Loading the package and setting a seed:

library(miceFast);library(data.table);library(magrittr)
set.seed(123456)

Description

Fast imputations under the object-oriented programming paradigm. There was used quantitative models with a closed-form solution. Thus package is based on linear algebra operations. The biggest improvement in time performance could be achieve for a calculation where a grouping variable have to be used. A single evaluation of a quantitative model for the multiple imputations is another major enhancement. Moreover there are offered a few functions built to work with popular R packages.

Performance

miceFast was compared1 with the mice package. For grouping option there was used a basic R looping and popular dplyr/data.table packages. Summing up, miceFast offer a relevant reduction of a calculations time for:

Example:

Performance Summary

Performance Summary

If you are interested about the procedure of testing performance check performance_validity.R file at the extdata folder.

system.file("extdata","performance_validity.R",package = "miceFast")

Additional plots for simulations with certain parameters (but feel free to change them) are located:

system.file("extdata","images",package = "miceFast")

Moreover there are offered a few functions built to work with the popular R packages such as ‘data.table’.

Motivations

Missing data is a common problem. The easiest solution is to delete observations for which a certain variable is missing. However this will sometimes deteriorate quality of a project. Another solution will be to use methods such as multiple/regular imputations to fill the missing data. Non missing independent variables could be used to approximate a missing observations for a dependent variable. R or Python language are user-friendly for data manipulation but parallely brings slower computations. Languages such as C++ gives an opportunity to boost our applications or projects.

The presented miceFast package was built under Rcpp packages and the C++ library Armadillo. The Rcpp package offers functionality of exporting full C++ capabilities to the R environment. More precisely miceFast and corrData are offered. The first module offers capabilities of imputations models with a closed-form solution. Thus package is based on linear algebra operations. The main upgrade is possibility of including a grouping and/or weighting (only for linear models) variable and functions enhancement by C++ capabilities. The second module was made for purpose of presenting the miceFast usage and performance. It provides functionality of generating correlated data with a discrete, binomial or continuous dependent variable and continuous independent variables.

Introduction for data.table users - using additional functions from miceFast:

Usage of fill_NA and fill_NA_N functions from miceFast - this functions should be resistant to glitches from an user activity perspective and a data structure.

data = cbind(as.matrix(mice::nhanes),intercept=1,index=1:nrow(mice::nhanes))
data_DT = data.table(data)

# simple mean imputation - intercept at position 5
data_DT[,bmi_imp:=fill_NA(x=as.matrix(.SD),
                         model="lm_bayes",
                         posit_y=2,
                         posit_x=5)] %>% 
# there is a new variable at position 7 - bmi_imp
  .[,hyp_imp:=fill_NA(x=as.matrix(.SD),
                     model="lda",
                     posit_y=3,
                     posit_x=c(1,7)),] %>% 
  .[,chl_imp:=fill_NA_N(x=as.matrix(.SD),
                       model="lm_noise",
                       posit_y=4,
                       posit_x=c(1,7,8),
                       times=10),]

head(data_DT,2)

Model with additional parameters: - data with the grouping/weighting variable

data = cbind(as.matrix(airquality[,-5]),intercept=1,index=1:nrow(airquality),
             # a numeric vector - positive values 
             weights = round(rgamma(nrow(airquality),3,3),1),
             # as.numeric is needed only for miceFast - see on next pages
             groups = airquality[,5])
data_DT = data.table(data)

# simple mean imputation - intercept at position 6
data_DT[,Ozone_imp:=fill_NA(x=as.matrix(.SD), 
                           model="lm_pred",
                           posit_y=1,
                           posit_x=c(6),w=.SD[['weights']]),by=.(groups)] %>% 
# avg of 10 multiple imputations - last posit_x equal to 9 not 10 
# because the groups variable is not included in .SD
  .[,Solar_R_imp:=fill_NA_N(as.matrix(.SD),
                           model="lm_bayes",
                           posit_y=2,
                           posit_x=c(3,4,5,6,9),w=.SD[['weights']],times=10),by=.(groups)]

data_DT[which(is.na(data_DT[,1]))[1],]

Genereting data with the corrData Module

Available constructors:

new(corrData,nr_cat,n_obs,means,cor_matrix)

new(corrData,n_obs,means,cor_matrix)

where:

relevant class methods:

type:character - possible options (“contin”,“binom”,“discrete”)

Imputing data with the miceFast Module:

Available constructors:

new(miceFast)

relevant class methods:

For a simple mean imputations add intercept to data and use “lm_pred”
The lda model is assessed only if there are more than 15 complete observations and for the lms models if the number of independent variables is smaller than the number of observations.

Imputations

miceFast module usage:

Remember that a matrix could be build only under a one data type so factor variables have to be melted use model.matrix to get numeric matrix from data.frame - see Tips in this document

#install.packages("mice")
data = cbind(as.matrix(mice::nhanes),intercept=1,index=1:nrow(mice::nhanes))
model = new(miceFast)
model$set_data(data) #providing data by a reference

model$update_var(2,model$impute("lm_pred",2,5)$imputations)
#OR not recommended
#data[,2] = model$impute("lm_pred",2,5)$imputations
#model$set_data(data) #Updating the object

model$update_var(3,model$impute("lda",3,c(1,2))$imputations) 

#Old slow syntax model$update_var(4,rowMeans(sapply(1:10,function(x) model$impute("lm_bayes",4,c(1,2,3))$imputations)))
#New syntax - impute_N
model$update_var(4,model$impute_N("lm_bayes",4,c(1,2,3),10)$imputations)

#When working with 'Big Data'
#it is recommended to occasionally manually invoke a garbage collector `gc()`

# Be careful with `update_var` because of the permanent update at the object and data
# That is why `update_var` could be used only ones for a certain column
# check which variables was updated - inside the object
model$which_updated()
## [1] 2 3 4
head(model$get_data(),3)
##      [,1]    [,2] [,3]     [,4] [,5] [,6]
## [1,]    1 26.5625    1 161.2406    1    1
## [2,]    2 22.7000    1 187.0000    1    2
## [3,]    1 26.5625    1 187.0000    1    3
head(data,3)
##   age     bmi hyp      chl intercept index
## 1   1 26.5625   1 161.2406         1     1
## 2   2 22.7000   1 187.0000         1     2
## 3   1 26.5625   1 187.0000         1     3
head(mice::nhanes,3)
##   age  bmi hyp chl
## 1   1   NA  NA  NA
## 2   2 22.7   1 187
## 3   1   NA   1 187
rm(model)

Model with additional parameters: - data sorted by the grouping variable

data = cbind(as.matrix(airquality[,-5]),intercept=1,index=1:nrow(airquality))
weights = rgamma(nrow(data),3,3) # a numeric vector - positive values
groups = as.numeric(airquality[,5]) # a numeric vector not integers - positive values - sorted increasingly

model = new(miceFast)
model$set_data(data) # providing data by a reference
model$set_w(weights) # providing by a reference
model$set_g(groups)  # providing by a reference

#impute adapt to provided parmaters like w or g
#Simple mean - permanent imputation at the object and data
model$update_var(1,model$impute("lm_pred",1,c(6))$imputations)

model$update_var(2,model$impute_N("lm_bayes",2,c(1,3,4,5,6),10)$imputations)

#Printing data and retrieving an old order
head(cbind(model$get_data(),model$get_g(),model$get_w())[order(model$get_index()),],4)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]      [,9]
## [1,]   41  190  7.4   67    1    1    1    5 0.8042191
## [2,]   36  118  8.0   72    2    1    2    5 1.5597434
## [3,]   12  149 12.6   74    3    1    3    5 0.4004544
## [4,]   18  313 11.5   62    4    1    4    5 0.4909557
head(airquality,3)
##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
head(cbind(model$get_data(),model$get_g(),model$get_w()),3)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]      [,9]
## [1,]   41  190  7.4   67    1    1    1    5 0.8042191
## [2,]   36  118  8.0   72    2    1    2    5 1.5597434
## [3,]   12  149 12.6   74    3    1    3    5 0.4004544
head(cbind(data,groups,weights),3)
##      Ozone Solar.R Wind Temp Day intercept index groups   weights
## [1,]    41     190  7.4   67   1         1     1      5 0.8042191
## [2,]    36     118  8.0   72   2         1     2      5 1.5597434
## [3,]    12     149 12.6   74   3         1     3      5 0.4004544
rm(model)

Model with additional parameters: - data not sorted by the grouping variable

data = cbind(as.matrix(airquality[,-5]),intercept = 1,index = 1:nrow(airquality))
weights = rgamma(nrow(data),3,3) # a numeric vector - positive values
#groups = as.numeric(airquality[,5]) # a numeric vector not integers - positive values
groups = as.numeric(sample(1:8,nrow(data),replace=T)) # a numeric vector not integers - positive values

model = new(miceFast)
model$set_data(data) # providing by a reference
model$set_w(weights) # providing by a reference
model$set_g(groups)  # providing by a reference
#impute adapt to provided parmaters like w or g
#Warning - if data is not sorted increasingly by the g then it would be done automatically 
#during a first imputation
#Simple mean - permanent imputation at the object and data
model$update_var(1,model$impute("lm_pred",1,6)$imputations)
## Warning in model$impute("lm_pred", 1, 6): 
##  Data was sorted by the grouping variable - use `get_index()` to retrieve an order
model$update_var(2,model$impute_N("lm_bayes",2,c(1,3,4,5,6),10)$imputations)

#Printing data and retrieving an old order
head(cbind(model$get_data(),model$get_g(),model$get_w())[order(model$get_index()),],4)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]     [,9]
## [1,]   41  190  7.4   67    1    1    1    8 1.670560
## [2,]   36  118  8.0   72    2    1    2    5 1.041644
## [3,]   12  149 12.6   74    3    1    3    5 1.680337
## [4,]   18  313 11.5   62    4    1    4    2 0.200267
head(airquality,4)
##   Ozone Solar.R Wind Temp Month Day
## 1    41     190  7.4   67     5   1
## 2    36     118  8.0   72     5   2
## 3    12     149 12.6   74     5   3
## 4    18     313 11.5   62     5   4
head(cbind(model$get_data(),model$get_g(),model$get_w()),4) #is ordered by g
##          [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]      [,9]
## [1,] 14.00000  274 10.9   68   14    1   14    1 1.3498206
## [2,] 30.00000  322 11.5   68   19    1   19    1 1.2570117
## [3,] 54.12112  266 14.9   58   26    1   26    1 0.6808177
## [4,] 54.12112  220  8.6   85    5    1   36    1 0.4164489
head(cbind(data,groups,weights),4) #is sorted by g cause we provide data by a reference
##         Ozone Solar.R Wind Temp Day intercept index groups   weights
## [1,] 14.00000     274 10.9   68  14         1    14      1 1.3498206
## [2,] 30.00000     322 11.5   68  19         1    19      1 1.2570117
## [3,] 54.12112     266 14.9   58  26         1    26      1 0.6808177
## [4,] 54.12112     220  8.6   85   5         1    36      1 0.4164489
rm(model)

Tips

matrix from data.frame

Remember that a matrix could be build only under a one data type so factor/character variables have to be melted. Sb could use model.matrix to get numeric matrix from a data.frame:

#str(mtcars)
mtcars$cyl= factor(mtcars$cyl)
mtcars$gear= factor(mtcars$gear)
mtcars_mat = model.matrix.lm(~.,mtcars,na.action="na.pass")
#str(mtcars_mat)

Variance inflation factors (VIF)

VIF measure how much the variance of the estimated regression coefficients are inflated. It helps to identify when the predictor variables are linearly related. You have to decide which variable should be delete. Values higher than 10 signal a potential collinearity problem.

airquality2 = airquality
airquality2$Temp2 = airquality2$Temp**2
#install.packages("car")
#car::vif(lm(Ozone ~ ., data=airquality2))

airquality2_mat = as.matrix(airquality2)
model = new(miceFast)
model$set_data(airquality2_mat)
as.vector(model$vifs(1,c(2,3,4,5,6,7)))
## [1]   1.176572   1.340626 227.509393   1.347135   1.011108 223.460971
data_DT = data.table(airquality2)
# VIF for variables at 1,3,4 positions - you include a y position to consider its NA values
as.vector(data_DT[,.(vifs=VIF(x=as.matrix(.SD),
                posit_y=1,
                posit_x=c(2,3,4,5,6,7)))][['vifs']])
## [1]   1.176572   1.340626 227.509393   1.347135   1.011108 223.460971

Bibliography

URL: http://dirk.eddelbuettel.com/code/rcpp/Rcpp-modules.pdf
Title: Exposing C++ functions and classes with Rcpp modules Dirk Eddelbuettel and Romain François
Author: http://dirk.eddelbuettel.com and https://romain.rbind.io/
Date: March 8, 2018

URL: http://dirk.eddelbuettel.com/papers/RcppArmadillo-intro.pdf
Title: RcppArmadillo: Easily Extending R with High-Performance C++ Code
Author: Dirk Eddelbuettel and Conrad Sanderson
Date: July 1, 2012

URL: http://www.stefvanbuuren.nl/publications/MICE%20in%20R%20-%20Draft.pdf
Title: MICE: Multivariate Imputation by Chained Equations in R
Author: Stef van Buuren
Date: 2013

URL: http://dirk.eddelbuettel.com/code/rcpp/Rcpp-introduction.pdf
Title: Extending R with C++: A Brief Introduction to Rcpp
Author: Dirk Eddelbuettel and James Joseph Balamuta
Date: March 8, 2018

URL: http://courses.cs.tamu.edu/rgutier/csce666_f13/
Title: CSCE 666: Pattern Analysis
Author: Ricardo Gutierrez-Osuna
Date: Fall 2013


  1. Environment: MRO 3.4.4 Intel MKL - i7 6700HQ and 24GB DDR4 2133. MRO (Microsoft R Open) provide to R a sophisticated library for linear algebra operations so remember about that when reading a performance comparison.