Principal components factor analysis

Use of extracted factors in multivariate dependency models

KEY CONCEPTS

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Factor Analysis

Interdependency technique

Assumptions of factor analysis

Latent variable (i.e. factor)

Research questions answered by factor analysis

Applications of factor analysis

Exploratory applications

Confirmatory applications

R factor analysis

Q factor analysis

Factor loadings

Steps in factor analysis

Initial v final solution

Factorability of an intercorrelation matrix

Bartlett's test of sphericity and its interpretation

Kaiser-Meyer-Olkin measure of sampling adequacy (KMO) and its interpretation

Identity matrix and the determinant of an identity matrix

Methods for extracting factors

Principal components

Maximum likelihood method

Principal axis method

Unwieghted least squares

Generalized least squares

Alpha method

Image factoring

Criteria for determining the number of factors

Eigenvalue greater than 1.0

Cattell's scree plot

Percent and cumulative percent of variance explained by the factors extracted

Component matrix and factor loadings

Communality of a variable

Determining what a factor measures and naming a factor

Factor rotation and its purpose

Varimax

Quartimax

Equimax

Orthogonal v oblique rotation

Reproduced correlation matrix

Computing factor scores

Factor score coefficient matrix

Using factor score in multivariate dependency models

Lecture Outline

✓ Identifying patterns of intercorrelation

✓ Factors v correlations

✓ Steps in the factor analysis process

✓ Testing for "factorability"

✓ Initial v final factor solutions

✓ Naming factors

✓ Factor rotation

✓ Computing factor scores

✓ Using factors scores in multivariate dependency models

Factor Analysis

Interdependency Technique

Seeks to find the latent factors that account for the patterns of collinearity among multiple metric variables

Assumptions...