MortalitySmooth (version 2.3.4)

Mort2Dsmooth_optimize: Optimize a 2D Penalized-Poisson IWLS over smoothing parameters

Description

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

Usage

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)

Arguments

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

Details

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.

References

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/.

See Also

Mort2Dsmooth_update, Mort2Dsmooth_estimate, Mort2Dsmooth.