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Grid search for the optimal 2ts model

Source: R/grid_search_2d.R
grid_search_2d.Rd

grid_search_2d() performs a grid search for the minimum AIC or BIC of the two time scales model.

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

Usage

grid_search_2d(
  lru,
  lrs,
  R,
  Y,
  Bu,
  Bs,
  Z = NULL,
  Iu,
  Is,
  Du,
  Ds,
  Wprior = NULL,
  ridge = 0,
  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, col = grey.colors(n = 10), plot_contour = FALSE, mark_optimal = TRUE,
    main_aic = "AIC grid", main_bic = "BIC grid")
)

Arguments

lru

A vector of log_10(rho_u) values.

lrs

A vector of log_10(rho_s) values.

R

A matrix (or 3d-array) of exposure times of dimension nu by ns (or nu by ns by n).

Y

A matrix (or 3d-array) of event counts of dimension nu by ns (or nu by ns by n).

Bu

A matrix of B-splines for the u time scale of dimension nu by cu.

Bs

A matrix of B-splines for the s time scale of dimension ns by cs.

Z

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

Iu

An identity matrix of dimension nbu by nbu.

Is

An identity matrix of dimension nbs by nbs.

Du

The difference matrix over u.

Ds

The difference matrix over s.

Wprior

An optional matrix of a-priori weights.

ridge

A ridge penalty parameter: default is 0. This is useful when, in some cases the algorithm shows convergence problems. In this case, set to a small number, for example 1e-4.

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(rho_u) and log_10(rho_s) values.

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

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

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

  • col The color palette to be used for the AIC/BIC plot. Default is grDevices::gray.colors(n=10).

  • plot_contour A Boolean. Default is TRUE. Adds white contour lines to the AIC/BIC plot.

  • mark_optimal A Boolean. Default is TRUE. If the plot of the AIC or BIC values is returned, marks the optimal combination of log_10(rho_u) and 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 h2tsfit with the following elements:

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

  • optimal_logrho The optimal couple of log_10(rho_u) and log_10(rho_s) values.

  • 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