Mort2Dsmooth_optimize: Optimize a 2D Penalized-Poisson IWLS over smoothing...
In MortalitySmooth: Smoothing and Forecasting Poisson Counts with P-Splines

Description Usage Arguments Details Author(s) References See Also

This is an internal function of package MortalitySmooth which optimizes the smoothing parameter for penalized B-splines within the function Mort2Dsmooth.

Mort2Dsmooth_optimize(x, y, Z, offset, wei,
                      psi2, Bx, By, nbx, nby,
                      RTBx, RTBy, Px, Py,
                      a.init,
                      MON, TOL1, TOL2,
                      RANGEx, RANGEy,
                      MAX.IT, MET)

`x`	vector for the abscissa of data.
`y`	vector for the ordinate of data.
`Z`	matrix of counts response.
`offset`	matrix with an a priori known component (optional).
`wei`	an optional matrix of weights to be used in the fitting process.
`psi2`	overdispersion parameter.
`Bx`	B-splines basis for the x-axis.
`By`	B-splines basis for the y-axis.
`nbx`	number of B-splines for the x-axis.
`nby`	number of B-splines for the y-axis.
`RTBx`	tensors product of B-splines basis for the x-axis.
`RTBy`	tensors product of B-splines basis for the y-axis.
`Px`	penalty factor for the x-axis.
`Py`	penalty factor for the y-axis.
`a.init`	matrix with the initial coefficients.
`MON`	Logical switch indicating if monitoring is required.
`TOL1`	The tolerance level in the IWLS algorithm.
`TOL2`	difference between two adjacent smoothing parameters in the grid search, log-scale.
`RANGEx`	range in which smoothing parameter for x should be searched.
`RANGEy`	range in which smoothing parameter for y should be searched.
`MAX.IT`	the maximum number of iterations
`MET`	the method for controlling the amount of smoothing

The function aims to find the optimal smoothing parameters within the given RANGEx and RANGEy in Mort2Dsmooth with method equal to 1 or 2 (BIC and AIC). It employs the function cleversearch from package svcm in two separate steps. First it searches using a rough grid (4 times TOL2) and the median of RANGEx and RANGEy as starting lambdas. Afterwards it searches in the restricted areas around the sub-optimal smoothing parameters, using a finer grid defined by TOL2.

This procedure allows to find precise smoothing parameters in an efficient way: we do not explore the full ranges of possible lambda values, but we optimize each parameter in turn, moving at most one grid step up or down. Furthermore the two steps routine reduces the risk of finding sub-optimal smoothing parameters.

Carlo G Camarda

Camarda, C. G. (2012). MortalitySmooth: An R Package for Smoothing Poisson Counts with P-Splines. Journal of Statistical Software. 50, 1-24. http://www.jstatsoft.org/v50/i01/.

Mort2Dsmooth_update, Mort2Dsmooth_estimate, Mort2Dsmooth.

MortalitySmooth documentation built on May 2, 2019, 6:07 a.m.