FrF2-package {FrF2}R Documentation

Fractional Factorial designs with 2-level factors

Description

This package creates regular and non-regular Fractional Factorial designs. Furthermore, analysis tools for Fractional Factorial designs with 2-level factors are offered (main effects and interaction plots for all factors simultaneously, cube plot for looking at the simultaneous effects of three factors, full or half normal plot, alias structure in a more readable format than with the built-in function alias).

The package is currently subject to intensive development; new functionality will be added, and existing structures, inputs and outputs may change in the future.

Details

The package is currently subject to intensive development; new functionality will be added, and existing structures, inputs and outputs may change in the future. Please contact me, if you have suggestions.

This package designs and analyses Fractional Factorial experiments with 2-level factors. Analysis facilities are meant for completely aliased designs only, i.e. e.g. not for analysing Plackett-Burman designs with interactions.

Regular (function FrF2) and non-regular (function pb) 2-level fractional factorial designs can be generated.

In terms of analysis, 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.

Author(s)

Ulrike Groemping

Maintainer: Ulrike Groemping <groemping@bht-berlin.de>

References

Box G. E. P, Hunter, W. C. and Hunter, J. S. (2005) Statistics for Experimenters, 2nd edition. New York: Wiley.

Chen, J., Sun, D.X. and Wu, C.F.J. (1993) A catalogue of 2-level and 3-level orthogonal arrays. International Statistical Review 61, 131-145.

Daniel, C. (1959) Use of Half Normal Plots in Interpreting Two Level Experiments. Technometrics, 1, 311-340.

Hedayat, A.S., Sloane, N.J.A. and Stufken, J. (1999) Orthogonal Arrays: Theory and Applications, Springer, New York.

Lenth, R.V. (1989) Quick and easy analysis of unreplicated factorials. Technometrics, 31, 469-473.

Plackett, R.L.; Burman, J.P. (1946) The design of optimum multifactorial experiments. Biometrika 33, 305-325.

See Also

BsMD-package, MEPlot, IAPlot, cubePlot, DanielPlot, aliases, FrF2, pb

Examples

    ### for examples on design generation, cf. functions pb and FrF2
  
    ### 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)

[Package FrF2 version 0.9-1 Index]