Named numeric vector. Names and values for parameters. These need to be provided in the following order. With K random parameters, K means for the underlying Normals, followed by the elements of the lower triangle of the Cholesky matrix, by row.

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

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 "estimate" (default), "prediction", "validate", "conditionals", "zero_LL", or "raw".

List grouping most common inputs. Created by function apollo_validateInputs.

List. Options controlling the EM process.

• stoppingCriterion: Numeric. Convergence criterion. The EM process will stop when improvements in the log-likelihood fall below this value. Default is 10^-5.

• EMmaxIterations: Numeric. Maximum number of iterations of the EM algorithm before stopping. Default is 100. Used only if apollo_control$HB is FALSE. Default is 200.

• postEM: Numeric scalar. Determines the number of tasks performed by this function after the EM algorithm has converged. Can take values 0, 1 or 2 only. If value is 0, only the EM algorithm will be performed, and the results will be a model object without a covariance matrix (i.e. estimates only.). If value is 1, after the EM algorithm the covariance matrix of the model will be calculated as well, and the result will be a model object with a covariance matrix. If value is 2, after the EM algorithm, the estimated parameter values will be used as starting value for a maximum likelihood estimation process, which will render a model object with a covariance matrix. Performing maximum likelihood estimation after the EM algorithm is useful, as there may be room for further improvement. Default is 2.

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

• transforms: List. Optional argument, with one entry per parameter, showing the inverse transform to return from beta to the underlying Normal. E.g. if the first parameter is specified as negative logormal inside apollo_randCoeff, then the entry in transforms should be transforms[[1]]=function(x) log(-x)

List. Options controlling the estimation process within each EM iteration. See apollo_estimate for details.