Type: Package
Title: Selecting Spatial Scale of Covariates in Regression Models
Version: 0.0.1
Date: 2016-08-29
Author: Lauren Grant, David Wheeler
Maintainer: Lauren Grant <pacele@vcu.edu>
Depends: tester, magic, pracma
Description: Fits spatial scale (SS) forward stepwise regression, SS incremental forward stagewise regression, SS least angle regression (LARS), and SS lasso models. All area-level covariates are considered at all available scales to enter a model, but the SS algorithms are constrained to select each area-level covariate at a single spatial scale.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyLoad: yes
NeedsCompilation: no
Packaged: 2016-08-29 16:07:16 UTC; Lauren
Repository: CRAN
Date/Publication: 2016-08-29 18:53:24

Selecting spatial scale of area-level covariates in regression models

Description

Fits spatial scale (SS) forward stepwise regression, SS incremental forward stagewise regression, SS least angle regression (LARS), and SS lasso models. All area-level covariates are considered at all available scales to enter a model, but the SS algorithms are constrained to select each area-level covariate at a single spatial scale.

Details

Package: spselect
Type: Package
Version: 0.0.1
Date: 2016-08-29
License: GPL (>=2)
LazyLoad: yes

Author(s)

Lauren Grant, David Wheeler

Maintainer: Lauren Grant <pacele@vcu.edu>

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.3D)
y.name <- "y"
ss <- c("ind", "ss1", "ss2")
mod_forward.step.ss_1 <- stepwise.ss(y, X.3D, y.name, ss, 1)

Input data X

Description

Simulated input data

Usage

data(X)

Format

A data frame with 20 observations on the following 5 variables:

x1

a numeric vector

ss1_x2

a numeric vector

ss2_x2

a numeric vector

ss1_x3

a numeric vector

ss2_x3

a numeric vector

Details

The data consist of simulated variables, including an individual-level covariate (x1) and two area-level covariates (x2, x3) available at two different spatial scales (ss1, ss2).

Examples

data(X)

Input data X.3D

Description

Simulated input data (in stacked array format)

Usage

data(X.3D)

Format

A 20x3x3 stacked array with the following stacks:

ind

a numeric array containing an individual-level variable (x1)

ss1

a numeric array containing area-level variables (x2, x3) available at ss1

ss2

a numeric array containing area-level variables (x2, x3) available at ss2

Details

The data consist of simulated variables, including an individual-level covariate (x1) and two area-level covariates (x2, x3) available at two different spatial scales (ss1, ss2). The data are in the form of a 3-D or stacked array, where each stack represents a particular level of covariates, including spatial scale. The first stack contains the individual-level variable; the second and third stacks contain the area-level variables at the ss1 and ss2 levels, respectively. Note that in cases where values are only present for a covariate at certain levels, that covariate is assigned missing values at all other levels.

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(X.3D)

Spatial scale least angle regression (LARS)

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"))

Spatial scale lasso

Description

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

Usage

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

Spatial scale incremental forward stagewise regression

Description

This function fits a spatial scale (SS) incremental forward stagewise regression model.

Usage

stagewise.ss(y, X, X.3D, ss, increment, tolerance, col.plot, verbose=TRUE, plot=TRUE)

Arguments

y

A numeric response vector

X

A data frame of numeric variables

X.3D

A 3-D or stacked array of numeric variables, where each stack represents a particular level of covariates (i.e., individual- and area-level variables at more than one spatial scale). In cases where values are only present for a covariate at certain levels, that covariate is assigned missing values at all other levels.

ss

A vector of names to identify the different levels of covariates available as potential candidates for model input

increment

A positive step size

tolerance

A small, positive value used as a stopping criterion when none of the predictors are correlated with the residuals. The algorithm stops if the overall maximum correlation is less than a specified tolerance.

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 forward stagewise regression approach. The function also provides summary details and plots a coefficient path plot.

Value

A list with the following items:

beta.final

Regression coefficient estimates from final model

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)
data(X.3D)
ss <- c("ind", "ss1", "ss2")
mod_forward.stage.ss_0.1 <- stagewise.ss(y, X ,X.3D, ss, 0.1, 0.1, c("black", "red", "green"))

Spatial scale forward stepwise regression

Description

This function fits a spatial scale (SS) forward stepwise regression model.

Usage

stepwise.ss(y, X.3D, y.name, ss, epsilon, verbose=TRUE)

Arguments

y

A numeric response vector

X.3D

A 3-D or stacked array of numeric variables, where each stack represents a particular level of covariates (i.e., individual- and area-level variables at more than one spatial scale). In cases where values are only present for a covariate at certain levels, that covariate is assigned missing values at all other levels.

y.name

A name for y

ss

A vector of names to identify the different levels of covariates available as potential candidates for model input

epsilon

A positive value used as a stopping criterion when there is inadequate improvement in the model's performance. The algorithm stops if the difference in the Akaike information criterion (AIC) between the current model and the proposed model is less than epsilon.

verbose

If TRUE, details are printed as the algorithm progresses

Details

This function estimates coefficients using the SS forward stepwise regression approach. The function also estimates the model fit and provides summary details.

Value

A list with the following items:

beta.final

Regression coefficient estimates from final model

aic.final

AIC for final model

summary.final

Summary output of final model

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.3D)
y.name <- "y"
ss <- c("ind", "ss1", "ss2")
mod_forward.step.ss_1 <- stepwise.ss(y, X.3D, y.name, ss, 1)

Response data y

Description

Simulated response data

Usage

data(y)

Format

A numeric response vector with 20 observations

Examples

data(y)