Calculates the Hessian, variance-covariance matrix and standard errors of an Apollo model as defined by its likelihood function
and apollo_inputs list of settings. Performs automatic scaling for increased numeric stability.
apollo_varcov(apollo_beta, apollo_fixed, varcov_settings)List with the following elements
apollo_beta: Named numerical vector. Parameter estimates (model$estimate, not scaled).
corrmat: Numerical matrix. Correlation between parameter estimates.
hessian: Numerical matrix. Hessian of the model at parameter estimates (model$estimate).
hessianScaling: Named numeric vector. Scales used on the paramaters to calculate the Hessian (non-fixed only).
methodsAttempted: Character vector. Name of methods attempted to calculate the Hessian.
methodUsed: Character. Name of method used to calculate the Hessian.
robcorrmat: Numerical matrix. Robust correlation between parameter estimates.
robse: Named numerical vector. Robust standard errors of parameter estimates.
robvarcov: Numerical matrix. Robust variance-covariance matrix.
se: Named numerical vector. Standard errors of parameter estimates.
varcov: Numerical matrix. Variance-covariance matrix.
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.
Character vector. Names of fixed parameters.
List of settings defining the behaviour of this function. It must contain at least one of
the following: apollo_logLike, apollo_grad or apollo_inputs together with apollo_probabilities.
apollo_grad: Function to calculate the gradient of the model, as returned by apollo_makeGrad.
apollo_inputs: List grouping most common inputs. Created by function apollo_validateInputs.
apollo_logLike: Function to calculate the log-likelihood of the model, as returned by apollo_makeLogLike.
apollo_probabilities: apollo_probabilities Function. Returns probabilities of the model to be estimated. Must receive three arguments:
apollo_beta: Named numeric vector. Names and values of model parameters.
apollo_inputs: List containing options of the model. See apollo_validateInputs.
functionality: Character. Can be either
"components", "conditionals", "estimate" (default), "gradient", "output", "prediction", "preprocess", "raw", "report", "shares_LL", "validate" or "zero_LL".
BHHH_matrix: Matrix. Optional input, providing the BHHH matrix so it does not get recalculated.
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.
numDeriv_method: Character. Method used for numerical differentiation. Can be "Richardson" or "simple", Only used if analytic gradients are available. See argument method in grad for more details.
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.
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.
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 of computation): apollo_grad,
apollo_logLike, or (apollo_probabilities and apollo_inputs). If more than one is provided,
then the priority is: apollo_grad, apollo_logLike, (apollo_probabilities and apollo_inputs).