2

Consider a map with two concentration ellipses like this below. The Vomit_y group is (almost?) perfectly vertical, while the Vomit_n group seems to be oriented at about 45 degrees. I understand that Vomit_y displays no correlation between Dim1 and Dim2, while Vomit_n displays a strong correlation. What interesting things might this tell me about the differences between the two groups? How would that differ if, say, the two ellipses were "parallel" but non-overlapping, or if they were oriented at 90 degrees to each other?

Individuals factor map - MCA with two concentration ellipses:

image

Shayan Shafiq
  • 633
  • 6
  • 17
Brett Reynolds
  • 55
  • 8

1 Answers1

1

  1. You have created this map from a MCA. Hope you have categorical data and that you are aware that this technique (as PCA) tries to find some structures behind your dataset. Thus the map does not represent the raw values rather than a relational model from the associations between the variables of your sample.

  2. Hope you have already consider a principal normalization in order for us to be able to discuss about the relative positions of the points of the two groups.

  3. You can associate points between columns and rows comparing the angles they create to the origin. As the angle is getting smaller, the association level rises.

Actual Answer:

  1. Since you would like to compare the two groups as ellipses, there seems no way I can think of in order to make it work.

  2. However if the two ellipses are at 90 degrees with each other you can create a new orthogonal system which has a new origin, the intersection of the perpendicular bisectors of the big axes of the ellipses. In this way you are going to create a new orthogonal system that could explain your relations normalizing them. That way the thesis of each point will explain the relationship between the columns and rows rather than their angles. Please read:

Interpretation of CA

PCA vs CA

Transfer origin:

image

The idea is to transfer the origin to the new one in order to have the positions as a metric for the relations.

Shayan Shafiq
  • 633
  • 6
  • 17
M. Cris
  • 300
  • 2
  • 8
  • 1. yes 2. no, I'll look into this. But I don't understand the idea of normalizing categorical data. I'll also look at the links. Thank you! – Brett Reynolds Dec 31 '19 at 11:58
  • 1
    Please understand that you are not going to normalize the data rather the metric of their relationship which is their angle to the origin. – M. Cris Dec 31 '19 at 12:02
  • I'm using the R package factoMineR and ggplot2. I don't see any options for principal normalization. – Brett Reynolds Dec 31 '19 at 12:39