PSE function

Pseudo standard error of effects

Computes a pseudo standard error using any of a variety of built-in methods, or a user-supplied one.

PSE(effects, method = "Zahn", verbose = FALSE)

ME(effects, method = "Zahn", alpha = .05, ...)

Arguments

• effects: Numeric vector of effects or contrasts to be explored.
• method: Character value. The name of the method to be used. See Details.
• verbose: Logical value. If TRUE, the parameters (if any) generated by the method's setup code are printed.
• alpha: Numeric significance level, between 0 and 1.
• ...: Additional arguments passed to ref.dist. If a matching reference distribution is already available in .Last.ref.dist, these arguments have no effect.

Details

The PSE function implements methods of estimating the standard error of effects estimates from unreplicated designs. The underlying assumption is that the effects all have the same variance, and that effect sparsity assumption applies, whereby the majority of the effects are inactive and only a handful are active. The method may be any directed method (as described in Hamada and Balakrishnan (1998). A number of built-in methods are available; see the list below.

Users may easily write their own method. The method "foo" would be implemented by writing a function foo_pse <- function(effects) { ... } and saving it where it can be found in the search path. An example can be found by listing unrepx:::Lenth_pse.

If the user-supplied function needs to use weights, coefficients, or other parameters that depend on length(effects) that would be cumbersome in simulations (e.g., in ref.dist), the user may instead provide a function foo_pse <- function(effects, parm) { ... }, along with attr(foo_pse, "setup") <- function(n.effects) { ... } which returns the parm argument (say, a list) to be used when length(effects) = n.effects. The setup function is called automatically if the "setup" attribute exists, and if so, the function is expected to have the second argument. See a listing of unrepx:::Zahn_pse for an example.

Returns

PSE returns a single numeric value, named in the style method_PSE. ME returns a named numeric vector of length 2, containing the margin of error ME and the simultaneous margin of error SME.

Built-in methods

• Daniel: The 68.3rd quantile of the absolute effects. See Daniel (1959).
• Dong: The RMS method, applied after excluding all effects that exceed 2.5 * PSE(effects, "SMedian") in absolute value. See Dong (19??).
• JuanPena: An iterated median method whereby we repeatedly calculate the median of the absolute effects that don't exceed 3.5 times the previous median, until it stabilizes. The estimate is the final median, divided by .6578. See Juan and Pena (1992).
• Lenth: The SMedian method, applied after excluding all effects that exceed 2.5 * PSE(effects, "SMedian") in absolute value. See Lenth (1989).
• RMS: Square root of the mean of the squared effects. This is not a good PSE in the presence of active effects, but it is provided for sake of comparisons.
• SMedian: 1.5 times the median of the absolute effects.
• Zahn, WZahn: The Zahn method is the slope of the least-squares line fitted to the first $m$ points of hnplot(effects, horiz = FALSE), where m = floor(.683 * length(effects)). (This line is fitted through the origin.) The WZahn method is an experimental version of Zahn's method, based on weighted least-squares with weights decreasing linearly from $m - .5$ to $.5$, but bounded above by $.65m$.

References

Daniel, C (1959) Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments. Technometrics, 1(4), 311-341

Dong, F (1993) On the Identification of Active Contrasts in Unreplicated Fractional Factorials. Statistica Sinica 3, 209-217

Hamada and Balakrishnan (1998) Analyzing Unreplicated Factorial Experiments: A Review With Some New Proposals. Statistica Sinica 8, 1-41

Juan, J and Pena, D (1992) A Simple Method to Identify Significant Effects in Unreplicated Two-Level Factorial Designs. Communications in Statistics: Theory and Methods 21, 1383-1403

Lenth, R (1989) Quick and Easy Analysis of Unrelicated Factorials Technometrics 31(4), 469-473

Zahn, D (1975) Modifications of and Revised Critical Values for the Half-Normal Plot. Technometrics 17(2), 189-200

Author(s)

Russell V. Lenth

Examples

require("unrepx")

PSE(shnkEff, method = "Lenth")