zppr: Wrapper for Projection Pursuit Regression with RFA data

In martindurocher/pprRFA: Projection pursuit regression for regional frequency analysis

Description

Wrapping function for the ppr methods in stats packages. Mainly used as initial steps for the ppr2gam method

Usage

# To create a rfa data object
new_rfa_data <- function(annual,attrib)

# To add or change the hydrologial variables to fit
set_response.rfa <- function(self,z)

# To fit a PPR model
zppr(self, w=NULL, criteria = 'wls', nterms = 1, ...)

Arguments

annual	Dataset of the hydrological variable, First row must be a identification number (or string) for a site. Second row must be a year. Third row must be the annual maximum values.
attrib	Dataset of the site characteristics. The first row must be the same identification number as in annual.
z	Dataset of the hydrological variables to predict (response). The first row is the site identification, the second row is the response variable and the third row is its sampling variance.
self	Data object, output from new_rfa_data
w	Weights for the sites. Default is the length of the time series calculated from annual
criteria	Least-squares criteria used to fit the PPR model. Choice are : Ordinary = 'ols', "weigthed = " wls, generalized = 'gls'
nterms	Number of terms in the PPR model
...	Additional parameter for the ppr method. See the documentation of respective function for more delails

Details

A projection pursuit regression (PPR) is a model of the form

$ mu + sum_p left[ g_p (alpha_p X) right] $

where $alpha_p$ are direction vectors, X is a design matrix of covariates and $g_p$ are smooth functions.

An iterative procedure is used to estimate jointly $mu$, $alpha_p$ and smooth functions $g_p$ by least-squares. See Friedman & Stuetzle (1981)

If generalized least-squares are used (criteria == gls), the total error is characterized by a sampling error and a model error. See Tasker & Stedinger (1989). The resulting covariance matrix isgit

$sigma^2 I + Sigma$

where $sigma^2$ is the variance of the model error and $Sigma$ is the covariance matrix (diagonal) of the sampling error. First a PPR model with is fitted using ordinary least-squares (criteria == ols) to estimate the $sigma^2$ by the empirical residual variance. Afterwards, the gls weights are calculated. This process is not iterated. An improved solution is later obtained by the ppr2gam method.

Author(s)

Martin Durocher <[e-mail]>

References

Durocher, M., Chebana, F., & Ouarda, T. B. M. J. (2015). A Nonlinear Approach to Regional Flood Frequency Analysis Using Projection Pursuit Regression. Journal of Hydrometeorology (In press). doi:10.1175/JHM-D-14-0227.1

Friedman, J. H., & Stuetzle, W. (1981). Projection Pursuit Regression. Journal of the American Statistical Association, 76, 817<e2><80><93>823. doi:10.1080/01621459.1981.10477729

Hwang, J.-N., Lay, S.-R., Maechler, M., Martin, R. D., & Schimert, J. (1994). Regression modeling in back-propagation and projection pursuit learning. Neural Networks, IEEE Transactions on, 5(3), 342<e2><80><93>353. doi:10.1109/72.286906

Tasker, G., & Stedinger, J. (1989). An operational GLS model for hydrologic regression. Journal of Hydrology, 111(1), 361<e2><80><93>375. doi:10.1016/0022-1694(89)90268-0

See Also

ppr, ppr2gam

Examples

#See ppr2gam method

martindurocher/pprRFA documentation built on May 21, 2019, 12:38 p.m.