ApplyStatisticalTests: Statistical epistemic tests the imputed values.

Description

ApplyStatisticalTests applies the epistemic goodness-of-fit test for fuzzy data to check the quality of the imputed values.

Usage

ApplyStatisticalTests(
  trueData,
  imputedData,
  imputedMask,
  trapezoidal = TRUE,
  cutsNumber = 100,
  K = 50,
  ...
)

Value

The output is given as a matrix (the rows are related to various types of the test and subsamples, the columns - to the variables plus the overall mean).

Arguments

trueData: Name of the input matrix (or data frame) with the true values of the variables.
imputedData: Name of the input matrix (or data frame) with the imputed values.
imputedMask: Matrix (or data frame) with logical values where TRUE indicates the cells with the imputed values.
trapezoidal: Logical value depending on the type of fuzzy values (triangular or trapezoidal ones) in the dataset.
cutsNumber: Number of cuts for the epistemic bootstrap tests.
K: Value of K for the res epistemic test.
...: Additional parameters passed to other functions.

Details

The procedure applies three types of the epistemic goodness-of-fit Kolmogorov-Smirnov tests (avs - averaging statistic, ms - multi-statistic, res - resampling algorithm) from the FuzzySimRes package to check the quality of the imputed values. To do this, three subsamples are used:

true - the dataset trueData without imputed values vs the values from the same dataset that are then imputed,
imputed - the dataset trueData without imputed values vs only the imputed values from imputedData,
parts - only the imputed values from the dataset trueData vs their counterparts from imputedData.

To assess the respective imputation quality, p-values for true and imputed should be close to each other, and in the case of parts, they should exceed the selected significance level.

All of the input datasets can be given as matrices or data frames. The statistical tests are performed only for the input values that are proper fuzzy numbers (triangular or trapezoidal ones).

Examples

Run this code


# seed PRNG

set.seed(1234)

# load the necessary library

library(FuzzySimRes)

# generate sample of trapezoidal fuzzy numbers with FuzzySimRes library

list1<-SimulateSample(20,originalPD="rnorm",parOriginalPD=list(mean=0,sd=1),
incrCorePD="rexp", parIncrCorePD=list(rate=2),
suppLeftPD="runif",parSuppLeftPD=list(min=0,max=0.6),
suppRightPD="runif", parSuppRightPD=list(min=0,max=0.6),
type="trapezoidal")

# convert fuzzy data into a matrix

matrix1 <- FuzzyNumbersToMatrix(list1$value)

# check starting values

head(matrix1)

# add some NAs to the matrix

matrix1NA <- IntroducingNA(matrix1,percentage = 0.1)

head(matrix1NA)

# impute missing values (with possible repetitions!)

matrix1DImp <- FuzzyImputation(matrix1NA,method="dimp",checkFuzzy=TRUE)

# find cells with NAs

matrix1Mask <- is.na(matrix1NA)

# apply statistical epistemic bootstrap tests

ApplyStatisticalTests(matrix1,matrix1DImp,matrix1Mask,cutsNumber = 100, K=10)