EFA

=> In FA, indicators have an individual error term (due to measurement error and uniqueness [see next slides])

• Overlapping area among all variables: Variance due to the common factor

• Nonoverlapping area for any variable: Variance that is unique to that particular variable: Uniqueness

• Consists of (1) Specificity, a true (i.e., reliable) source of variance that is not common to any other variable (e.g., writing proficiency performance affected by different genres: argumentative vs. narrative writing); and (2) random error of measurement, i.e. unreliability (e).

Total amount of systematic variance of a variable, called communality (h2)

= Common factor variance + group factor variance

1. All of the observable random variables Zj have mean zero and variance 1, i.e., are z-standardized variables

2. All of the latent factors have mean zero and variance 1, i.e., are z-standardized variables

3. All error terms have mean zero (linearity assumption)

4. The factors are uncorrelated (orthogonal model)

5. The error terms are uncorrelated across observable variables

   (i.e., assumption of random errors)

6. The error terms are uncorrelated with the factor variables

   (i.e., assumption of random errors)