interact_code.Rmd

---
title: "Study of Interaction Patterns in Primary School Children Network"
author: "Utsab Shrestha"
date: "May 25,2020"
output: html_document
knit: (function(input_file, encoding) {
  out_dir <- 'docs';
  rmarkdown::render(input_file,
 encoding=encoding,
 output_file=file.path(dirname(input_file), out_dir, 'interactcode.html'))})
---
```{r global_options, include = FALSE}
library(knitr)
setwd("~/Github Project R/InteractPattern")
read_chunk("proj_data.R")
knitr::opts_chunk$set(echo = FALSE,warning = FALSE,message = FALSE, fig.align="center")
```
## Steps to setup data
  
### Step 1: Load the data in gephi
The files were in GEXF format. I loaded the files in gephi and explored different layouts to visualize the network data. 

```{r C1}
```
### Step 3: Export the node and edge csv file from Gephi
Since I could not load the GEXF file in R, I had to export the edge and node files as CSV file from gephi and read the table in R and write as a graph file.


```{r C2}
```
### Step 3: Convert edge and node data into igraph

```{r C3}
```

### Step 4: Summary

```{r C4}
```
```{r C5}
```
### Degree Distribution by Grade and Gender

```{r C6}
```
### Heatmap of interactions by Grade
```{r C7}
```
### Data pre-processing
```{r C8}
```
### Degree Distribution Histogram
```{r C9}
```
### Network properties
```{r C10}
```
### Degree Boxplot by Grade 
```{r C11}
```
### Giant Components
```{r C12}
```
### Centrality Measures Corr Plot
```{r C13}
```
### Betweeness and Closeness Distributon
```{r C14}
```
### ERGM Models
```{r C15}
```

### Model 1 for Day 1
simple model
no mcmc stored
```{r C16}
```
### Model 2
added Age difference and MCMC burnin

```{r C17}
```
### Model 3
added Degree 1
```{r C18}
```
### Model 4
updated degree(2:4) based on GOF from Model 3 and added gwesp
```{r C19}
```
### Model 6
added Degree 9, nodematch for Grade and increased burnin computation
This is much better model.
MCMC statistics show some autocorrelation but the joint pvalue is better.
```{r C21}
```

### Model 1 for Day 2
Simple model to begin with
```{r C22}
```
### Model 2 and 3

added age difference and nodemix for gender
```{r C23}
```

### Model 4
added Nodematch for Grade and Degrees based on GOF and also increased computational power
```{r C24}
```
### Model 5
AIC and BIC are still not looking good. P-values are not significant. GOF is not performing well
```{r C25}
```
### Model 6
MCMC statistics have high correlations, and joint p-value is also 0.
```{r C26}
```
### Model 7
Still the model does not perform well with updated degree
```{r C27}
```
### CUG test 
High Assortativity on both Grade and Gender attributes.
The Grade has higher assortativity so the assortativity is higher than random generated graphs.
```{r C28}
```
### QAP test
Assortativity test passes for QAP test also. High Assotativity for Grade than Gender. The nodes were not randomly assortative.
```{r C29}
```

### Conditional Probability For Grade Match, Male-Male, Female-Female, Male-Female Edges forming
Highest probability for Same grade nodes to form an edge
```{r C30}
```