apollo: apollo_varcov – R documentation

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apollo_varcov

Calculates varcov matrix of an Apollo model

Description

Calculates the Hessian, varcov matrix and s.e. of an Apollo model as defined buy its likelihood function and apollo_inputs list of settings. Performs automatic scaling for increased numeric stability.

Usage

apollo_varcov(apollo_beta, apollo_fixed, varcov_settings)

Arguments

apollo_beta

Named numeric vector. Names and values of parameters at which to calculate the covariance matrix. Values _must not be scaled_, and they must include any fixed parameter.

apollo_fixed

Character vector. Names of fixed parameters.

varcov_settings

List of settings defining the behaviour of this function. It must contain at least one of teh following: apollo_logLike, apollo_grad or apollo_inputs.

hessianRoutine: Character. Name of routine used to calculate the Hessian. Valid values are "analytic", "numDeriv", "maxLik" or "none" to avoid estimating the Hessian and covariance matrix.
scaleBeta: Logical. If TRUE (default), parameters are scaled by their own value before calculating the Hessian to increase numerical stability. However, the output is de-scaled, so they are in the same scale as the apollo_beta argument.
numDeriv_settings: List. Additional arguments to the Richardson method used by numDeriv to calculate the Hessian. See argument method.args in grad for more details.
apollo_logLike: Function to calculate the loglikelihood of the model, as returned by apollo_makeLogLike.
apollo_grad: Function to calculate the gradient of the model, as returned by apollo_makeGrad.
apollo_probabilities: Function. Likelihood function of the model. Must receive three arguments:
- apollo_beta: Named numeric vector.
- apollo_inputs: List of settings.
- functionality: Character.
apollo_inputs: List of inputs to estimate a model, as returned by apollo_validateInputs.

Details

It calculates the Hessian, variance-covariance, and standard errors at apollo_beta values of an estimated model. At least one of the following settings must be provided (ordered by speed): apollo_grad, apollo_logLike, or (apollo_probabilities and apollo_inputs). If more than one is provided, then the priority is: apollo_inputs, apollo_logLike, (apollo_probabilities and apollo_inputs).

Value

List with the following elements

hessian: Numerical matrix. Hessian of the model at parameter estimates (model$estimate).
varcov: Numerical matrix. Variance-covariance matrix.
se: Named numerical vector. Standard errors of parameter estimates.
corrmat: Numerical matrix. Correlation between parameter estimates.
robvarcov: Numerical matrix. Robust variance-covariance matrix.
robse: Named numerical vector. Robust standard errors of parameter estimates.
robcorrmat: Numerical matrix. Robust correlation between parameter estimates.
apollo_beta: Named numerical vector. Parameter estimates (model$estimate, not scaled).
methodUsed: Character. Name of method used to calculate the Hessian.
methodsAttempted: Character vector. Name of methods attempted to calculate the Hessian.
hessianScaling: Named numeric vector. Scales used on the paramaters to calculate the Hessian (non-fixed only).

apollo

Tools for Choice Model Estimation and Application

v0.2.4

GPL-2

Authors

Stephane Hess [aut], David Palma [aut, cre]

Initial release