# MixModel: Fit mixture and mixture process variable models. In mixexp: Design and Analysis of Mixture Experiments

## Description

This function fits mixture models (1)-(4) and mixture process models (5)-(6) described in Lawson and Willden(2015) "Mixture Experiments in R, using mixexp", Journal Statistical Software http://www/jstatsoft.org/, and prints the correct R square and standard errors of model coefficients.

## Usage

 `1` ```MixModel(frame, response, mixcomps=NULL,model,procvars=NULL) ```

## Arguments

 `frame` a data frame containing columns with the mixture components, process variables, and responses `response` a character variable containing the column name of the response variable in frame to be fit `mixcomps` a character vector of column names of the mixture components in frame `model` an integer in the range of 1 to 6, indicating the model to be fit: 1. y = sum from 1 to q (β(i)x(i)) + ε. 2. y = sum from i=1 to q (β(i)x(i)) + sum from i=1 to q-1 sum j=i+1 to q (β(ij)x(i)x(j)) + ε. 3. y = sum from i=1 to q (β(i)x(i)) + sum from i=1 to q-1 sum j=i+1 to q (β(ij)x(i)x(j)) + sum i=1 to q-1 sum j=i+1 to q (δ(ij)x(i)x(j)(x(i)-x(j)) + sum i=1 to q-2 sum j=i+1 to q-1 sum k=j+1 to q (β(ijk)x(i)x(j)x(k)) + ε. 4. y = sum from i=1 to q (β(i)x(i)) + sum from i=1 to q-1 sum j=i+1 to q (β(ij)x(i)x(j)) + sum i=1 to q-2 sum j=i+1 to q-1 sum k=j+1 to q (β(ijk)x(i)x(j)x(k)) + ε. 5. y = (sum from i=1 to q (β(i)x(i)) + sum from i=1 to q-1 sum j=i+1 to q (β(ij)x(i)x(j))) (α(0)+sum from l=1 to p (α(l)z(l)) + sum from l=1 to p-1 sum from m=l+1 to p (α(lm)z(l)z(m)))+ ε. 6. y = sum from i=1 to q (β^0(i)x(i)) + sum from i=1 to q-1 sum j=i+1 to q (β^0(ij)x(i)x(j)) + sum from k=1 to m[sum from i=1 to q β^1x(i)]z(k) + sum k=1 to m-1 sum from l=k+1 to m α(kl)z(k)z(l) + sum from k=1 to m α(kk)z^2(k)+ ε where x(i) are mixture components, and z(j) are process variables. `procvars` a character vector of column names of the process variables in frame to be included in the model. Leave this out if there are no process variables in the frame

## Author(s)

John S. Lawson [email protected]

## References

1. "John Lawson, Cameron Willden (2016).", "Mixture Experiments in R Using mixexp.", "Journal of Statistical Software, Code Snippets, 72(2), 1-20.", "doi:10.18637/jss.v072.c02"

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```# example from Lawson(2014), quadratic model library(daewr) data(pest) mixvars<-c("x1","x2","x3") MixModel(pest,"y",mixvars,2) # example from Myers and Montgomery(2002), special cubic model library(mixexp) etch<-SCD(3) etch<-Fillv(3,etch) etch<-rbind(etch[1:7, ],etch[1:3, ],etch[7, ], etch[etch\$x1==2/3, ], etch[etch\$x2==2/3, ],etch[etch\$x3==2/3, ]) erate<-c(540,330,295,610,425,330,800,560,350,260,850,710,640,460) etch<-cbind(etch,erate) mixvars<-c("x1","x2","x3") response<-c("erate") MixModel(etch,response,mixvars,4) # example Mixture process variable model from Sahni, Pieple and Naes(2009) library(daewr) mixvars<-c("x1","x2","x3") procvars<-c("z1","z2") data(MPV) MixModel(MPV,"y",mixvars,5,procvars) #### Kowalski Cornell and Vining Simplified model on data from Gallant et. al. (2008) data(Burn) testBNM<-MixModel(Burn,"y",mixcomps=c("Course","Fine","Binder"),model=6,procvars=c("z")) ```

mixexp documentation built on May 29, 2017, 7:09 p.m.