The Common Factor Model
PSY544 – Introduction to Factor Analysis
Week 4

Homework!
•Homework assignment 1 will be out this week
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•I’ll send you an email, along with the deadline
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The data model in factor analysis



The data model in factor analysis



The data model in factor analysis



The data model in factor analysis



The data model in factor analysis



The data model in factor analysis
•The data model represents a typical observation in the population. It is intended to explain the
structure of the raw data (i.e., the scores on manifest variables)
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•The data model is accompanied by assumptions about the joint distribution of the elements in z and
u and implies a model for the population covariance matrix. The model for the covariance matrix is
known as the covariance structure and is intended to explain the variances and covariances of the
manifest variables, not the raw data.
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•Before we proceed to derive the covariance structure model, we’ll talk about the important
distributional assumptions and lay down some notational rules.

Assumptions



Notation



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Deriving the mean and covariance structures



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



Correlation structure



An example
•Remember the example correlation matrix I have shown earlier?
•(4 performance measures: paragraph comprehension, vocabulary, arithmetic skills, and mathematical
problem solving)
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An example