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apollo (version 0.3.4)

apollo_emdc2: 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")

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"

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