Introduction to EFA

Factor Analysis in R

Jennifer Brussow

Psychometrician

Psycho + metrics

brainbulb

psycho = "of the mind"

metrics = "related to measurement"

Learning objectives

Run a unidimensional exploratory factor analysis (EFA)
View and interpret items' factor loadings
Interpret individuals' factor scores

Factor Analysis' relationship to other analyses

Classical Test Theory: Scores are the unweighted sum of item scores.
Factor Analysis: Scores are an empirically weighted sum of item scores, where weights are determined by the items' correlations to each other.
Structural Equation Modeling: Extends factor analyses to allow the relationships between latent variables to be modeled.

Types of Factor Analysis

Exploratory Factor Analysis (EFA):

Used during development
Explore factor structure
Evaluate items

Confirmatory Factor Analysis (CFA):

Validate a measure
Used after development

Package

Package: The psych package

Developed by William Revelle.
More info at The Personality Project.

library(psych)

Dataset

The gcbs dataset: Generic Conspiracist Beliefs Survey

Take the assessment at Open Source Psychometrics Project
Full test is 75 items measuring five conspiracist facets

str(gcbs)

'data.frame':    2495 obs. of  15 variables:
 $ Q1 : int  5 5 2 5 5 1 4 5 1 1 ...
 $ Q2 : int  5 5 4 4 4 1 3 4 1 2 ...
 $ Q3 : int  3 5 1 1 1 1 3 3 1 1 ...
 $ Q4 : int  5 5 2 2 4 1 3 3 1 1 ...
 $ Q5 : int  5 5 2 4 4 1 4 4 1 1 ...
 ...

Item types

Government malfeasance (GM)
Extraterrestrial coverup (ET)
Malevolent global conspiracies (MG)
Personal wellbeing (PW)
Control of information (CI)

More information in Brotherton, French, & Pickering (2013)

Hierarchical Factor Structure

singlefactor_diag

EFA_model <- fa(gcbs)
fa.diagram(EFA_model)
EFA_model$loadings

Loadings:
    MR1  
Q1  0.703
Q2  0.719
Q3  0.638
Q4  0.770
Q5  0.672
Q6  0.746
Q7  0.734
Q8  0.654
Q9  0.695
Q10 0.565
...

fa_diagram

Let's practice!

Factor Analysis in R