Computes bootstrapped confidence intervals for the mean and median distance between the optima of two response surface models. Models can be thin plate splines or quadratic polynomials.
CRcompare(X1,y1,X2,y2,lambda=0.04,responseType='TPS',nosim1and2=200,
alpha=0.05,LB1,UB1,triangularRegion1=FALSE, vertex11=NULL, vertex21=NULL,
maximization1=TRUE,outputPDFFile1="CR_plot1.pdf",outputOptimafile1="Optima1.txt"
,LB2,UB2,triangularRegion2=FALSE, vertex12=NULL, vertex22=NULL, maximization2=
TRUE,outputPDFFile2="CR_plot2.pdf",outputOptimafile2="Optima2.txt",xlab1and2=
"Protein eaten (mg)",ylab1and2="Carbohydrates eaten (mg)")nx2 matrix with the values of the 2 regressors (experimental factors) in the n observations associated with response 1
nx1 vector of response no. 1 value observations
nx2 matrix with the values of the 2 regressors (experimental factors) in the n observations associated with response 2
nx1 vector of response no. 2 value observations
smoothing penalty if a TPS model is selected (default=0.04)
use 'TPS' if fitting thin plate spline responses, 'Quad' if fitting quadratic polynomials
number of simulations (default=200)
confidence level (0<alpha<1; default=0.05)
2x1 vectors of lower and upper bounds for search region where optima may lie for response 1
logical: if TRUE it will constrain the optimum points of response 1 to lie inside a triangle defined by the coordinates (0,0), and those in "vertex11", and "vertex21", see below). NOTE: use TRUE when the treatments form a triangular experimental region in shape. If FALSE, maxima will only be constrained to lie inside the rectangular region defined by LB1 and UB1. Default is FALSE.
2x1 vectors with coordinates defining two of the 3 vertices of a triangular region for searching the optima of response 1. Must be provided if triangularRegion is TRUE (NOTE: vertices numbered clockwise, vertex0=c(0,0) always)
logical: if TRUE (default) it maximizes response 1, if FALSE it minimizes it
name of the PDF file where the CR plot of response 1 is saved (default: "CRplot1.pdf")
name of text file for saving the coordinates of the optima of response 1 (default: "Optima1.txt")
2x1 vectors of lower and upper bounds for search region where optima may lie for response 2
logical: if TRUE it will constrain the optimum points of response 2 to lie inside a triangle defined by the coordinates (0,0), and those in "vertex12", and "vertex22", see below (in addition to being constrained to lie inside the region defined by LB and UB). NOTE: use TRUE when the treatments form a triangular experimental region in shape. If FALSE, maxima will only be constrained to lie inside the rectangular region defined by LB2 and UB2. Default is FALSE.
see vertex22
2x1 vectors with coordinates defining two of the 3 vertices of a triangular region for searching the optima of response 2. Must be provided if triangularRegion is TRUE (NOTE: vertices numbered clockwise, vertex0=c(0,0) always)
logical: if TRUE (default) it maximizes response 2 if FALSE it minimizes it
name of the PDF file where the CR plot of response 2 is saved (default: "CRplot2.pdf")
name of text file for saving the coordinates of the optima of response 2 (default: "Optima2.txt")
text label for x axis in confidence region plot for the optima of each response (default: "Protein eaten, mg")
text label for y axis in confidence region plot for the optima of each response (default: "Carbohydrates eaten, mg")
vector of distances between pairs of points taken from each set of optima
mean of all pairwise distances
median of all pairwise distances
(1-alpha)*100% confidence interval for the mean of the distances using bca bootstrapping
(1-alpha)*100% confidence interval for the mean of the distances using bca bootstrapping.
Note: ciMean and ciMedian are vectors with 5 columns, containing the significance level, the next two containing the indices of the order statistics used in the calculations and the final two the calculated endpoints of the CI's.
Computes distribution-free bootstrapped confidence intervals on the mean and median distance between the optima of two different responses. The responses can be Thin Plate Spline models or Quadratic polynomial models. Program calls OptRegionTps.R or OptRegionQuad.R to compute confidence regions on the optima of each response, next computes all pairwise distances between points in each CR, and finally bootstraps the distances to compute bca bootstrapped confidence intervals for the mean and median distance.
Usage assuming all default options:
out<-CRcompare(X1=X1,y1=y1,X2=X2,y2=y2,LB1=LB1,UB1=UB1,LB2=LB2,UB2=UB2)
Del Castillo, E., Hunt, J., Rapkin, J., and Zarmehri, S. , "Confidence regions for the location of response surface optima: the R package OptimaRegion".
# NOT RUN {
## Example: two randomly generated data sets, quadratic polynomial responses.
X1<-cbind(runif(100,-2,2),runif(100,-2,2))
y1<-as.matrix(72-11.78*X1[,1]+0.74*X1[,2]-7.25*X1[,1]^2-7.55*X1[,2]^2-4.85*X1[,1]*X1[,2]+
rnorm(100,0,8))
X2<-cbind(runif(100,-2,2),runif(100,-2,2))
y2<-as.matrix(72-11.78*X2[,1]+0.74*X2[,2]-7.25*X2[,1]^2-7.55*X2[,2]^2-4.85*X2[,1]*X2[,2]+
rnorm(100,0,8))
out<-CRcompare(X1=X1,y1=y1,X2=X2,y2=y2,responseType='Quad',nosim1and2=200,
alpha=0.05,LB1=c(-2,-2),UB1=c(2,2),LB2=c(-2,-2),UB2=c(2,2))
# }
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