Generate an Active Contrast (Bayes) Plot

DESCRIPTION:

Calculates posterior probabilities that individual effects are active and generates a barplot that compares those probabilities. The user supplies priors on the probability of an effect being active, and on the difference in scale between active and inactive effects.

USAGE:

acplot(x, alpha=0.4, k=5, ...) 

REQUIRED ARGUMENTS:

x
an object of class fac.aov, typically created by fitting a fractional factorial model using fac.aov.

OPTIONAL ARGUMENTS:

alpha
prior probability that any one effect is active. Haaland (1989) recommends alpha=0.4 as a good starting value. Box and Meyer (1986) recommend alpha=0.2.
k
scale factor for active effects. Haaland (1989) recommend k=5 as a good starting value. Box and Meyer (1986) recommend k=10.
...
parameters passed to the plotting function.

METHOD:

Posterior probabilities are calculated by the function accalc which takes alpha and k as parameters. The function accalc calls a C function which was adapted from Stephenson et al. (1989). The basic assumption of this approach is that the effects arise from a scale contaminated normal; namely,

alpha*N(0,sigma^2) + (1-alpha)*N(0,k^2*sigma^2)

VALUE:

NULL

SIDE EFFECTS:

an active contrast plot is produced on the current graphics device.

REFERENCES:

Box and Meyer (1986), An analysis for unreplicated fractional factorials, Technometrics, 28, 11-18.

Haaland, P. D. (1989), Experimental Design in Biotechnology, New York: Marcel Dekker.

Stephenson, W. R., F. L. Hulting, and K. Moore (1989), Posterior probabilities for identifying active effects in unreplicated experiments, Journal of Quality Technology, 21, 202-212.

SEE ALSO:

, , .

EXAMPLES:

buffer.fac <- fac.aov(buffer.df) 
acplot(buffer.fac,0.2,10) 
acplot(buffer.fac,0.4,5)