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2012-02-07T17:50:27.600
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Courtesy of some generous advice from my colleagues, I now have one function that creates simulated data given a specified number of groups, a set of contrasts, a set of regression coefficients, a specified N per cell, and a specified within-group variance <pre><code>sim.factor <- function(levels, contr, beta, perCell, errorVar){ # Build design matrix X X <- cbind(rep(1,levels*perCell), kronecker(contr, rep(1,perCell))) # Generate y y <- X %*% beta + rnorm(levels*perCell, sd=sqrt(errorVar)) # Build and return data frame dat <- cbind.data.frame(y, X[,-1]) names(dat)[-1] <- colnames(contr) return(dat) } </code></pre> I also wrote a function that, given a set of regression coefficients, N per cell, number of groups, set of orthogonal contrasts, desired delta-R^2 for a contrast of interest, returns the required within-group variance: <pre><code>ws.var <- function(levels, contr, beta, perCell, dc){ # Build design matrix X X <- cbind(rep(1,levels), contr) # Generate the expected means means <- X %*% beta # Find the sum of squares due to each contrast var <- (t(means) %*% contr)^2 / apply(contr^2 / perCell, 2, sum) # Calculate the within-conditions sum of squares wvar <- var[1] / dc - sum(var) # Convert the sum of squares to variance errorVar <- wvar / (3 * (perCell - 1)) return(errorVar) } </code></pre> After doing some testing as follows, the functions seem to generate the desired delta R^2 for contrast c1. <pre><code>contr <- contr.helmert(3) colnames(contr) <- c("c1","c2") beta <- c(0, 1, 0) perCell <- 50 levels = 3 dc <- .08 N <- 1000 # Calculate the error variance errorVar <- ws.var(levels, contr, beta, perCell, dc) # To store delta R^2 values d1 <- vector("numeric", length = N) # Use the functions for(i in 1:N) { d <- sim.factor(levels=3, contr=contr, beta=beta, perCell=perCell, errorVar=errorVar) d1[i] <- lm.sumSquares(lm(y ~ c1 + c2, data = d))[1, 2] # From the lmSupport package } m <- round(mean(d1), digits = 3) bmp("Testing simulation functions.bmp") hist(d1, xlab = "Percentage of variance due to c1", main = "") text(.18, 180, labels = paste("Mean =", m)) dev.off() </code></pre> Patrick
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1. PORandom draws from an ANOVA-like design with given population effect sizes
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1. USPatrick S. Forscher
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