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Grid search for the optimal 1ts model

Source: R/grid_search_1d.R
grid_search_1d.Rd

grid_search_1d() performs a grid search for the minimum AIC or BIC of the one time scale model.

It finds the optimal values of log_10(rho_s) and returns the estimated optimal model.

Usage

grid_search_1d(
  r,
  y,
  Z = NULL,
  lrho,
  Bs,
  Ds,
  Wprior = NULL,
  optim_criterion = c("aic", "bic"),
  control_algorithm = list(maxiter = 20, conv_crit = 1e-05, verbose = FALSE, monitor_ev =
    FALSE),
  par_gridsearch = list(plot_aic = FALSE, plot_bic = FALSE, return_aic = TRUE, return_bic
    = TRUE, mark_optimal = TRUE, main_aic = "AIC grid", main_bic = "BIC grid")
)

Arguments

r

A vector of exposure times of length ns, or an array of dimension ns by n.

y

A vector of event counts of length ns, or an array of dimension ns by n.

Z

(optional) A regression matrix of covariates of dimension n by p.

lrho

A vector of log_10(rho_s) values.

Bs

A matrix of B-splines for the time scale s.

Ds

The difference matrix of the penalty.

Wprior

An optional vector of a-priori weights.

optim_criterion

The criterion to be used for optimization: "aic" (default) or "bic". BIC penalized model complexity more strongly than AIC, so that its usage is recommended when a smoother fit is preferable (see also Camarda, 2012).

control_algorithm

A list with optional values for the parameters of the iterative processes:

  • maxiter The maximum number of iteration for the IWSL algorithm. Default is 20.

  • conv_crit The convergence criteria, expressed as difference between estimates at iteration i and i+1. Default is 1e-5.

  • verbose A Boolean. Default is FALSE. If TRUE monitors the iteration process.

  • monitor_ev A Boolean. Default is FALSE. If TRUE monitors the evaluation of the model over the log_10(rho_s) values.

par_gridsearch

A list of parameters for the grid_search:

  • plot_aic A Boolean. Default is FALSE. If TRUE, plot the AIC values over the grid of log_10(rhos) values.

  • plot_bic A Boolean. Default is FALSE. If TRUE, plot the BIC values over the grid of log_10(rhos) values.

  • return_aic A Boolean. Default is TRUE. Return the AIC values.

  • return_bic A Boolean. Default is TRUE. Return the BIC values.

  • mark_optimal A Boolean. Default is TRUE. If the plot of the AIC or BIC values is returned, marks the optimal log_10(rho_s) in the plot.

  • main_aic The title of the AIC plot. Default is "AIC grid".

  • main_bic The title of the BIC plot. Default is "BIC grid".

Value

An object of class h1tsfit with the following elements:

  • optimal_model A list containing the results of the optimal model.

  • optimal_logrho The optimal value of log10(rho_s).

  • P_optimal The optimal penalty matrix P.

  • AIC (if par_gridsearch$return_aic == TRUE) The vector of AIC values.

  • BIC (if par_gridsearch$return_bic == TRUE) The vector of BIC values.

References

Camarda, C. G. (2012). "MortalitySmooth: An R Package for Smoothing Poisson Counts with P-Splines." Journal of Statistical Software, 50(1), 1–24. https://doi.org/10.18637/jss.v050.i01