apollo_estimate {apollo}

Estimates model

Description

Estimates a model using the likelihood function defined by apollo_probabilities.

Usage

apollo_estimate(
  apollo_beta,
  apollo_fixed,
  apollo_probabilities,
  apollo_inputs,
  estimate_settings = NA
)

Arguments

apollo_beta

Named numeric vector. Names and values for parameters.

apollo_fixed

Character vector. Names (as defined in apollo_beta) of parameters whose value should not change during estimation.

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".

apollo_inputs

List grouping most common inputs. Created by function apollo_validateInputs.

estimate_settings

List. Contains settings for this function. User input is required for all settings except those with a default or marked as optional.

• bgw_settings: List. Additional arguments to the BGW optimisation method. See bgw_mle for more details.

• bootstrapSE: Numeric. Number of bootstrap samples to calculate standard errors. Default is 0, meaning no bootstrap s.e. will be calculated. Number must zero or a positive integer. Only used if apollo_control$estMethod!="HB".

• bootstrapSeed: Numeric scalar (integer). Random number generator seed to generate the bootstrap samples. Only used if bootstrapSE>0. Default is 24.

• constraints: Character vector. Linear constraints on parameters to estimate. For example c('b1>0', 'b1 + 2*b2>1'). Only >, < and = can be used. Inequalities cannot be mixed with equality constraints, e.g. c(b1-b2=0, b2>0) will fail. All parameter names must be on the left side. Fixed parameters cannot go into constraints. Alternatively, constraints can be defined as in maxLik. Constraints can only be used with maximum likelihood estimation and the BFGS routine in particular.

• estimationRoutine: Character. Estimation method. Can take values "bfgs", "bgw", "bhhh", or "nr". Used only if apollo_control$HB is FALSE. Default is "bgw".

• hessianRoutine: Character. Name of routine used to calculate the Hessian of the log-likelihood function after estimation. Valid values are "analytic" (default), "numDeriv" (to use the numeric routine in package numDeric), "maxLik" (to use the numeric routine in packahe maxLik), and "none" to avoid calculating the Hessian and the covariance matrix. Only used if apollo_control$HB=FALSE.

• maxIterations: Numeric. Maximum number of iterations of the estimation routine before stopping. Used only if apollo_control$HB is FALSE. Default is 200.

• maxLik_settings: List. Additional settings for maxLik. See argument control in maxBFGS, maxBHHH and maxNM for more details. Only used for maximum likelihood estimation.

• numDeriv_method: Character. Method used for numerical differentiation when calculating the covariance matrix. 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 method used by numDeriv to calculate the Hessian. See argument method.args in grad for more details.

• printLevel: Higher values render more verbous outputs. Can take values 0, 1, 2 or 3. Ignored if apollo_control$HB is TRUE. Default is 3.

• scaleAfterConvergence: Logical. Used to increase numerical precision of convergence. If TRUE, parameters are scaled to 1 after convergence, and the estimation is repeated from this new starting values. Results are reported scaled back, so it is a transparent process for the user. Default is TRUE.

• scaleHessian: Logical. If TRUE, parameters are scaled to 1 for Hessian estimation. Default is TRUE.

• scaling: Named vector. Names of elements should match those in apollo_beta. Optional scaling for parameters. If provided, for each parameter i, (apollo_beta[i]/scaling[i]) is optimised, but scaling[i]*(apollo_beta[i]/scaling[i]) is used during estimation. For example, if parameter b3=10, while b1 and b2 are close to 1, then setting scaling = c(b3=10) can help estimation, specially the calculation of the Hessian. Reports will still be based on the non-scaled parameters.

• silent: Logical. If TRUE, no information is printed to the console during estimation. Default is FALSE.

• validateGrad: Logical. If TRUE, the analytical gradient (if used) is compared to the numerical one. Default is FALSE.

• writeIter: Logical. Writes value of the parameters in each iteration to a csv file. Works only if estimation_routine=="bfgs"|"bgw". Default is TRUE.

Details

This is the main function of the Apollo package. The estimation process begins by running a number of checks on the apollo_probabilities function provided by the user. If all checks are passed, estimation begins. There is no limit to estimation time other than reaching the maximum number of iterations. If Bayesian estimation is used, estimation will finish once the predefined number of iterations are completed. By default, this functions writes the estimated parameter values in each iteration to a file in the working/output directory. Writing can be turned off by setting estimate_settings$writeIter to FALSE. By default, final results are not written into a file nor printed to the console, so users must make sure to call function apollo_modelOutput and/or apollo_saveOutput afterwards. Users are strongly encouraged to visit http://www.apollochoicemodelling.com/ to download examples on how to use the Apollo package. The webpage also provides a detailed manual for the package, as well as a user-group to get further help.

Value

model object