### Load and prepare the ozone dataset

Source: http://factominer.free.fr/missMDA/ozone.R

Imports the ozone dataset from a URL and separates continuous variables for analysis.

```R
don <- read.table("http://factominer.free.fr/missMDA/ozoneNA.csv",header=TRUE,sep=",",row.names=1, stringsAsFactors = TRUE)
WindDirection <- don[,12]
don <- don[,1:11]           #### keep the continuous variables
```

--------------------------------

### Visualize Missing Data Patterns

Source: http://factominer.free.fr/missMDA/ecological.csv

Uses the VIM package to aggregate missing data patterns and MCA to visualize the structure of missingness.

```R
#### Visualize the pattern
library(VIM)
aggr(Ecolo)
aggr(Ecolo,only.miss=TRUE,numbers=TRUE,sortVar=TRUE)
res <- summary(aggr(Ecolo,prop=TRUE,combined=TRUE))$combinations
res[rev(order(res[,2])),]

mis.ind <- matrix("o",nrow=nrow(Ecolo),ncol=ncol(Ecolo))
mis.ind[is.na(Ecolo)] <- "m"
dimnames(mis.ind) <- dimnames(Ecolo)
library(FactoMineR)
resMCA <- MCA(mis.ind)
plot(resMCA,invis="ind",title="MCA graph of the categories")
```

--------------------------------

### Estimate parameters using EM algorithm

Source: http://factominer.free.fr/missMDA/ozone.R

Uses the norm package to estimate mean and covariance parameters via the EM algorithm.

```R
library(norm)
pre <- prelim.norm(as.matrix(don))
thetahat <- em.norm(pre)
getparam.norm(pre,thetahat)
```

--------------------------------

### Perform multiple imputation

Source: http://factominer.free.fr/missMDA/ozone.R

Implements multiple imputation using Amelia, mice, and missMDA packages.

```R
don <- read.table("ozoneNA.csv",header=TRUE,sep=",",row.names=1)
WindDirection <- don[,12]
don <- don[,1:11]           #### keep the continuous variables

library(Amelia)
res.amelia <- amelia(don,m=100,p2s=0)

library(mice)
res.mice <- mice(don,m=100,defaultMethod="norm", printFlag=F) # here the variability of the regression parameters is obtained by bootstrap

library(missMDA)
res.MIPCA <- MIPCA(don,ncp=2)
```

--------------------------------

### Visualize missing data patterns

Source: http://factominer.free.fr/missMDA/ozone.R

Uses the VIM package to aggregate and plot missing value distributions and associations.

```R
library(VIM)
aggr(don)
aggr(don,only.miss=TRUE,sortVar=TRUE)
res <- summary(aggr(don,prop=TRUE,combined=TRUE))$combinations
res[rev(order(res[,2])),]
 
matrixplot(don,sortby=2)
marginplot(don[,c("T9","maxO3")])
```

--------------------------------

### Create categorical missing indicator matrix

Source: http://factominer.free.fr/missMDA/ozone.R

Generates a matrix identifying observed ('o') and missing ('m') values, followed by Multiple Correspondence Analysis.

```R
# Creation of a categorical data set with "o" when observed and "m" when missing
mis.ind <- matrix("o",nrow=nrow(don),ncol=ncol(don))
mis.ind[is.na(don)] <- "m"
dimnames(mis.ind) <- dimnames(don)
mis.ind

# Performing a multiple correspondence analysis to visualize the association
library(FactoMineR)
resMCA <- MCA(mis.ind)
plot(resMCA,invis="ind",title="MCA graph of the categories")
```

--------------------------------

### Visualize and pool multiple imputation results

Source: http://factominer.free.fr/missMDA/ozone.R

Checks imputation quality via density plots and pools regression results across imputed datasets.

```R
## Checking and visualization of the imputations 
plot(res.amelia)
par(mfrow=c(1,1))
compare.density(res.amelia, var="T12")
overimpute(res.amelia, var="maxO3")
# visualization with PCA 
plot(res.MIPCA,choice= "ind.supp"); plot(res.MIPCA,choice="var")

## Pooling the results 

lm.mice.out <- with(res.mice, lm(maxO3 ~ T9+T12+T15+Ne9+Ne12+Ne15+Vx9+Vx12+Vx15+maxO3v))
pool.mice <- pool(lm.mice.out)
resultmice <- summary(pool.mice)

require(mice)
imp<-prelim(res.mi=res.MIPCA,X=ozone[,1:11])
fit <- with(data=imp,exp=lm(maxO3~T9+T12+T15+Ne9+Ne12+Ne15+Vx9+Vx12+Vx15+maxO3v))
res.pool<-pool(fit)
summary(res.pool)
```

--------------------------------

### Visualize imputation uncertainty

Source: http://factominer.free.fr/missMDA/PCA.html

Visualizes the uncertainties generated by multiple imputation in a PCA context.

```R
library(missMDA)  
 data(orange)  
 nb = estim_ncpPCA(orange,ncp.max=5)  
  res.comp = MIPCA(orange, ncp = nbdim$ncp, nboot = 1000)  
 plot(res.comp) 
```

--------------------------------

### Load and Clean Ecological Data

Source: http://factominer.free.fr/missMDA/ecological.csv

Imports the dataset and removes species rows that contain only missing values for continuous variables.

```R
Ecolo <- read.csv("ecological.csv", header = TRUE, sep=";",dec=",",stringsAsFactors = TRUE)

## Delete species with only missing values for contiuous variables
ind <- which(rowSums(is.na(Ecolo[,-1])) == 6)
biome <- Ecolo[-ind,1]    ### Keep a categorical variable
Ecolo <- Ecolo[-ind,-1]   ### Select continuous variables
dim(Ecolo)
```

--------------------------------

### Impute and Analyze Data

Source: http://factominer.free.fr/missMDA/ecological.csv

Performs PCA imputation using missMDA and visualizes the results with PCA.

```R
### Impute the incomplete data set
library(missMDA)
### nb <- estim_ncpPCA(Ecolo,method.cv="Kfold",nbsim=100) ### Time consuming!
res.comp <- imputePCA(Ecolo,ncp=2)

#Perform a PCA on the completed data set
imp <- cbind.data.frame(res.comp$completeObs,biome)
res.pca <- PCA(imp,quali.sup=7,graph=FALSE)
plot(res.pca, hab=7, lab="quali")
plot(res.pca, hab=7, lab="quali",invisible="ind")
plot(res.pca, choix="var")
```

--------------------------------

### Perform multiple imputation for PCA

Source: http://factominer.free.fr/missMDA/PCA.html

Generates multiple imputed datasets using the PCA model to account for uncertainty.

```R
library(missMDA)  
 data(orange)  
 nb = estim_ncpPCA(orange,ncp.max=5)  
  res.comp = MIPCA(orange, ncp = nbdim$ncp, nboot = 1000)  
 
```

--------------------------------

### Perform single imputation

Source: http://factominer.free.fr/missMDA/ozone.R

Demonstrates single imputation using normal distribution draws or PCA-based methods.

```R
## Single imputation using a draw from a normal distribution
library(norm)
pre <- prelim.norm(as.matrix(don))
thetahat <- em.norm(pre)
rngseed(123)           ### must be done!
imp <- imp.norm(pre,thetahat,don)

## Single imputation with PCA 
library(missMDA)
nb <- estim_ncpPCA(don)
nb$ncp 
plot(0:5,nb$criterion,xlab="dim",ylab="MSEP")
res.comp <- imputePCA(don,ncp=2)
res.comp$completeObs
indvar="T9"
indNA=which(is.na(don[,indvar]))
plot(density(res.comp$completeObs[indNA,indvar]),main="Observed and imputed values for T9",xlab="T9")
lines(density(res.comp$completeObs[which(!((1:nrow(don))%in%indNA)),indvar]),col="red")
legend("topleft",text.col=c("black","red"),legend=c("Observed values","Imputations"))
#Performing a PCA on the completed data set
imp <- cbind.data.frame(res.comp$completeObs, WindDirection)
res.pca <- PCA(imp,quanti.sup=1,quali.sup=12)
plot(res.pca, hab=12, lab="quali")
plot(res.pca, choix="var")
res.pca$ind$coord #scores (principal components)
res.pca$var$coord
```

--------------------------------

### Analyze Missing Value Proportions

Source: http://factominer.free.fr/missMDA/ecological.csv

Calculates the overall proportion of missing values and checks the impact of listwise deletion.

```R
## proportion of missing values
sum(is.na(Ecolo))/(nrow(Ecolo)*ncol(Ecolo)) # 55% of missing values

## Delete species with missing values
dim(na.omit(Ecolo)) # only 72 remaining species!
```

--------------------------------

### Visualize Imputation Uncertainty with MIPCA

Source: http://factominer.free.fr/missMDA/trustMI.html

Estimate the number of dimensions for imputation and plot the results to assess uncertainty.

```R
library(missMDA)  
 data(orange)  
 nbdim = estim_ncpPCA(orange) # estimate the number of dimensions to impute  
  plot(res.comp)
```

--------------------------------

### Perform Multiple Imputation with PCA

Source: http://factominer.free.fr/missMDA/MI.html

Estimates the number of dimensions and performs multiple imputation for continuous data using PCA.

```R
library(missMDA)  
 data(orange)  
 nbdim = estim_ncpPCA(orange,ncp.max=5)  
  res.comp = MIPCA(orange, ncp = nbdim$ncp, nboot = 1000)  
 plot(res.comp)  
```

--------------------------------

### Perform Multiple Imputation with MCA

Source: http://factominer.free.fr/missMDA/MI.html

Estimates the number of dimensions and performs multiple imputation for qualitative data using MCA.

```R
library(missMDA)  
 data(vnf)  
 nbdim = estim_ncpMCA(vnf,ncp.max=5) ## Time-consuming, nb = 4  
  res = MIMCA(vnf, ncp=4,nboot=10)  
 plot(res) 
```

--------------------------------

### Impute missing values for PCA

Source: http://factominer.free.fr/missMDA/PCA.html

Estimates the optimal number of dimensions and imputes missing values in a dataset before performing PCA.

```R
library(missMDA)  
 data(orange)  
 nb = estim_ncpPCA(orange,ncp.max=5)  
  res.comp = imputePCA(orange,ncp=2)  
 res.pca = PCA(res.comp$completeObs)  
```

--------------------------------

### Impute missing values and perform MCA

Source: http://factominer.free.fr/missMDA/MCA.html

Estimates the number of dimensions, imputes the disjunctive data table, and performs MCA on the completed matrix.

```R
library(missMDA)  
 data(vnf)  
 nb = estim_ncpMCA(vnf,ncp.max=5)  
  tab.disj.comp = imputeMCA(vnf, ncp=4)$tab.disj  
 res.mca = MCA(vnf,tab.disj=tab.disj.comp) 
```

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