lars.ss: Spatial scale least angle regression (LARS)

In spselect: Selecting Spatial Scale of Covariates in Regression Models

Description

This function fits a spatial scale (SS) LARS model.

Usage

lars.ss(y, X, ss, a.lst, S.v, C.v, col.plot, verbose=TRUE, plot=TRUE)

Arguments

y	A numeric response vector
X	A data frame of numeric variables
ss	A vector of names to identify the different levels of covariates available as potential candidates for model input
a.lst	A list of identity matrices, where each column indicates a particular level or spatial scale for a specified covariate (e.g., ss1_x2)
S.v	A vector of positive integers, where each number denotes the number of spatial scales associated with a particular covariate
C.v	A vector, where all values are initialized to 0
col.plot	A vector of colors (corresponding to each SS) used in the coefficient path plot
verbose	If TRUE, details are printed as the algorithm progresses
plot	If TRUE, a coefficient path plot is generated

Details

This function estimates coefficients using the SS LARS modeling approach. The function also provides summary details and plots a coefficient path plot.

Value

A list with the following items:

beta	Regression coefficient estimates from all set of model solutions
beta.aic	Regression coefficient estimates from final model
ind.v	Vector of indices to denote the corresponding columns of X associated with each active predictor
aic.v	Vector of Akaike information criterion (AIC) values
stack.ss	Vector of indices to indicate the level at which each covariate enters the model

Author(s)

Lauren Grant, David Wheeler

References

Grant LP, Gennings C, Wheeler, DC. (2015). Selecting spatial scale of covariates in regression models of environmental exposures. Cancer Informatics, 14(S2), 81-96. doi: 10.4137/CIN.S17302

Examples

data(y)
data(X)

names.X <- colnames(X)

ss <- c("ind", "ss1", "ss2")

a.lst <- list(NULL)
a.lst[[1]] <- 1
dim(a.lst[[1]]) <- c(1,1)
dimnames(a.lst[[1]]) <- list(NULL, names.X[1])

a.lst[[2]] <- diag(2)
dimnames(a.lst[[2]]) <- list(NULL, names.X[c(2,3)])

a.lst[[3]] <- diag(2)
dimnames(a.lst[[3]]) <- list(NULL, names.X[c(4,5)])

S.v <- c(1,2,2) 
C.v <- rep(0,length(a.lst))

mod_LARS.ss <- lars.ss(y, X, ss, a.lst, S.v, C.v, c("black", "red", "green"))

Example output

Loading required package: tester
Loading required package: magic
Loading required package: abind
Loading required package: pracma

Attaching package: ‘pracma’

The following object is masked from ‘package:magic’:

    magic

Step 1: Set r=y and initialize all betas to 0. 
Step 2: Find the predictor that has the greatest absolute correlation with r. 
	 Note that LARS picks the maximal absolute current correlation. 
 
LARS Iteration 1
	Variable 2 added
	  Step 3: Compute c.hat.v and C.hat. 
            [,1]
x1      4.580816
ss1_x2 12.486376
ss1_x3  2.576488
ss2_x3  8.111859
	  Set s.j=sign{c.hat.v}, and calculate X.in, A.in, u.in, and a. 
	  Step 5: Calculate gamma.hat and d.v. 
	 	  Gamma values: 1.537737 0 0 2.235952 1.16986 
	 	  Gamma hat: 1.16986 
	  Step 6: Update betas and r. 
	 	  Beta.new: 0 0.2683842 0 0 0 
 
[1] 2
[1] 48.42314
LARS Iteration 2
	Variable 5 added
	  Step 3: Compute c.hat.v and C.hat. 
           [,1]
x1     5.495804
ss1_x2 7.387076
ss2_x3 7.387076
	  Step 4: Set s.j=sign{c.hat.v}, and calculate X.in, A.in, u.in, and a. 
	  Step 5: Calculate gamma.hat and d.v. 
	 	  Gamma values: 0.4194236 0 0 0 0 
	 	  Gamma hat: 0.4194236 
	  Step 6: Update betas and r.
	 	  Beta.new: 0 0.3320495 0 0 0.06366526 
[1] 2 5
[1] 45.96404
LARS Iteration 3
	Variable 1 added
	  Step 3: Compute c.hat.v and C.hat. 
           [,1]
x1     6.005505
ss1_x2 6.005505
ss2_x3 6.005505
	  Step 4: Set s.j=sign{c.hat.v}, and calculate X.in, A.in, u.in, and a. 
	  Step 5: Calculate gamma.hat and d.v. 
	 	  Gamma hat: 2.681512 
	  Step 6: Update betas and r.
	 	  Beta.new: 0.4703167 0.6784187 0 0 0.4442981 
[1] 2 5 1
[1] 36.09188
       x1    ss1_x2    ss2_x3 
0.4703167 0.6784187 0.4442981 
[1] "No. of vars in model = 3"
[1] "Total no. of vars considered = 5"

spselect documentation built on May 2, 2019, 3:32 a.m.