### Factor Analysis (Advanced Data Analysis from an Elementary Point of View)

Adding noise to PCA to get a statistical model. The factor analysis model,
or linear regression with unobserved independent variables. Assumptions of the
factor analysis model. Implications of the model: observable variables are
correlated only through shared factors; "tetrad equations" for one factor
models, more general correlation patterns for multiple factors. (Our first look
at latent variables and conditional independence.) Geometrically, the factor
model says the data have a Gaussian distribution on some low-dimensional plane,
plus noise moving them off the plane; and *that is all*. Estimation by
heroic linear algebra; estimation by maximum likelihood. The rotation problem,
and why it is unwise to reify factors. Other models which produce the same
correlation patterns as factor models; in particular the Thomson sampling
model, in which the appearance of factors arises from not knowing what the real
variables are or how to measure them.

PDF handout; lecture-18.R computational examples you should step through (not done in class); correlates of sleep in mammals data set for those examples; thomson-model.R

**Update**, 9 April: A correspondent points me
to this tweet, in
what I can only call a "let's you and him fight" spirit. While the implicit
charge against me by Adams is
not without some justice, if you don't want this to happen, you really
shouldn't brag about how many beauty pageants your child has won, or for that
matter dress the poor beast in such funny clothes.

Advanced Data Analysis from an Elementary Point of
View

Posted at March 30, 2011 23:06 | permanent link