---
title: "Prediction Power Heatmaps"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Prediction Power Heatmaps}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(out.width = "100%", cache = FALSE)
```

The function `make_pred_plot()` visualizes the output from `prediction_power()` as a heatmap. Each cell shows an expected conditional entropy value, where lower values indicate stronger prediction power. Diagonal entries correspond to prediction using a single predictor, while off-diagonal entries correspond to prediction using pairs of predictors.

```{r load-lib}
library(netropy)
```

We first edit the node attributes so that all variables have finite categorical range spaces. The variables years and age are discretized into three categories.

```{r data-edit}
df_att <- lawdata[[4]]
att_var <- data.frame(
  status    = df_att$status - 1,
  gender    = df_att$gender,
  office    = df_att$office - 1,
  years     = ifelse(df_att$years <= 3, 0,
                ifelse(df_att$years <= 13, 1, 2)),
  age       = ifelse(df_att$age <= 35, 0,
                ifelse(df_att$age <= 45, 1, 2)),
  practice  = df_att$practice,
  lawschool = df_att$lawschool - 1
)
```
The first rows of the edited attribute data are:

```{r}
head(att_var)
```

## Prediction Power
Assume we are interested in predicting `status`, which indicates whether a lawyer is an associate or a partner. We first compute the prediction power matrix:

```{r pred-pow}
pred_status <- prediction_power("status", att_var)
pred_status
```

### Heatmap Visualization
The matrix can be visualized using `make_pred_plot()`:

```{r pred-plot, fig.height=7, fig.width=8}
make_pred_plot(pred_status, "Prediction Power for Status")
```

Darker cells indicate lower expected conditional entropy and therefore stronger prediction power. The diagonal entries show prediction based on one variable, while the off-diagonal entries show prediction based on pairs of variables.

### Changing Plot Colors
The colors can be adjusted using the `low` and `high` arguments. For example:
```{r col-change, fig.height=7, fig.width=8}
make_pred_plot(
  pred_status,
  "Prediction Power for Status",
  low = "steelblue",
  high = "white"
)
```

### Changing Text Size
The size of the cell labels can be controlled with `text_size`:
```{r text-change, fig.height=7, fig.width=8}
make_pred_plot(
  pred_status,
  "Prediction Power for Status",
  text_size = 6
)
```


## References
> Frank, O., & Shafie, T. (2016). Multivariate entropy analysis of network data.
*Bulletin of Sociological Methodology/Bulletin de Méthodologie Sociologique*, 129(1), 45-63. [link](https://doi.org/10.1177%2F0759106315615511)