# INDSCAL using Hamlet II for multidimensional scaling

The last article was about the application of metric multidimensional scaling methods using MRSCAL in Hamlet II. This article shows the application of one of the other multidimensional scaling methods Individual Differences Scaling (INDSCAL) using Hamlet II. INDSCAL compares the co-occurrence of matrices obtained from comparable search lists. It helps to perform an internal metric analysis using the output from similarity matrices. It does so by calculating the weighted distance. Each text is defined by relationships of the content on the basis of the dimensional weights. In simpler terms, INDSCAL helps to explore the general associations among sequences of texts.

## Background of INDSCAL analysis

One of the results derived from INDSCAL analysis consists of different compared text sources and respective weights is the “subject space”.  All the compared text sources show points which plots according to their weights on the corresponding dimension. All the plotted points are known as vectors and drawn from their source. Their sizes remain almost similar to the amount of variance based on the text groups in the input data. Any text close to in-group space remains placed at 45° line in the middle axes. Whereas, the texts not related significantly, can be plotted at ‘0’ points of the axes. The right manner comparing weights in demonstrating these different texts is the degree of separation among their respective vectors. Texts with their weights close to each other have a tendency to occur near each other.

INDSCAL creates an optimized alignment of the axes. High prone to the loss of perfect placement, brings change in the weights if any modification in the rotation made. However, not appropriate to rotate the axes of the plotted group space, as it is already designed to derive the best possible orientation. This analysis uses the same series of matrices (“.mat”) saved from joint frequencies analysis.

## Steps to conduct INDSCAL using Hamlet II

Follow the below steps to perform INSCAL using Hamlet II.

1. Go to the main Tool Bar > MDS > Select matrices for INDividual differences SCALing. The figure below will appear.

How to select the matrices to compare using INDSCAL?

2. Click to select the matrices needed comparison using the INDSCAL MDS scaling technique. Then click on “Run INDSCAL” on the top right side. Note: Only the matrices created with the same parameters (same number of texts while running Joint Frequencies) comparable and analyzable.
3. Click on Data and click ‘run INDSCAL‘ (as in above image) to analyze the position where each point situated in all three dimensions. It shows the distances between the displayed vectors in the resulting graph (figure below)

Tool Bar in INDSCAL

4. Click on “Next” and “Previous” buttons (as in the above image) provided on the same output window to toggle the graphs type between Subject Space and Group Space. The Group Space plot will show a combination of the vocabulary used in all three subjects based on their relative weights to different dimensions as presented in the above image.

## Steps to edit outcome from INDSCAL using Hamlet II

1. Clicking on each of the text vector points available in Subject Spaces using the right mouse button will open another window showing individual configurations of the vocabulary items as in the image below.
2. Click “View/Edit data” to explore the data points and their weights. It also allows the user to make changes in the current data file as in the image underneath.
3. In Normalized Subject Space, one can easily find the same configurations used to plot the graph and see the graph by clicking on “Analyze subject space”.

Tool Bar in INDSCAL

4. Once satisfied with the resulting plot and edits made, click on “Save Display” to save the graphical representation of the same configurations.
5. Exit the output window [X], and save the results if for future reference.

In Normalized Group Space, one can explore the plotting points (weights) of configurations will be available along with the correlation between these text vectors and mean square. Basic drawing functions are also available in this type of configuration and plots. These drawing functions allow the user to draw, mark, write text and erase on the output window. Indicated in the below figure.

## Interpreting a plot derived from using the INDSCAL

Plot derived from using the INDSCAL multidimensional scaling

The above-resulting plot derived by using the INDSCAL multidimensional scaling method to explore and compare the relationships among the sequences of texts. The variance of angle among the objects in this space represents the significance of the relationship they carry with each other. Closely look at the resulted graph, and infer that “Hamlet” and “sample matrix” closely related in terms of the sequences of texts used. On the other hand, “babel matrix” contains a whole different set of texts making it different from other sets. Therefore, “babel matrix” situated on different dimensions shows an insignificant relationship with the other two matrices.

This article talks about the application of Individual Differences Scaling (INDSCAL) and it also takes through the interpretation of the results derived from this particular type of multi-dimensional scaling method. The next article shows the application of Procrustean Individual Differences Scaling (PINDIS) along with its interpretation.

### Avishek Majumder

Research Analyst at Project Guru
Avishek is a Master in Biotechnology and has previously worked with Lifecell International Private Limited. Apart from data analysis and biological research, he loves photography and reading. He loves to play football and basketball in his spare time with an avid interest in adventure and nature. He was also a member of the Scouts in his school and has attended Military training.

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