each model component (if multiple components are present), at the level of individual draws and observations.

• "conditionals": For conditionals, produces likelihood of the full model, at the level of individual inter-individual draws.

• "estimate": For model estimation, produces likelihood of the full model, at the level of individual decision-makers, after averaging across draws.

• "gradient": For model estimation, produces analytical gradients of the likelihood, where possible.

• "output": Prepares output for post-estimation reporting.

• "prediction": For model prediction, produces probabilities for individual alternatives and individual model components (if multiple components are present) at the level of an observation, after averaging across draws.

• "preprocess": Prepares likelihood functions for use in estimation.

• "raw": For debugging, produces probabilities of all alternatives and individual model components at the level of an observation, at the level of individual draws.

• "report": Prepares output summarising model and choiceset structure.

• "shares_LL": Produces overall model likelihood with constants only.

• "validate": Validates model specification, produces likelihood of the full model, at the level of individual decision-makers, after averaging across draws.

• "zero_LL": Produces overall model likelihood with all parameters at zero.

Details

In this implementation of the Nested Logit model, each nest must have a lambda parameter associated to it. For the model to be consistent with utility maximisation, the estimated value of the Lambda parameter of all nests should be between 0 and 1. Lambda parameters are inversely proportional to the correlation between the error terms of alternatives in a nest. If lambda=1, then there is no relevant correlation between the unobserved utility of alternatives in that nest. The tree must contain an upper nest called "root". The lambda parameter of the root is automatically set to 1 if not specified in nlNests, but can be changed by the user if desired (though not advised).

Value

The returned object depends on the value of argument functionality as follows.

• "components": Same as "estimate"

• "conditionals": Same as "estimate"

• "estimate": vector/matrix/array. Returns the probabilities for the chosen alternative for each observation.

• "gradient": Not implemented.

• "output": Same as "estimate" but also writes summary of input data to internal Apollo log.

• "prediction": List of vectors/matrices/arrays. Returns a list with the probabilities for all alternatives, with an extra element for the probability of the chosen alternative.

• "preprocess": Returns a list with pre-processed inputs, based on nl_settings.

• "raw": Same as "prediction"

• "report": List with tree structure and choice overview.

• "shares_LL": vector/matrix/array. Returns the probability of the chosen alternative when only constants are estimated.

• "validate": Same as "estimate", but it also runs a set of tests to validate the function inputs.

• "zero_LL": vector/matrix/array. Returns the probability of the chosen alternative when all parameters are zero.