apollo_emdc2 {apollo}

Extended MDC

Description

Calculates the likelihood function of the extended MDC model. Can also predict and validate inputs.

Usage

apollo_emdc2(emdc_settings, functionality = "estimate")

Arguments

emdc_settings

List of settings for the model. It includes the following.

• continuousChoice: Named list of numeric vectors. Amount consumed of each inside good. Outside good must not be included. Can also be called "X".

• avail: Named list of numeric vectors. Availability of each product. Can also be called "A".

• utilityOutside: Numeric vector (or matrix or array). Shadow price of the budget. Must be normalised to 0 for at least one individual. Default is 0 for every observation. Can also be called "V0".

• utilities: Named list of numeric vectors (or matrices or arrays). Base utility of each product. Can also be called "V".

• gamma: Named list of numeric vectors. Satiation parameter of each product.

• sigma: Numeric scalar. Scale parameter.

• delta: Lower triangular numeric matrix, or list of lists. Complementarity/substitution parameter.

• cost: Named list of numeric vectors. Price of each product.

• nRep: Scalar positive integer. Number of repetitions used when predictiong

• nIter: Vector of two positive integers. Number of maximum iterations used during prediction, for the upper and lower iterative levels.

• tolerance: Positive scalar Tolerance of the prediction algorithm.

• rawPrediction: Scalar logical. When functionality is equal to "prediction", it returns the full set of simulations. Defaults is FALSE.

functionality

Character. Either "validate", "zero_LL", "estimate", "conditionals", "raw", "output" or "prediction"

Details

This model extends the traditional multiple discrete-continuous (MDC) framework by (i) dropping the need to define a budget, (ii) making the marginal utility of the outside good deterministic, and (iii) including complementarity and substitution in the model formulation. See the following working paper for more details:

Palma, D. & Hess, S. (Working Paper) Some adaptations of Multiple Discrete-Continuous Extreme Value (MDCEV) models for a computationally tractable treatment of complementarity and substitution effects, and reduced influence of budget assumptions

Avilable at: http://stephanehess.me.uk/publications.html

Value

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

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

• "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.

• "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.

• "conditionals": Same as "estimate"

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

• "raw": Same as "prediction"