MDS

Question 1

what is MDS

Answer 1

a set of data analysis techniques that display the structure in the data in pictures

pictures have 2 dimensions (x,y) MDS reduces dimensions of data to 2 dimensions. uses this to draw the picture

Question 2

when is MDS most helpful

Answer 2

when you have data with many dimensions and you reduce these down to 2

use these 2 to group things together

Question 3

how many dimmensions do I need to display the objects

Answer 3

• 1 less than however many objects/data points you have.
• n objects can have their relationships represented in n-1 dimmensions.
• 3 objects can be represented in 2 dimmensions while 4 objects need 3 dimmensions

Since humans can’t easily visualise relationships in higher dimensional space we simplify. 3 is what most people can do. anything above that gets tricky

MDS helps reduce that number of dimmension

Question 4

discuss MDS protocol

Answer 4

takes initial matrix with n-1 dimmensions then twists it to reduce it to 2

it will go down in steps removing one at a time until it reaches 2 then creates a plot

Question 5

data is a matrix of the relationships between different cities

Answer 5

can input this directly then perform the MDS analysis or you can enter the raw data and ask SPSS to generate your distance matrix for the analysis

Question 6

what kind of matrix does the data need to be in for MDS analysis

Answer 6

dissimilarity matrix such that larger values indicate 2 things are more different

Question 7

what is stress (MDS output)

Answer 7

matrix stress

a standardised summation of the difference between the distances in the data matrix and the corresponding distances between the objects on the plot

basically compares the distances you had originally to the 2D reduced version. measure of goodness of fit. tells us how well to 2D configuration of points, how well that matches the original configuration of points

• varies from 0-1
• the lower the value the better
• < 0.1 excellent ; > 0.15 unacceptable
• if it’s large it tells us the original higher-dimensional representation of the data is not represented well by your new 2D solution - so having taken out so many dimensions has a cost - the fit does not aqequatly represent the data

Question 8

what is RSQ (MDS output)

Answer 8

proportion of explained variance

porportion of variance explained in the original higher dimensionalal space (the reference)

RSQ tells us how much of this variance is explained by the new 2D solution

• varies from 0-1
• the higher the value the better

Question 9

multidimensional scaling using a Euclidean distance model

Answer 9

Question 10

What super important meaning do the dimensions of x and y axis in the Euclidean distance model mean

Answer 10

Nothing!!! They are meaningless! And the orientation of the diagram is arbitrary

Extracts dimensions but wont’ attach any meaning to them. Does whatever works best to reduce the data into two dimensions. And to maximise RSQ and minimise the stress

2 dimensions used to represent the data - using origional rating/judgments of similarity

Question 11

Scatter plot of linear fit also outputted in MDS – what is this

Answer 11

Plots the deviation/disparity. Think of this as a relationship between the original and fitted distance based on the 2d model. We want this to match very well. Objects that are very dissimilar in the original should be dissimilar in the new solution

Ideally want all the points to lie across the diagonal

Question 12

if the stress is less than .1 and RSQ is .99 and scatter plot is diagonal. what can we say

Answer 12

There is an excellent fit between the higher dimensional original data and 2d solution

can say about 99% of the data in. the original distance space is explained for by the distances in the lower 2 dimensional space.

we see this also in teh scatter plot with most points going across the diagonal

Question 13

what do we need to ask after seeing the 2D masterpiece MDS has produces

Answer 13

The points closest together - do they make sense?

yes.

Question 14

key points for MDS

Answer 14

• Need to be aware of the data – needs to be dissimilarity matrix that goes into calculations
• Raw data can be converted into these, done fairly automatically in SPSS
• In terms of output: RSQ, stress and looking at scatter plot diagonals
• Again exploratory technique – no p value no final solution
• provided only with a plot - a visual representation of your data to show you any sensible way the data might be grouped together
• Just given a plot that can help you determine a sensible way to group objects