EXPLORATORY FACTOR ANALYSIS (EFA) P. Soukup

What is EFA? a statistical method used to uncover the underlying structure of a relatively large set of variables Example: intelligence Mainly for phenomenons that can not be measured directly (other examples?)

Some pictures instead of equations

Exploratory factor analysis:

Exploratory factor analysis: observed (manifest) Factors=unobserved (latent variables, that we try to identify

Exploratory factor analysis – equations? (just set of regressions) observed (manifest) Factors=unobserved (latent variables, that we try to identify

Steps? 1. big set of manifest variables 2. we try to extract small number of latent variables (factors) Many questions: 1. How to extract factors? 2. How many factors? 3. How to interpret factors?.....

Exploratory and confirmatory (EFA) factor analysis (CFA) CAN YOU SEE SOME DIFFERENCE?

Assumptions about data set of related continous (cardinal) variables (how we can measure relationship?) Expectation about some hidden dimension (factor) behind data

Statistical „test“ for assumptions Bartlett’s test (stat. sig. result=EFA can be useful) KMO (value>0.5) – this is not formal test just criteria Example in SPSS

Steps? 1. Extraction of factors (first solution) 2. Decision about nr. of factors 3. Interpretation: if complicated try rotate factors

Extraction techniques

Possible approaches Principal components (PC): the first factor accounts for as much common variance as possible, then the second factor next most variance, and so on mostly used does not offer confidence intervals and significance tests Maximum likelihood (ML): the best choice when data are normally distributed permits statistical significance testing rarely used Example in SPSS

Basic results in SPSS Percentage of expl. variance Factor loadings – i.e. correlation of factor and manifest variables (main tool for interpretation)

How to select nr. of factors Many approaches: Minimum level of explained variance Kaiser's eigenvalue-greater-than-one rule Cattell's scree plot Example in SPSS Problem: Different reccomendations

Interpretation of factors Factor loadings are the key Correlation between factor and manifest variable Interpretation: try to find what the items have in common= meaning of the factor Example in SPSS Problem: Impossible to find interpretation Solution: Rotation of factors

Rotation of factors Orthogonal rotation: factors are uncorrelated Mostly used technique is varimax Problem: for many constructs we expect they are related Oblique rotation: Factors are related Mostly used technique is direct oblimin More complicated (more outputs including correlation matrix for factors) Example in SPSS

Saving of factors (factor scores) Factor score = value of factor for every unit in my data set Continous variable Can be used for next analysis Replace original (manifest variables) Example in SPSS