# Linear Discriminant Analysis: Using subject as classification

I have a problem where I need to identify from which subject a particular set of data points came. More specifically, my problem is that I need to demonstrate that my subjects (N=9) can be discriminated from one another, with the future goal of classifying them based on the IV's. Each subject has repeated measures of the same variables. My data can be thought of as the following:

Subject    Session    x1    x2
A                1    5    110
A                2    7    115
B                1    15    84
B                2    12    91
.                .    .     .
.                .    .     .
.                .    .     .
I                1    18    106
I                2    15    100


Is using LDA a valid approach to classify subjects based on measured variables? I am concerned that this is not the case, since each group has only 1 subject (as it is defined as the subject!).

I am aware that special precautions must be taken with the repeated measures design of the data; however, as of now I am more concerned with the validity of using LDA to classify subjects.

• (Your nick is very appealing, I like it) Do I understand correctly that for you, "Subject" is class, "Session" is some condition or treatment (what is it, by the way?), and X1 X2 are some quantitative characteristics? – ttnphns Jul 12 '13 at 17:51
• Thank you! Everything is correct except your interpretation of "Session"; there is no treatment involved. Session simply means we recorded the same data a second time in precisely the same conditions for that subject. Hopefully I am not misusing terminology. Does "repeated measures" usually imply that data from the same subject is recorded under different experimental manipulation? – Pseudo_Scientist Jul 12 '13 at 17:53
• I think I may have made sense of my problem. I was concerned of violating the assumption of independence between observations in each group, since this is obviously violated as the data comes from the same subject. However, in my application this is a non-issue because I am trying to classify that particular subject anyways. Because I'm not trying to generalize these results to a different population I should be fine, right? i would be in trouble if I had 10 observations from two subjects, one male and one female, and then tried to generalize these results to differentiate between sexes. – Pseudo_Scientist Jul 12 '13 at 18:17
• So, levels 1 and 2 of Session have no expected systematic difference. Then it is simply error factor (not repeated measures). I turns as if you have "groups" A,B,...,I with just 2 independent observations in each, n=2. Despite it too little for an inference, you may do LDA if you reason X1 X2 distribution is bivariate normal. You man use other methods, too. – ttnphns Jul 12 '13 at 18:28
• Okay, great! This was just an exemplary dataset--there are more than two observations per subject (as well as more than two IV's). Thank you for your help. – Pseudo_Scientist Jul 12 '13 at 18:43