---
title: "MDS Analysis"
author: "Danielle Daidone"
date: 8/3/23
output: html_document
---

This script runs multidimensional scaling analyses on any matrix output by create_FC_similarity_matrices.Rmd.  It outputs 1,2,3,4 and 5 dimensional solutions as text files and produces a stress plot to help you decide on the most appropriate number of dimensions. It also produces plots of the solutions, but note that the solutions are unrotated and thus may not be easily interpretable.


Download and load relevant packages
See documentation: 
smacof (for MDS): https://rdrr.io/cran/smacof/man/smacofSym.html 
```{r}
if(!require(rmarkdown)){install.packages("rmarkdown")}
library(rmarkdown)
if(!require(smacof)){install.packages("smacof")}
library(smacof)
```

PART 1: OPEN AND CHECK DATASET
 
Set working directory  - Change to match your filepath
```{r setup, include=FALSE}
knitr::opts_knit$set(root.dir = "C:/Users/Danielle/OneDrive - UNC-Wilmington/CV/Website/FC analysis info")
```

Open dataset - Change to match your desired *dis*similarity matrix
```{r}
# Note that the dissimilarity text files are tab delimited files with headers
FCmatrixAll=read.table("Output_Matrix_AllContexts_percent_dis.txt",sep="\t",header=TRUE)
```

Look at the first few rows of the dataset
```{r}
head(FCmatrixAll)
```

Run ordinal multi-dimensional scaling (MDS) - 1 dimensional solution
```{r}
# ndim is the number of dimensions
MDS1Dim = mds(FCmatrixAll, ndim = 1, type = "ordinal")

# view Kruskal stress
MDS1Dim

# get dim scores
dimscores = MDS1Dim$conf

# write dim scores out to a text file in your working directory
write.table(dimscores,file="MDS_1D.txt",sep="\t",quote=FALSE)

```

Run ordinal multi-dimensional scaling (MDS) - 2 dimensional solution
```{r}
# ndim is the number of dimensions
MDS2Dim = mds(FCmatrixAll, ndim = 2, type = "ordinal")

# view Kruskal stress
MDS2Dim

# get dim scores
dimscores = MDS2Dim$conf

# write dim scores out to a text file in your working directory
write.table(dimscores,file="MDS_2D.txt",sep="\t",quote=FALSE)

#plot
plot(MDS2Dim, plot.type = "confplot", plot.dim = c(1,2))

```

Run ordinal multi-dimensional scaling (MDS) - 3 dimensional solution
```{r}
# ndim is the number of dimensions
MDS3Dim = mds(FCmatrixAll, ndim = 3, type = "ordinal")

# view Kruskal stress
MDS3Dim

# get dim scores
dimscores = MDS3Dim$conf

# write dim scores out to a text file in your working directory
write.table(dimscores,file="MDS_3D.txt",sep="\t",quote=FALSE)

#plot dim 1 by dim 2
plot(MDS3Dim, plot.type = "confplot", plot.dim = c(1,2))

#plot dim 1 by dim 3 (as if looking into previous plot from the top)
plot(MDS3Dim, plot.type = "confplot", plot.dim = c(1,3))

```

Run ordinal multi-dimensional scaling (MDS) - 4 dimensional solution
```{r}
# ndim is the number of dimensions
MDS4Dim = mds(FCmatrixAll, ndim = 4, type = "ordinal")

# view Kruskal stress
MDS4Dim

# get dim scores
dimscores = MDS4Dim$conf

# write dim scores out to a text file in your working directory
write.table(dimscores,file="MDS_4D.txt",sep="\t",quote=FALSE)

#plot dim 1 by dim 2
plot(MDS4Dim, plot.type = "confplot", plot.dim = c(1,2))

#plot dim 1 by dim 3 (as if looking into previous plot from the top)
plot(MDS4Dim, plot.type = "confplot", plot.dim = c(1,3))

```

Run ordinal multi-dimensional scaling (MDS) - 5 dimensional solution
```{r}
# ndim is the number of dimensions
MDS5Dim = mds(FCmatrixAll, ndim = 5, type = "ordinal")

# view Kruskal stress
MDS5Dim

# get dim scores
dimscores = MDS5Dim$conf

# write dim scores out to a text file in your working directory
write.table(dimscores,file="MDS_5D.txt",sep="\t",quote=FALSE)

#plot dim 1 by dim 2
plot(MDS5Dim, plot.type = "confplot", plot.dim = c(1,2))

#plot dim 1 by dim 3 (as if looking into previous plot from the top)
plot(MDS5Dim, plot.type = "confplot", plot.dim = c(1,3))

```

Create stress plot
```{r}
stressvalues = c(MDS1Dim$stress,MDS2Dim$stress,MDS3Dim$stress,MDS4Dim$stress,MDS5Dim$stress)
dimensions = c(1,2,3,4,5)
plot(dimensions,stressvalues)
```