---
title: "Additional visualizations of variance structure"
author:
- name: "[Gabriel Hoffman](http://gabrielhoffman.github.io)"
  affiliation: | 
    Icahn School of Medicine at Mount Sinai, New York
output:
  rmarkdown::html_document:
    highlight: pygments
    toc: true
    toc_depth: 2
    fig_width: 6
    fig_height: 6
  # BiocStyle::html_document:
  #   toc_float: false
  BiocStyle::pdf_document: default
package: variancePartition
abstract: |
  The correlation structure between samples in complex study designs can be decomposed into the contribution of multiple dimensions of variation.  \Rpackage{variancePartition} provides a statistical and visualization framework to interpret sources of variation.  Here I describe a visualization of the correlation structure between samples for a single gene.<br>  
  variancePartition v`r packageVersion("variancePartition")`<br> 
  `r format(Sys.time(),'%B %d, %Y %H:%M:%S')`<br> 
vignette: |
  %\VignetteIndexEntry{2) Additional visualizations}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r knitr, echo=FALSE, results='hide'}
library("knitr")
opts_chunk$set(tidy=FALSE,dev="png",fig.show="show",
               # fig.width=7,fig.height=7, 
               echo=TRUE,
               message=FALSE, warning=FALSE)
``` 


```{r initialize, cache=FALSE, echo=FALSE}
# load library
library('variancePartition')
```
 In the example dataset described in the main vignette, samples are correlated because they can come from the same individual or the same tissue.  The function \Rfunction{plotCorrStructure} shows the correlation structure caused by each variable as well and the joint correlation structure.  Figure \ref{fig:plotCorr}a,b shows the correlation between samples from the same individual where (a) shows the samples sorted based on clustering of the correlation matrix and (b) shows the original order.  Figure \ref{fig:plotCorr}c,d shows the same type of plot except demonstrating the effect of tissue.  The total correlation structure from summing individual and tissue correlation matricies is shown in \ref{fig:plotCorrAll}a,b.  The code to generate these plots is shown below. 

# Plot variance structure
```{r corStruct, results='hide'}
# Fit linear mixed model and examine correlation stucture
# for one gene
data(varPartData)

form <- ~ Age + (1|Individual) + (1|Tissue)

fitList <- fitVarPartModel( geneExpr[1:2,], form, info )

# focus on one gene
fit = fitList[[1]]
```

## By Individual
### Reorder samples
```{r corStructa,out.width = "50%"}
# Figure 1a
# correlation structure based on similarity within Individual
# reorder samples based on clustering
plotCorrStructure( fit, "Individual" )
```

### Original order of samples
```{r corStructb,out.width = "50%"}
# Figure 1b
# use original order of samples
plotCorrStructure( fit, "Individual", reorder=FALSE )
```

## By Tissue
### Reorder samples
```{r corStructc,out.width = "50%"}
# Figure 1c
# correlation structure based on similarity within Tissue
# reorder samples based on clustering
plotCorrStructure( fit, "Tissue" )
```

### Original order of samples
```{r corStructd,out.width = "50%"}
# Figure 1d
# use original order of samples
plotCorrStructure( fit, "Tissue", reorder=FALSE )
```

## By Individual and Tissue
### Reorder samples
```{r corStructe,out.width = "50%"}
# Figure 2a
# correlation structure based on similarity within 
# Individual *and* Tissue, reorder samples based on clustering
plotCorrStructure( fit )
```

### Original order of samples
```{r corStructf,out.width = "50%"}
# Figure 2b
# use original order of samples
plotCorrStructure( fit, reorder=FALSE )
```