Calculates the likelihood function of the extended MDC model. Can also predict and validate inputs.
apollo_emdc2(emdc_settings, functionality = "estimate")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"
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.
Character. Either "validate", "zero_LL", "estimate", "conditionals", "raw", "output" or "prediction"
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