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# Remove most objects from the working environment
rm(list = ls())
options(stringsAsFactors = F)
# 18.2. Identifying missing values
# install.packages("VIM")
data(sleep, package="VIM")
# list the rows that do not have missing values
sleep[complete.cases(sleep),]
# list the rows that have one or more missing values
sleep[!complete.cases(sleep),]
sum(is.na(sleep$Dream))
# [1] 12
mean(is.na(sleep$Dream))
# [1] 0.1935484
mean(!complete.cases(sleep))
# [1] 0.3225806
# 18.3.1. Tabulating missing values
# install.packages("mice")
library(mice)
data(sleep, package = "VIM")
md.pattern(sleep) # figure 18.2
# 18.3.2. Exploring missing data visually
library("VIM")
aggr(sleep, prop=FALSE, numbers=TRUE) # figure 18.2-2
matrixplot(sleep, sortby = "BrainWgt") # figure 18.3
marginplot(sleep[c("Gest", "Dream")], pch = c(20),
col = c("darkgray", "red", "blue")) # figure 18.4
# 18.3.3. Using correlations to explore missing values
x <- as.data.frame(abs(is.na(sleep)))
head(sleep, 5)
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# 1 6654.000 5712.0 NA NA 3.3 38.6 645 3 5 3
# 2 1.000 6.6 6.3 2.0 8.3 4.5 42 3 1 3
# 3 3.385 44.5 NA NA 12.5 14.0 60 1 1 1
# 4 0.920 5.7 NA NA 16.5 NA 25 5 2 3
# 5 2547.000 4603.0 2.1 1.8 3.9 69.0 624 3 5 4
head(x, 5)
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# 1 0 0 1 1 0 0 0 0 0 0
# 2 0 0 0 0 0 0 0 0 0 0
# 3 0 0 1 1 0 0 0 0 0 0
# 4 0 0 1 1 0 1 0 0 0 0
# 5 0 0 0 0 0 0 0 0 0 0
y <- x[which(apply(x, 2, sum) > 0)]
cor(y)
# NonD Dream Sleep Span Gest
# NonD 1.00000000 0.90711474 0.48626454 0.01519577 -0.14182716
# Dream 0.90711474 1.00000000 0.20370138 0.03752394 -0.12865350
# Sleep 0.48626454 0.20370138 1.00000000 -0.06896552 -0.06896552
# Span 0.01519577 0.03752394 -0.06896552 1.00000000 0.19827586
# Gest -0.14182716 -0.12865350 -0.06896552 0.19827586 1.00000000
cor(sleep, y, use = "pairwise.complete.obs")
# NonD Dream Sleep Span Gest
# BodyWgt 0.22682614 0.22259108 0.001684992 -0.05831706 -0.05396818
# BrainWgt 0.17945923 0.16321105 0.007859438 -0.07921370 -0.07332961
# NonD NA NA NA -0.04314514 -0.04553485
# Dream -0.18895206 NA -0.188952059 0.11699247 0.22774685
# Sleep -0.08023157 -0.08023157 NA 0.09638044 0.03976464
# Span 0.08336361 0.05981377 0.005238852 NA -0.06527277
# Gest 0.20239201 0.05140232 0.159701523 -0.17495305 NA
# Pred 0.04758438 -0.06834378 0.202462711 0.02313860 -0.20101655
# Exp 0.24546836 0.12740768 0.260772984 -0.19291879 -0.19291879
# Danger 0.06528387 -0.06724755 0.208883617 -0.06666498 -0.20443928
#=======================================================================
# 18.6. Complete-case analysis(listwise deletion)
options(digits = 1)
cor(na.omit(sleep))
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# BodyWgt 1.00 0.96 -0.4 -0.07 -0.3 0.47 0.71 0.10 0.4 0.26
# BrainWgt 0.96 1.00 -0.4 -0.07 -0.3 0.63 0.73 -0.02 0.3 0.15
# NonD -0.39 -0.39 1.0 0.52 1.0 -0.37 -0.61 -0.35 -0.6 -0.53
# Dream -0.07 -0.07 0.5 1.00 0.7 -0.27 -0.41 -0.40 -0.5 -0.57
# Sleep -0.34 -0.34 1.0 0.72 1.0 -0.38 -0.61 -0.40 -0.6 -0.60
# Span 0.47 0.63 -0.4 -0.27 -0.4 1.00 0.65 -0.17 0.3 0.01
# Gest 0.71 0.73 -0.6 -0.41 -0.6 0.65 1.00 0.09 0.6 0.31
# Pred 0.10 -0.02 -0.4 -0.40 -0.4 -0.17 0.09 1.00 0.6 0.93
# Exp 0.41 0.32 -0.6 -0.50 -0.6 0.32 0.57 0.63 1.0 0.79
# Danger 0.26 0.15 -0.5 -0.57 -0.6 0.01 0.31 0.93 0.8 1.00
# alternative
# cor(sleep, use="complete.obs)
#========================================================================
fit <- lm(Dream ~ Span + Gest, data = na.omit(sleep))
summary(fit)
# Call:
# lm(formula = Dream ~ Span + Gest, data = na.omit(sleep))
#
# Residuals:
# Min 1Q Median 3Q Max
# -2.333 -0.915 -0.221 0.382 4.183
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 2.480122 0.298476 8.31 3.7e-10 ***
# Span -0.000472 0.013130 -0.04 0.971
# Gest -0.004394 0.002081 -2.11 0.041 *
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 1 on 39 degrees of freedom
# Multiple R-squared: 0.167, Adjusted R-squared: 0.125
# F-statistic: 3.92 on 2 and 39 DF, p-value: 0.0282
# 18.7. Multiple imputation
library(mice)
data(sleep, package = "VIM")
imp <- mice(sleep, seed = 1234)
fit <- with(imp, lm(Dream ~ Span + Gest))
pooled <- pool(fit)
summary(pooled)
# term estimate std.error statistic df p.value
# 1 (Intercept) 2.597 0.249 10.4 52 2e-14
# 2 Span -0.004 0.012 -0.3 56 7e-01
# 3 Gest -0.004 0.001 -3.0 55 5e-03
imp
# Class: mids
# Number of multiple imputations: 5
# Imputation methods:
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# "" "" "pmm" "pmm" "pmm" "pmm" "pmm" "" "" ""
# PredictorMatrix:
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# BodyWgt 0 1 1 1 1 1 1 1 1 1
# BrainWgt 1 0 1 1 1 1 1 1 1 1
# NonD 1 1 0 1 1 1 1 1 1 1
# Dream 1 1 1 0 1 1 1 1 1 1
# Sleep 1 1 1 1 0 1 1 1 1 1
# Span 1 1 1 1 1 0 1 1 1 1
# Number of logged events: 5
# it im dep meth out
# 1 3 2 Span pmm Sleep
# 2 3 2 Gest pmm Sleep
# 3 4 2 Span pmm Sleep
# 4 4 2 Gest pmm Sleep
# 5 4 4 Span pmm Sleep
imp$imp$Dream
# 1 2 3 4 5
# 1 0.0 0.5 0.5 0.5 0.3
# 3 0.5 1.4 1.5 1.5 1.3
# 4 3.6 4.1 3.1 4.1 2.7
# 14 0.3 1.0 0.5 0.0 0.0
# 24 3.6 0.8 1.4 1.4 0.9
# 26 2.4 0.5 3.9 3.4 1.2
# 30 2.6 0.8 2.4 2.2 3.1
# 31 0.6 1.3 1.2 1.8 2.1
# 47 1.3 1.8 1.8 1.8 3.9
# 53 0.5 0.5 0.6 0.5 0.3
# 55 2.6 3.6 2.4 1.8 0.5
# 62 1.5 3.4 3.9 3.4 2.2
str(imp)
options(digits = 3)
dataset3 <- complete(imp, action = 3)
head(dataset3,10)
# 18.8.1. Pairwise deletion
cor(sleep, use = "pairwise.complete.obs")
# BodyWgt BrainWgt NonD Dream Sleep Span Gest Pred Exp Danger
# BodyWgt 1.0000 0.9342 -0.376 -0.109 -0.307 0.3025 0.651 0.0595 0.338 0.1336
# BrainWgt 0.9342 1.0000 -0.369 -0.105 -0.358 0.5093 0.747 0.0339 0.368 0.1459
# NonD -0.3759 -0.3692 1.000 0.514 0.963 -0.3844 -0.595 -0.3182 -0.544 -0.4839
# Dream -0.1094 -0.1051 0.514 1.000 0.727 -0.2957 -0.451 -0.4475 -0.537 -0.5793
# Sleep -0.3072 -0.3581 0.963 0.727 1.000 -0.4102 -0.631 -0.3958 -0.642 -0.5877
# Span 0.3025 0.5093 -0.384 -0.296 -0.410 1.0000 0.615 -0.1025 0.360 0.0618
# Gest 0.6511 0.7472 -0.595 -0.451 -0.631 0.6148 1.000 0.2005 0.638 0.3786
# Pred 0.0595 0.0339 -0.318 -0.447 -0.396 -0.1025 0.201 1.0000 0.618 0.9160
# Exp 0.3383 0.3678 -0.544 -0.537 -0.642 0.3604 0.638 0.6182 1.000 0.7872
# Danger 0.1336 0.1459 -0.484 -0.579 -0.588 0.0618 0.379 0.9160 0.787 1.0000
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