| FrF2-package {FrF2} | R Documentation |
This package analyses Fractional Factorial designs with 2-level factors; it is meant for completely aliased designs only, i.e. e.g. not for analysing Plackett- Burman designs with interactions.
The package enables convenient main effects and interaction plots for all factors simultaneously and offers a cube plot for looking at the simultaneous effects of three factors. An enhanced DanielPlot function (modified from BsMD) is provided. Furthermore, the alias structure for Fractional Factorial 2-level designs is output in a more readable format than with the built-in function alias.
This package analyses Fractional Factorial designs with 2-level factors; it is meant for completely aliased designs only, i.e. e.g. not for analysing Plackett- Burman designs with interactions.
The package works on linear models and enables convenient main effects and
interaction plots (functions MEPlot and IAPlot) similar to those
offered by Minitab software for all factors simultaneously, even though especially the
interactions are often aliased, i.e. the model is typically singular.
For the (rare) case of suspected three-factor-interactions, function
cubePlot displays a cube with corners labeled with the (modeled)
means of three factors simultaneously.
Furthermore, the function DanielPlot from package BsMD has been
modified to automatically label effects significant according to the
Lenth-criterion, and to provide more usage comfort to the analyst.
Finally, the function aliases determines the alias structure of a
Fractional Factorial 2-level design in a format more suitable for human readers
than the output from the built-in function alias.
Ulrike Groemping
Maintainer: Ulrike Groemping <groemping@tfh-berlin.de>
Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005) Statistics for Experimenters, 2nd edition. New York: Wiley.
Daniel, C. (1959) Use of Half Normal Plots in Interpreting Two Level Experiments. Technometrics, 1, 311-340.
Lenth, R.V. (1989) Quick and easy analysis of unreplicated factorials. Technometrics, 31, 469-473.
BsMD-package, MEPlot, IAPlot,
cubePlot, DanielPlot, aliases
### Injection Molding Experiment. Box et al. 1978.
data(BM93.e3.data) #from BsMD
iMdat <- BM93.e3.data[1:16,2:10] #only original experiment
# make data more user-friendly
colnames(iMdat) <- c("MoldTemp","Moisture","HoldPress","CavityThick","BoostPress",
"CycleTime","GateSize","ScrewSpeed", "y")
# linear model with all main effects and 2-factor interactions
iM.lm <- lm(y ~ (.)^2, data = iMdat)
# determine aliases
aliases(iM.lm)
# coded version
aliases(iM.lm, code=TRUE)
# normal plot of effects, default is autolabel with alpha=0.05
DanielPlot(iM.lm)
DanielPlot(iM.lm,code=TRUE)
DanielPlot(iM.lm,code=TRUE,alpha=0.5)
# half normal plot of effects
DanielPlot(iM.lm,code=TRUE,alpha=0.5,half=TRUE)
# main effects plots
MEPlot(iM.lm)
# interaction plots
IAPlot(iM.lm)
# interaction plots with attention drawn to aliases
IAPlot(iM.lm, show.alias=TRUE)
# alias groups corresponding to interaction plots
aliases(iM.lm)$aliases[9:15]
# cube plot of three factors
# (not very useful for this model, for demonstration only)
## per default, modeled means are shown
## this does not make a difference here, since the main effect of
## ScrewSpeed is confounded with the MoldTemp:HoldPress:BoostPress
## interaction, so that the three-factor-interaction is indirectly included
## in the modeled means
cubePlot(iM.lm, "MoldTemp", "HoldPress", "BoostPress")
## modeled means without a three-factor interaction
cubePlot(lm(y ~ (MoldTemp+HoldPress+BoostPress)^2, data = iMdat),
"MoldTemp", "HoldPress", "BoostPress")
## modeled=FALSE reverts to showing the apparent three-factor interaction
cubePlot(lm(y ~ (MoldTemp+HoldPress+BoostPress)^2, data = iMdat),
"MoldTemp", "HoldPress", "BoostPress", modeled=FALSE)
## cubePlot also works on raw data
cubePlot(iMdat$y, iMdat$MoldTemp, iMdat$HoldPress, iMdat$BoostPress)