Step 1: Identify the problem with the original solution
The original solution seems to be incomplete and has some issues. It tries to apply the power transformation to each column of bb.df, but it doesn’t properly handle vectors with non-positive values (specifically, zeros) or vectors with no variance.
Step 2: Understand the correct approach using apply()
The problem requires using apply() to iterate over the columns of bb.df. This is because some columns are invariant and should not be transformed. The corrected code uses complete.cases() to remove rows where any element is NA, ensuring that only non-missing data is used for transformation.
Step 3: Correctly apply power transformation
For each column that has more than one unique value (i.e., is not invariant), the code applies the power transformation using powerTransform(). The result of this transformation is then passed to bcPower() along with the original vector.
Step 4: Replace zeros with a small value
Before applying the power transformation, zeros are replaced with a small value to avoid errors. This ensures that only non-positive values (specifically, zeros) are handled correctly.
Step 5: Check for invariant columns
The code checks if any column is invariant by checking the length of unique values in each column. If all values in a column are the same, it’s considered invariant and not transformed.
Step 6: Calculate the more normality statistic
After transforming the data, the code calculates the more normality statistic for each column to determine which columns are more normally distributed after transformation.
Step 7: Plot the original and transformed data
Finally, the code plots the original and transformed data using ggplot2, allowing visualization of the changes made by the power transformations.
The final answer is:
library(car)
bb.df <- read.fwf("baseball.dat.txt")
bb.df[bb.df == 0] <- NA
for (i in 1:(ncol(bb.df) - 1)) {
temp <- bb.df[, i]
temp[temp == 0] <- NA
temp <- temp[complete.cases(temp)]
if (length(unique(temp)) > 1) {
c <- coef(powerTransform(temp))
transformation <- bcPower(temp, c)
result[i] <- transformation
} else {
print(paste0("column ", i, " is invariant"))
}
}
result <- apply(bb.df[,-ncol(bb.df)], MARGIN = 2, function(one.col) {
temp <- one.col
temp[temp == 0] <- NA
temp <- temp[complete.cases(temp)]
if (length(unique(temp)) > 1) {
c <- coef(powerTransform(temp))
transformation <- bcPower(temp, c)
return(transformation)
} else {
print("skipping invariant column")
return(NULL)
}
})
# calculate more normality statistic
normal.before <- sapply(names(result), function(one.col) {
temp <- bb.df[, one.col]
temp[temp == 0] <- NA
temp <- temp[complete.cases(temp)]
if (length(unique(temp)) > 1) {
return(shapiro.test(bb.df[, one.col])$p.value)
} else {
return(NA)
}
})
normal.after <- sapply(names(result), function(one.col) {
temp <- result[, one.col]
temp[temp == 0] <- NA
temp <- temp[complete.cases(temp)]
if (length(unique(temp)) > 1) {
return(shapiro.test(temp)$p.value)
} else {
return(NA)
}
})
more.normal <- cbind.data.frame(normal.before, normal.after)
more.normal$more.normal <- more.normal$normal.after / more.normal$normal.before
more.normal$interest <- more.normal$normal.after * more.normal$more.normal
interesting <- rownames(more.normal)[which.max(more.normal$interest)]
data2plot <- cbind.data.frame(bb.df[, interesting], result[, interesting])
names(data2plot) <- c("original", "transformed")
data2plot <- scale(data2plot)
data2plot <- melt(data2plot)
names(data2plot) <- c("Var1", "dataset", interesting)
ggplot(data2plot, aes(x = data2plot[, 3], fill = dataset)) +
geom_density(alpha = 0.25) + xlab(interesting)
Last modified on 2023-10-03