When assessing a patient, many psychiatrists use a standard questionnaire called the Minnesota Multiphasic Personality Inventory (MMPI). The patient’s answers are used to figure out where they lie on eighteeen different subscales of psychology, things like “masculinity”, “paranoia” and “cynicism”. Here’s the full list:

1. Hypochondriasis
2. Depression
3. Hysteria
4. Psychopathic Deviate
5. Paranoia
6. Psychasthenia
7. Schizophrenia
8. Masculinity/Femininity
9. Social Introversion
10. Demoralization
11. Somatic Complaints
12. Low Positive Emotions
13. Cynicism
14. Antisocial Behavior
15. Ideas of Persecution
16. Dysfunctional Negative Emotions
17. Aberrant Experiences
18. Hypomanic Activation

But what if some of these scales really measure the same thing? Or what if there are other scales, which the test doesn’t take into account? Using a math technique called “singular value decomposition“, we can take the test data collected over many years, and use it to figure out what the main variables of psychiatry are, at least as measured by this one test.

The results show that most of the variance in the data lies along three linear axes. That is, if we know where you lie along three different scales, we can predict very well where you’ll lie on the others – there are three main patterns of dysfunction. The three scales are:

– Low positive emotions, which correlates highly with depression, introversion, and hysteria

– Schizophrenia, which correlates highly with dysfunctional emotions, aberrant experiences, and paranoia

– Masculinity, which correlates highly with hypomania

Are the three scales independent? The depression and schizophrenia scales are linearly independent, but the hypomania/masculinity scale is negatively correlated with the depression scale (correlation coefficient ~= -0.7). If we do some more sophisticated analysis with Laplacian eigenmaps, we see that the data forms a flat, two dimensional surface in this three dimensional space. So, we only really need to know two coordinates in order to predict the others. Call them the negative emotion dimension, with depression on one side of the axis and masculinity/hypomania on the other, and the delusion/paranoia dimension.

(Data Colored By Psychasthenia)

(Data Colored By Masculinity)

Hence, we can hypothesize that two main axes (the negative emotion axis and the delusion/paranoia axis) govern psychiatric traits, and the other sixteen axes are mostly some combination of those two.

(This post is derived from the mathematical analysis and commentary of Sarah Constantin, a grad student at Yale University, who has agreed to have it published here.)