Calculate Posterior Probabilities that Effects are Active

DESCRIPTION:

Calculates posterior probabilities that the individual effects are active. The user supplies priors on the probability of an effect being active, and on the difference in scale between active and inactive effects. The basic assumption of this approach is that the effects arise from a scale contaminated normal; that is,

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

USAGE:

accalc(alpha, k, effects) 

REQUIRED ARGUMENTS:

alpha
prior probability that any one effect is active.
k
scale factor for active effects.
effects
vector of effects from the analysis of a fractional factorial design.

VALUE:

Returns a list including the values of alpha, k, the effects and the posterior probabilities.

METHOD:

The function accalc calls a C function which was adapted from Stephenson et al. (1989). The posterior probabilities are calculated by an analytical method if there are 16 effects or less, and numerical integration for more than 16 effects. The function accalc is called by the function acplot which generates active contrast plots.

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) 
accalc(.2,10,buffer.fac$feffects)