---
title: "Cellwise Robust Multi-Group Gaussian Mixture Model"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Cellwise Robust Multi-Group Gaussian Mixture Model}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  warning = FALSE, 
  fig.dim = c(7, 4.5),
  comment = "#>"
)
```


This vignette reproduces the weather example described in Puchhammer, Wilms and Filzmoser (2025). The original data is from Geosphere Austria (2022) and included in this package.

```{r setup}
library(ssMRCD)
library(ggplot2)
library(dplyr)
```

## Data Preparation

The original data from GeoSphere Austria (2022) is pre-cleaned and saved in the data frame object `weatherAUT2021`. Additional information can be found on the helping page.

```{r metadata, eval = FALSE}
# get meta data for the data set
? weatherAUT2021
```

```{r load data, eval = TRUE}
# load the data
data("weatherAUT2021")

# inspect the data
head(weatherAUT2021)

# select variables, station names and number of observations
data = weatherAUT2021 %>% select(p:rel)
stations = weatherAUT2021$name
n = dim(data)[1]
```

The predefined groups are based in the underlying geographical landscape consisting of Alpine mountains, hills and flatter areas in Austria. 

```{r build groups}
# build 5 groups of observations based on spatial proximity and geography
cut_lon = c(min(weatherAUT2021$lon)-0.2, 12, 16, max(weatherAUT2021$lon) + 0.2)
cut_lat = c(min(weatherAUT2021$lat)-0.2, 48, max(weatherAUT2021$lat) + 0.2)
groups = ssMRCD::groups_gridbased(weatherAUT2021$lon, 
                                  weatherAUT2021$lat, 
                                  cut_lon, 
                                  cut_lat)
N = length(unique(groups))
table(groups)
```


```{r run model}
# calculate MG-GMM
model = cellMGGMM(X = data, groups = groups,
                  nsteps = 100, alpha = 0.5,
                  maxcond = 100)
```


```{r mixture probabilities}
# mixture probabilities
cat("Pi (in %):\n")
round(model$pi_groups*100, 2)
```


```{r percentage of outlier}
# percentage of outliers
cat("% Outliers per group and variable:\n")
round(sapply(1:N, function(x) colMeans(1-model$W[groups == x, ]))*100, 2)
```


```{r residuals}
# calculate residuals
res = residuals_mggmm(X = data, 
                groups = groups,
                Sigma = model$Sigma,
                mu = model$mu, 
                probs = model$probs,
                W = model$W)
```


## References

GeoSphere Austria (2022): <https://data.hub.geosphere.at>.

Puchhammer P., Wilms I. and Filzmoser P. (2025): A smooth multi-group Gaussian Mixture Model for cellwise robust covariance estimation. <https://doi.org/10.48550/arXiv.2504.02547>