---
title: "Custom Network Statistics"
author: "Donny Williams"
date: "5/19/2020"
bibliography: ../inst/REFERENCES.bib
output: 
  rmarkdown::html_vignette:
    toc: yes
vignette: >
  %\VignetteIndexEntry{Custom Network Statistics}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---


# Background
This vignette describes a new feature to **BGGM** (`2.0.0`) that allows for 
computing custom network statistics (e.g., centrality). The new function is
called `roll_your_own` and it was suggested by a user of **BGGM**  ([see feature request here](https://github.com/donaldRwilliams/BGGM/issues/12)).

# Basic Idea
The basic idea is to compute the chosen network statistic for each of the sampled partial 
correlation matrices, resulting in a distribution. All that is required is to define a function
that takes either a partial correlation matrix or a weighted adjacency matrix 
(the partial correlation matrix with values set to zero) as the first argument. 
Several examples are provided below.



### R packages
```{r, eval = FALSE}
# need the developmental version
if (!requireNamespace("remotes")) { 
  install.packages("remotes")   
}   

# install from github
remotes::install_github("donaldRwilliams/BGGM")
```


### Data
In all examples, a subset of `ptsd` data is used. The subset includes two of the "communities" of 
symptoms [details for these data can be found in @armour2017network]. The data are ordinal (5-level Likert).
```{r, warning =FALSE, message=FALSE}
# need these packages
library(BGGM)
library(ggplot2)
library(assortnet)
library(networktools)

# data
Y <- ptsd[,1:7]
```

### Fit Model
For these data, the GGM is estimated with a semi-parametric copula [@hoff2007extending]. 
In **BGGM**, this implemented with `type = mixed` which is kind of a misnomer because the data do not 
have to be "mixed" (consisting of continuous and discrete variables). 
Note that the model is fitted only once which highlights that only the posterior samples 
are needed to compute any network statistic.

```{r, message=FALSE, warning=FALSE, eval=FALSE}
library(BGGM)

# copula ggm
fit <- estimate(Y, type = "mixed", iter = 1000)
```


# Examples

## Expected Influence
The first example computes expected influence [@robinaugh2016identifying]. The first step is to define a function
```{r}
# define function
f <- function(x,...){
  networktools::expectedInf(x,...)$step1
}
```

Note that `x` takes the matrix which is then passed to `expectedInf`. The `...` allows for 
passing additional arguments to the `expectedInf` function. An example is provided below. 
With the function defined, the next step is to compute the network statistic.

```{r, eval = FALSE, message=FALSE, results='hide'}
# iter = 250 for demonstrative purposes
# (but note even 1000 iters takes less than 1 second)
# compute
net_stat <- roll_your_own(object = fit,
                          FUN = f,
                          select = FALSE,
                          iter = 250)
# print
net_stat

#> BGGM: Bayesian Gaussian Graphical Models 
#> --- 
#> Network Stats: Roll Your Own
#> Posterior Samples: 250 
#> --- 
#> Estimates: 
#> 
#>  Node Post.mean Post.sd Cred.lb Cred.ub
#>     1     0.701   0.099   0.508   0.871
#>     2     0.912   0.113   0.722   1.179
#>     3     0.985   0.112   0.742   1.199
#>     4     1.056   0.105   0.851   1.247
#>     5     1.056   0.116   0.862   1.288
#>     6     0.491   0.092   0.329   0.679
#>     7     0.698   0.098   0.521   0.878
#> --- 
```



The option `select = FALSE` indicates to compute the statistics from the partial correlation matrices (nothing set to zero). This can be changed with `select = TRUE`. Internally, each of the sampled
partial correlation matrices is multiplied by the adjacency matrix.
```{r, eval = FALSE, results='hide'}
net_stat <- roll_your_own(object = fit,
                          FUN = f,
                          select = TRUE,
                          iter = 250)

# print
net_stat

#> BGGM: Bayesian Gaussian Graphical Models 
#> --- 
#> Network Stats: Roll Your Own
#> Posterior Samples: 250 
#> --- 
#> Estimates: 
#> 
#>  Node Post.mean Post.sd Cred.lb Cred.ub
#>     1     0.636   0.136   0.386   0.874
#>     2     0.792   0.113   0.580   0.996
#>     3     0.777   0.122   0.544   1.001
#>     4     0.910   0.121   0.667   1.143
#>     5     0.525   0.104   0.331   0.727
#>     6     0.484   0.110   0.270   0.686
#>     7     0.247   0.081   0.088   0.412
#> --- 
```


The results are then plotted with 
```{r, message=FALSE, eval=FALSE}
plot(net_stat)
```
![](../man/figures/netstat_ridge.png)

## Bridge Strength
The next example computes bridge strength [@jones2019bridge]. This requires the user to define clusters or "communities".

```{r, eval = FALSE, message=FALSE, results='hide'}
# clusters
communities <- substring(colnames(Y), 1, 1)

# function is slow
f <- function(x, ...){
networktools::bridge(x, ...)$`Bridge Strength`
}


# compute
net_stat <- roll_your_own(object = fit,
                          FUN = f, 
                          communities = communities,
                          iter = 250)

# print
net_stat

#> BGGM: Bayesian Gaussian Graphical Models 
#> --- 
#> Network Stats: Roll Your Own
#> Posterior Samples: 250 
#> --- 
#> Estimates: 
#> 
#>  Node Post.mean Post.sd Cred.lb Cred.ub
#>     1     0.162   0.082   0.035   0.347
#>     2     0.250   0.113   0.061   0.501
#>     3     0.180   0.104   0.049   0.480
#>     4     0.280   0.098   0.090   0.480
#>     5     0.375   0.093   0.196   0.558
#>     6     0.617   0.166   0.339   1.002
#>     7     0.628   0.166   0.400   1.025
#> --- 
```


Notice `communities`. This is passed to `...` in the function `f`, which, in turn, is passed to the function `bridge`. Any number of arguments can be passed this way. Here are the results


This can then be plotted and further customized (the returned object is a `ggplot`)
```{r, message = FALSE, eval=FALSE}
plot(net_stat, 
     fill = "lightblue") + 
  ggtitle("Bridge Strength") + 
  xlab("Score")
```

![](../man/figures/netstat_bridge.png)

## Assortment
The next example computes assortment [@newman2003mixing].


```{r, eval = FALSE, message=FALSE, results='hide'}
# clusters
communities <- substring(colnames(Y), 1, 1)

# define function
f <- function(x,...){
  assortnet::assortment.discrete(x, ...)$r
}

net_stat <- roll_your_own(object = fit,
                          FUN = f,
                          types = communities,
                          weighted = TRUE,
                          SE = FALSE, M = 1, 
                          iter = 250)

# print
net_stat

#> BGGM: Bayesian Gaussian Graphical Models 
#> --- 
#> Network Stats: Roll Your Own
#> Posterior Samples: 250 
#> --- 
#> Estimates: 
#> 
#>  Post.mean Post.sd Cred.lb Cred.ub
#>      0.261   0.124   -0.01   0.469
#> --- 
```

This example demonstrate that `...` can take several arguments. The results are stored in the `net_stat` object. They can be accessed with 

```{r, eval=FALSE}
hist(net_stat$results, main = "Assortment")
```

![](../man/figures/netstat_assort.png)

# Note
The function `roll_your_own` is expecting the custom function to return either a single number or a number for each node. This ensures all the printing and plotting functions work. However, you could return anything you want and then access the results to plot, summarize, etc.

# References
