---
title: "Handling Missing Values with plssem"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Handling Missing Values with plssem}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = FALSE
)

library(plssem)
```

The `pls()` function offers some very basic approaches for handling missing
values in the data, specified via the `missing` argument. Currently, 
there are three options.

  1. Listwise deletion (`missing = "listwise"`)
  2. Mean imputation (`missing = "mean"`)
  3. k nearest neighbors (kNN) imputation (`missing = "kNN"`)

The last two options are single imputation approaches. The `pls()` function
does not currently offer any multiple imputation approaches, but we show
how this can be done by the user itself, using the `mice` package, at the
end of the vignette.

# Listwise Deletion

With `missing="listwise"` (the default) any observation (i.e., a row) containing
missing values for the variables used in the model are removed. Here we
can see an example.

```{r}
model <- "Survived ~ Age + Female + Age:Female"
fit <- pls(model, data = titanic, missing = "listwise", ordered = "Survived")
```

# Mean Imputation

With `missing="mean"` missing values are imputed with (univariate) expected 
values. For continous values missing values are imputed using the mean.
For ordinal variables with more than two categories, missing values are imputed
with the median. For binary ordered variables missing values are imputed
with the mode.

In our example, missing values in `Age` are imputed with the mean of age.
Both `Survived` and `Female` are binary variables, where the missing values
get imputed with the most common value.

```{r}
model <- "Survived ~ Age + Female + Age:Female"
fit <- pls(model, data = titanic, missing = "mean", ordered = "Survived")
```

# kNN Imputation

With `missing="kNN"` missing values are imputed by finding the k nearest 
(complete data) neighbors of an observation with missing data. The values
of the values of the k neighbors are then aggregated using either the mean, median or the
mode, depending on the data type of the variable. The k number of neighbors
to be used, can be specified using the `knn.k` argument.

```{r}
model <- "Survived ~ Age + Female + Age:Female"
fit <- pls(model, data = titanic, missing = "kNN",
           ordered = "Survived", knn.k = 5) # use the 5 nearest neighbors
```

# Multiple Imputation

Multiple imputation cannot be performed just using the `pls()` function,
but it can be performed using other available multiple imputation packages
in `R`. Here we use the `mice` package, but other packages can be used
as well (e.g., the `Amelia` package).

```{r}
library(mice)

m <- 20 # Number of imputations
vars <- c("Survived", "Age", "Female") # Variables to impute/use in the analysis

imputations <- mice(titanic[vars], m = m)

COEF <- NULL # Matrix with estimated coefficients for each imputation
BOOT <- NULL # Matrix with all the bootstraps from all imputations

model <- "Survived ~ Age + Female + Age:Female"

for (i in seq_len(m)) {
  fit.i <- pls(model, data = complete(imputations, i), # get the ith imputation
               ordered = "Survived",
               bootstrap = TRUE,
               boot.R = 100,
               boot.parallel = "multicore", # Use parallel bootstrap
               boot.ncpus = 2L)

  COEF <- rbind(COEF, coef(fit.i))
  BOOT <- rbind(BOOT, boot(fit.i))
}

apply(COEF, MARGIN = 2, FUN = mean) # Mean estimate across imputations
apply(BOOT, MARGIN = 2, FUN = sd)   # Standard errors
```
