CreatingComparisonMatrices.Rmd

---
title: "Creating Comparison Matrices"
output: html_document
date: "2025-05-07"
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

In order to specify which groups are compared by a hypothesis, a comparison matrix is used. This comparison matrix enables you to test different group comparisons, where each row corresponds to a unique group comparison. NOTE: different comparison matrices should be used for different fundamental hypothesis types.


In a comparison matrix:  
- Each column represents a different cell type.  
- Each row represents a different group comparison.  
- Each value represents the magnitude of a group's inclusion in the hypothesis. For our models, a hypothesis compares two groups, A and B. Each group can be made up of multiple cell types.  
- If there are multiple cell types in a hypothesis group, each cell type will usually be represented equally in its hypothesis group. Ex: if two cell types are in hypothesis group A, each cell type gets a value of 1/2. if three cell types are in hypothesis group B, each cell type gets a value of -1/3. If a cell type is not considered in a group comparison, its value is 0.  
- Each row must sum to 0.  

Comparison matrices can be created easily using the matrix() function:  

```{r matrix_example}

cell_types = c('celltype1','celltype2','celltype3','celltype4','celltype5')
n_cell_types = length(cell_types)

group_comparisons = c('grouping1','grouping2','grouping3')
n_group_comparisons = length(group_comparisons)

data = c(1/2, 1/2,-1/2,-1/2, 0,
         1/3, 1/3, 1/3,-1/2, -1/2,
         0,   0,   0,   1,  -1)

m = matrix(data,
           nrow = n_group_comparisons,
           ncol = n_cell_types,
           dimnames = list(group_comparisons, cell_types),
           byrow = TRUE)

m

```

In this matrix, there are 5 cell types and 3 group comparisons:  
- Group comparison 1 compares cell types 1 & 2 against cell types 3 & 4.  
- Group comparison 2 compares cell types 1, 2 & 3 against cell types 4 & 5.  
- Group comparison 3 compares cell type 4 against cell type 5.