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07- grsmd

  • Computes the root mean square distance between predicted and corresponding observed values in an orthogonal multivariate space.
  • This value is the mean Mahalanobis distance between observed and imputed values in a space defined by observations and variables were observed and predicted values are defined.
  • The statistic provides a way to compare imputation (or prediction) results.
  • While it is designed to work with imputation, the function can be used with objects that inherit from lm or with matrices and data frames that follow the column naming convention.
install.packages("yaImpute")
library(yaImpute)

library(magrittr)
library(dplyr)
Installing package into '/home/nbcommon/R'
(as 'lib' is unspecified)

Iris Example

data(iris)
set.seed(12345)
# form some test data
refs=sample(rownames(iris),50)

x <- iris[,1:2] # Sepal.Length Sepal.Width
tail(x)
dim(x)
y <- iris[refs,3:4] # Petal.Length Petal.Width
tail(y)
dim(y)
# build yai objects using 2 methods
msn <- yai(x=x,y=y)
mal <- yai(x=x,y=y,method="mahalanobis")
lmFit=lm(as.matrix(y) ~ ., data=x[refs,])
# compute the average distances between observed and imputed (predicted)
grmsd(msn,mal,lmFit)

# use the all variables and observations in iris
# Species is a factor and is automatically deleted with a warning
grmsd(msn,mal,ancillaryData=iris[,1:4])

# here is an example using lm, and another using column
# means as predictions.
impMean <- y
colnames(impMean) <- paste0(colnames(impMean),".o")
impMean <- cbind(impMean,y)
tail(impMean)
dim(impMean)
# set the predictions to the mean's of the variables
impMean[,"Petal.Length"] <- mean(impMean[,"Petal.Length"])
impMean[,"Petal.Width"] <- mean(impMean[,"Petal.Width"])
grmsd(msn, mal, lmFit=lm(as.matrix(y) ~ ., data=x[refs,]), impMean )
# compare to using function rmsd (values match):
msnimp <- na.omit(impute(msn))
grmsd(msnimp[,c("Petal.Length","Petal.Length.o")])
rmsd(msnimp[,c("Petal.Length","Petal.Length.o")],scale=TRUE)
# these are multivariate cases and they don't match
# because the covariance of the two variables is > 0.


grmsd(msnimp)
colSums(rmsd(msnimp,scale=TRUE))/2
# get the vectors and make a boxplot, identify outliers

stats <- boxplot(grmsd(msn,mal,ancillaryData=iris[,-5],rtnVectors=TRUE),
ylab="Mahalanobis distance")

stats$out