Full factorial design (2^4) without replicates in R (Why I can not graph the daniel plot in R)

Question

I'm trying to analyse a full factorial design 2^4 with center points and star points, without replicates. However, I'm trying to graph the Daniel plot, but I has couldn't. The R code ( https://docs.google.com/document/d/1hrODFpL4tWnWr9CPL9g_myALMQ926SsNS9Ncy5MnhA0/edit?usp=sharing ).

library(Rcmdr)    
library(RcmdrPlugin.DoE)    
library(FrF2)

Design.1 <- fac.design(nfactors= 4,
                       replications= 1 ,
                       repeat.only= FALSE , 
                       blocks= 1 ,
                       randomize= FALSE ,
                       seed= 28059 ,
                       nlevels=c( 2,2,2,2 ), 
                       factor.names=list(Temperature=c(100,160), 
                                         Time=c(1.5,4), 
                                         Acid=c(0,3), 
                                         Biomass=c(10,30) ) )

Design.1.withcenterpts <- add.center(Design.1, ncenter= 2, distribute= 1)

CCD <- ccd.augment(Design.1.withcenterpts, alpha= 1, ncenter=c(1) ,
                   randomize= FALSE, seed= 3647 )

attach(CCD)

y.response= c(33.8, 61.19, 46.76, 49.21, 91.17, 97.14, 97.34, 9.88, 40.05, 41.93, 50.07, 
              62.83, 98.72, 6.45, 99.48, 14.48, 95, 97.99, 97.96, 12.97, 99.78, 74, 
              51.82, 59.79, 83.38, 81.63, 94.07)

CCD <- add.response(CCD, y.response, replace=FALSE)
DanielPlot(CCD)

Answer 1

This is a respons surface design. You usually build these in sequence starting with a screening design eg 2⁴ full or fractional design with replicated centerpoints as a first iteration. The Daniels plot is very good when identifying the 20 procent dominant effects (active subspace) of investigated factors and should be used in this stage. If all four factors are found active you can add starpoints given that the screening design have indicated proximity to a hyperspace "max" or "min" value. If all factors are active you usually analyse the results with least square analysis.You do not delete factors in response surface analysis based on statistical significance as this would imply that a guessed zero value would be a better best estimate than the actual estimate. The short answer is therefore:

The DANIELS plot is not used when analyzing response surfaces.

Ref: "Statistics for experimenters" Box Hunter and Hunter Wileys 2005 chapter 11 and 12.

Note that that you should be able to plot the model residuals in a Daniels plot.

Answer 2

The Daniel's plot just only work over a fit model, created from regression. For example:

model<-lm(y.response~Temperatura*Time*Acid*Biomass,data=CCD)

It will create the model. I suggest:

BsM2::DanielPlot(model)

to create the plot.