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I know that principal component analysis (PCA) and [exploratory] factor analysis (EFA) are meant to be examples of the General Linear Model, but I've never been able to find a good way of explaining this to students.

You can assume the student already understands and can read equations relating to simple regression, multiple regression, ANOVA, ANCOVA, etc. You can also assume that the student can read and understand General Linear Models
(as in the following, taken from https://en.wikipedia.org/wiki/Design_matrix) expressed in matrix form:

Simple linear regression in matrix form

The student could understand statements of that sort in relation to multiple regression or ANOVA, and perhaps also in relation to more complex scenarios.

However, they don't see the link with these models and PCA or EFA.

kjetil b halvorsen
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user1205901 - Reinstate Monica
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    Why do you want PCA to be an example og a GLM? I have never seen it treated like that!, what do you gain? – kjetil b halvorsen Mar 16 '16 at 13:03
  • Almost any linear transform or modelling can be seen as (general) linear model. So to show it to the student just show the PCA and FA model formulas. Just one link among many: http://stats.stackexchange.com/a/94104/3277. – ttnphns Mar 16 '16 at 13:16
  • Since PCA is not based on any distributional assumptions--it is strictly about relationships among *fixed* vectors--any link to the general linear model would have to be indirect and somewhat artificial. – whuber Feb 20 '22 at 13:32

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