# LGBc: This function does the calculations for the LGB Method to... In daewr: Design and Analysis of Experiments with R

## Description

This function uses the LGB Method to detect significant effects in unreplicated fractional factorials.

## Usage

 `1` ```LGBc(Beta, alpha = 0.05, rpt = TRUE, plt = TRUE, pltl = TRUE) ```

## Arguments

 `Beta` input - this is the numeric vector of effects or coefficients to be tested `alpha` input - This is the significance level of the test `rpt` input - this is a logical variable that controls whether the report is written (default is TRUE) `plt` input - this is a logical variable that controls whether a half-normal plot is made (default is TRUE) `pltl` input - this is a logical variable that controls whether the significance limit line is drawn on the half-normal plot (default is TRUE)

John Lawson

## References

Lawson, J., Grimshaw, S., Burt, J. (1998) "A quantitative method for identifying active contrasts in unreplicated factorial experiments based on the half-normal plot", Computational Statistics and Data Analysis, 26, 425-436.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71``` ```data(chem) modf<-lm(y~A*B*C*D,data=chem) sig<-LGBc(coef(modf)[-1],rpt=FALSE) ## The function is currently defined as function (Beta, alpha = 0.05, rpt = TRUE, plt = TRUE, pltl = TRUE) { siglev <- c(0.1, 0.05, 0.025, 0.01) df <- c(7, 8, 11, 15, 16, 17, 26, 31, 32, 35, 63, 127) crittab <- matrix(c(1.265, 1.196, 1.161, 1.122, 1.11, 1.106, 1.072, 1.063, 1.06, 1.059, 1.037, 1.023, 1.534, 1.385, 1.291, 1.201, 1.186, 1.178, 1.115, 1.099, 1.093, 1.091, 1.056, 1.034, 1.889, 1.606, 1.449, 1.297, 1.274, 1.26, 1.165, 1.14, 1.13, 1.127, 1.074, 1.043, 2.506, 2.026, 1.74, 1.447, 1.421, 1.377, 1.232, 1.197, 1.185, 1.178, 1.096, 1.058), ncol = 4, byrow = FALSE) colind <- which(siglev == alpha, arr.ind = TRUE) if (length(colind) == 0) { stop("this function works only when alpha= .1, .05, .025 or .01") } rowind <- which(df == length(Beta), arr.ind = TRUE) if (length(rowind) == 0) { stop("this function works only for coefficent vectors of length 7,8,11,15,16,26,31,32,35,63,or 127") } critL <- crittab[rowind, colind] acj <- abs(Beta) ranks <- rank(acj, ties.method = "first") s0 <- 1.5 * median(acj) p <- (ranks - 0.5)/length(Beta) z <- qnorm((p + 1)/2) moda <- lm(acj ~ -1 + z) beta1 <- moda\$coef sel <- acj < 2.5 * s0 modi <- lm(acj[sel] ~ -1 + z[sel]) beta2 <- modi\$coef Rn <- beta1/beta2 pred <- beta2 * z n <- length(acj[sel]) df <- n - 1 sig <- sqrt(sum(modi\$residuals^2)/df) se.pred <- sig * (1 + 1/n + (z^2)/sum(z[sel]^2))^0.5 pred.lim <- pred + qt(0.975, df) * se.pred sigi <- c(rep("no", length(Beta))) sel2 <- acj > pred.lim sigi[sel2] <- "yes" if (plt) { plot(z, acj, xlab = "Half Normal Scores", ylab = "Absoulute Effects") lines(sort(z), sort(pred), lty = 1) for (i in 1:length(Beta)) { if (sigi[i] == "yes") text(z[i], acj[i], names(Beta)[i], pos = 1) } if (pltl) { lines(sort(z), sort(pred.lim), lty = 3) } } if (rpt) { cat("Effect Report", "\n") cat(" ", "\n") cat("Label Half Effect Sig(.05)", "\n") cat(paste(format(names(Beta), width = 8), format(Beta, width = 8), " ", format(sigi, width = 10), "\n"), sep = "") cat(" ", "\n") cat("Lawson, Grimshaw & Burt Rn Statistic = ", Rn, "\n") cat("95th percentile of Rn = ", critL, "\n") } return(sigi) } ```

daewr documentation built on May 29, 2017, 6:11 p.m.