library(miceFast);library(data.table);library(magrittr);library(mice);library(car);library(dplyr);library(ggplot2)
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:

• Linear Discriminant Analysis around (x5)
• where a grouping variable have to be used (around x10 depending on data dimensions and number of groups and even more than x100 although compared to data.table only a few times faster or even the same) because of pre-sorting by grouping variable
• multiple imputations is faster around x(a number of multiple imputations) because the core of a model is evaluated only ones.
• Variance inflation factors (VIF) (x5) because the unnecessary linear regression is not evaluated - we need only inverse of X’X

Example (2019-08-07):

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/dplyr 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

# airquality dataset with additional variables
data(air_miss)

### Intro: data.table

# VIF - values bigger than 10 (around) suggest that there might be a collinearity problem.
# VIF is high for Solar.R and x_character which is obvious - x_character is a factor version of numeric Solar.R
air_miss[,.(VIF(.SD,posit_y='Ozone',
posit_x=c('Solar.R',
'Wind',
'Temp',
'x_character',
'Day',
'weights',
'groups')))] 
##           V1
## 1: 24.745513
## 2:  1.454293
## 3:  3.185972
## 4: 41.604156
## 5:  1.098760
## 6:  1.162264
## 7:  3.068433
# IMPUTATIONS
# Imputations with a grouping option (models are separately assessed for each group)
# taking into account provided weights
air_miss[,Solar_R_imp := fill_NA_N(x=.SD,
model="lm_bayes",
posit_y='Solar.R',
posit_x=c('Wind','Temp','Intercept'),
w=.SD[['weights']],
times=100),by=.(groups)] %>%
# Imputations - discrete variable
.[,x_character_imp := fill_NA(x=.SD,
model="lda",
posit_y='x_character',
posit_x=c('Wind','Temp','groups'))] %>%
# logreg was used because almost log-normal distribution of Ozone
# imputations around mean
.[,Ozone_imp1 := fill_NA(x=.SD,
model="lm_bayes",
posit_y='Ozone',
posit_x=c('Intercept'),
logreg=TRUE)] %>%
# imputations using positions - Intercept, Temp
.[,Ozone_imp2 := fill_NA(x=.SD,
model="lm_bayes",
posit_y=1,
posit_x=c(4,6),
logreg=TRUE)] %>%
# model with a factor independent variable
# multiple imputations (average of x30 imputations)
# with a factor independent variable, weights and logreg options
.[,Ozone_imp3 := fill_NA_N(x=.SD,
model="lm_noise",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.SD[['weights']],
logreg=TRUE,
times=30)] %>%
.[,Ozone_imp4 := fill_NA_N(x=.SD,
model="lm_bayes",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.SD[['weights']],
logreg=TRUE,
times=30)] %>%
.[,Ozone_imp5 := fill_NA(x=.SD,
model="lm_pred",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.SD[['weights']],
logreg=TRUE),.(groups)] %>%

# Average of a few methods
.[,Ozone_imp_mix := apply(.SD,1,mean),.SDcols=Ozone_imp1:Ozone_imp5] %>%

# Protecting against collinearity or low number of observations - across small groups
# Be carful when using a data.table grouping option
# because of lack of protection against collinearity or low number of observations.
# There could be used a tryCatch(fill_NA(...),error=function(e) return(...))

.[,Ozone_chac_imp := tryCatch(fill_NA(x=.SD,
model="lda",
posit_y='Ozone_chac',
posit_x=c('Intercept','Month','Day','Temp','x_character_imp'),
w=.SD[['weights']]),
error=function(e) .SD[['Ozone_chac']]),.(groups)] 

### Intro: dplyr

# VIF - values bigger than 10 (around) suggest that there might be a collinearity problem.
# VIF is high for Solar.R and x_character which is obvious - x_character is a factor version of numeric Solar.R
air_miss %>% do(vifs=VIF(.,posit_y='Ozone',
posit_x=c('Solar.R',
'Wind',
'Temp',
'x_character',
'Day',
'weights',
'groups'))) %>% unlist()
##     vifs1     vifs2     vifs3     vifs4     vifs5     vifs6     vifs7
## 24.745513  1.454293  3.185972 41.604156  1.098760  1.162264  3.068433
# IMPUTATIONS
air_miss = air_miss %>%
# Imputations with a grouping option (models are separately assessed for each group)
# taking into account provided weights
group_by(groups) %>%
do(mutate(.,Solar_R_imp = fill_NA(x=.,
model="lm_pred",
posit_y='Solar.R',
posit_x=c('Wind','Temp','Intercept'),
w=.[['weights']]))) %>%
ungroup() %>%
# Imputations - discrete variable
mutate(x_character_imp = fill_NA(x=.,
model="lda",
posit_y='x_character',
posit_x=c('Wind','Temp'))) %>%
# logreg was used because almost log-normal distribution of Ozone
# imputations around mean
mutate(Ozone_imp1 = fill_NA(x=.,
model="lm_bayes",
posit_y='Ozone',
posit_x=c('Intercept'),
logreg=TRUE)) %>%
# imputations using positions - Intercept, Temp
mutate(Ozone_imp2 = fill_NA(x=.,
model="lm_bayes",
posit_y=1,
posit_x=c(4,6),
logreg=TRUE)) %>%
# multiple imputations (average of x30 imputations)
# with a factor independent variable, weights and logreg options
mutate(Ozone_imp3 = fill_NA_N(x=.,
model="lm_noise",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.[['weights']],
logreg=TRUE,
times=30)) %>%
mutate(Ozone_imp4 = fill_NA_N(x=.,
model="lm_bayes",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.[['weights']],
logreg=TRUE,
times=30)) %>%
group_by(groups) %>%
do(mutate(.,Ozone_imp5 = fill_NA(x=.,
model="lm_pred",
posit_y='Ozone',
posit_x=c('Intercept','x_character_imp','Wind','Temp'),
w=.[['weights']],
logreg=TRUE))) %>%
ungroup() %>%
# Average of a few methods
mutate(Ozone_imp_mix = rowMeans(select(.,starts_with("Ozone_imp")))) %>%

# Protecting against collinearity or low number of observations - across small groups
# Be carful when using a data.table grouping option
# because of lack of protection against collinearity or low number of observations.
# There could be used a tryCatch(fill_NA(...),error=function(e) return(...))
group_by(groups) %>%
do(mutate(.,Ozone_chac_imp = tryCatch(fill_NA(x=.,
model="lda",
posit_y='Ozone_chac',
posit_x=c('Intercept','Month','Day','Temp','x_character_imp'),
w=.[['weights']]),
error=function(e) .[['Ozone_chac']]))) %>%
ungroup()

### results - visualization

# Distribution of imputations vs Distribution of initial data
air_miss$Ozone_NA = ifelse(is.na(air_miss$Ozone),'imputations','complete')
air_miss = as.data.table(air_miss)

air_miss[,c('Ozone','Ozone_imp_mix','Ozone_NA')] %>%
melt(id=c('Ozone_NA'),measure=c('Ozone','Ozone_imp_mix')) %>%
.[(((Ozone_NA=='imputations') & (variable=='Ozone_imp_mix'))|((Ozone_NA=='complete') & (variable=='Ozone'))),] %>%
ggplot2::ggplot(.,ggplot2::aes(x=value,fill=variable)) +
ggplot2::geom_density() + ggplot2::facet_wrap(Ozone_NA ~.,scales='free')

## 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:

• nr_cat : number of categories for discrete dependent variable
• n_obs : number of observations
• means: center independent variables
• cor_mat : positive defined correlation matrix

relevant class methods:

• fill("type") : generating data [return a numeric matrix] - data with correlated variables where first variable is of binomial,discrete or continuous type.

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

## Imputing data with the miceFast Module:

Available constructors:

new(miceFast)

relevant class methods:

• set_data(x) - providing the data by a reference - a numeric matrix [void]
• get_data() - retrieving the data [return a numeric matrix] - the same values as provided by reference x, recommended to use x directly
• set_g(g) - providing the grouping variable by a reference - a numeric vector - positive values [void]
• get_g() - retrieving the grouping variable [return a numeric vector] - the same values as provided by reference g, recommended to use g directly
• set_w(w) - providing the weighting variable by a reference - a numeric vector - positive values
• get_w() - retrieving the weighting variable [return a numeric vector] - the same values as provided by reference w, recommended to use w directly
• get_index() - getting the index [return a integer vector] - useful after automatic sorting procedure
• impute("model",posit_y,posit_x) - impute data under characteristics form object like a optional grouping or weighting variable [return a list with 3 vectors: a numeric vector “imputations” dependent variable with replaced Na values, a integer vector “index_imputed” positions where data was imputed, a integer vector “index_full” positions which were used to assess the model]
• impute_N("model2",posit_y,posit_x,times) - multiple imputations - impute data under characteristics form object like a optional grouping or weighting variable - works for (“lm_bayes”,“lm_noise”) - [return a list with 3 vectors: a numeric vector “imputations” dependent variable with replaced Na values by average of N results, a integer vector “index_imputed” positions where data was imputed, a integer vector “index_full” positions which were used to assess the model]
• update_var(posit_y,imputations) - permanently update variable at the object and data. WARNING, use it only if you are sure about model parameters. [void]
• get_models() - possible quantitative models for a certain type of dependent variable [return a character vector: recommended models for impute and impute_N methods]
• get_model() - a recommended quantitative model for a certain type of dependent variable [return a character: recommended model for impute and impute_N methods] - useful while looping
• which_updated() - which variables were modified by update_var at the object (and data) [return a integer vector: positions at provided data at which variables were update by update_var method]
• sort_byg() - sort data by the grouping variable [void]
• is_sorted_byg() - is data sorted by the grouping variable [void]
• vifs(posit_y,posit_x) - Variance inflation factors (VIF) [return a numeric vector: VIF for all variables provided by posit_x] x : numeric matrix - variables
g : numeric vector - you could build it form several discrete variables
w: numeric vector with positive values - weights for weighted linear regressions
model: character - a possible options (“lda”,“lm_pred”,“lm_bayes”,“lm_noise”)
posit_y: integer - a position of dependent variable
posit_x: integer vector - positions of independent variables
imputations : numeric vector - imputations
times : integer - number of multiple imputations

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    1 159.0947    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   1 159.0947         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$get_index()),],4) ## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] ## [1,] 41 190 7.4 67 1 1 1 5 1.2809043 ## [2,] 36 118 8.0 72 2 1 2 5 0.3350294 ## [3,] 12 149 12.6 74 3 1 3 5 0.1997905 ## [4,] 18 313 11.5 62 4 1 4 5 0.9479004 head(airquality,3) ## Ozone Solar.R Wind Temp Month Day ## 1 41 190 7.4 67 5 1 ## 2 36 118 8.0 72 5 2 ## 3 12 149 12.6 74 5 3 head(cbind(model$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 1.2809043
## [2,]   36  118  8.0   72    2    1    2    5 0.3350294
## [3,]   12  149 12.6   74    3    1    3    5 0.1997905
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 1.2809043
## [2,]    36     118  8.0   72   2         1     2      5 0.3350294
## [3,]    12     149 12.6   74   3         1     3      5 0.1997905
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    2 1.4921661
## [2,]   36  118  8.0   72    2    1    2    4 1.0500448
## [3,]   12  149 12.6   74    3    1    3    6 0.9895894
## [4,]   18  313 11.5   62    4    1    4    2 0.9625453
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$get_w()),4) #is ordered by g ## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] ## [1,] 28.00000 267.9306 14.9 66 6 1 6 1 0.2724912 ## [2,] 8.00000 19.0000 20.1 61 9 1 9 1 1.3350642 ## [3,] 22.72215 194.0000 8.6 69 10 1 10 1 0.2948290 ## [4,] 22.72215 287.0000 9.7 74 2 1 33 1 1.1360816 head(cbind(data,groups,weights),4) #is sorted by g cause we provide data by a reference ## Ozone Solar.R Wind Temp Day intercept index groups weights ## [1,] 28.00000 267.9306 14.9 66 6 1 6 1 0.2724912 ## [2,] 8.00000 19.0000 20.1 61 9 1 9 1 1.3350642 ## [3,] 22.72215 194.0000 8.6 69 10 1 10 1 0.2948290 ## [4,] 22.72215 287.0000 9.7 74 2 1 33 1 1.1360816 rm(model) ### Tips matrix from data.frame Remember that a matrix could be build only under a one data type so factor/character variables have to be melted. Sb could use model.matrix to get numeric matrix from a data.frame: #str(mtcars) mtcars$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$Temp**2 airquality2$Month = factor(airquality2\$Month)

car::vif(lm(Ozone ~ ., data=airquality2))
##               GVIF Df GVIF^(1/(2*Df))
## Solar.R   1.230156  1        1.109124
## Wind      1.415414  1        1.189712
## Temp    264.800283  1       16.272685
## Month     2.774325  4        1.136043
## Day       1.038574  1        1.019105
## Temp2   249.766363  1       15.803998
data_DT = data.table(airquality2)
data_DT[,.(vifs=VIF(x=.SD,
posit_y='Ozone',
posit_x=c('Solar.R','Wind','Temp','Month','Day','Temp2'),correct=FALSE))][['vifs']]
## [1]   1.230156   1.415414 264.800283   2.774325   1.038574 249.766363
data_DT[,.(vifs=VIF(x=.SD,
posit_y=1,
posit_x=c(2,3,4,5,6,7),correct=TRUE))][['vifs']]
## [1]  1.109124  1.189712 16.272685  1.136043  1.019105 15.803998

## 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

Title: RcppArmadillo: Easily Extending R with High-Performance C++ Code
Author: Dirk Eddelbuettel and Conrad Sanderson
Date: July 1, 2012

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

Title: MICE: Multivariate Imputation by Chained Equations in R
Author: Stef van Buuren
Date: 2013

Title: CSCE 666: Pattern Analysis
Author: Ricardo Gutierrez-Osuna
Date: Fall 2013

1. Environment: MRO 3.5.3 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.