Understanding Factor Analysis
What is Factor Analysis?
- Factor analysis is a correlational technique to
determine meaningful clusters of shared variance.
- Factor Analysis should be driven by a researcher who has a deep and
genuine interest in relevant theory in order to get optimal value from
choosing the right type of factor analysis and interpreting the factor
- Factor analysis beings begins
with a large number of variables and then tries to reduce the
interrelationships amongst the variables to a few number of clusters or
- Factor analysis finds relationships
or natural connections where variables are maximally correlated with one
another and minimally correlated with other variables, and then groups the
- After this process has been done many times a pattern appears of
relationships or factors that capture the essence of all of the data
- Summary: Factor analysis refers to a collection of statistical methods for
reducing correlational data into a smaller number of dimensions or factors
Factor Analysis Readings
graduate-level, &/or non-social science orientation)
Types of Factor Analysis
Exploratory Factor Analysis
- Principle Components
- Principle Axis Factoring
Confirmatory Factor Analysis
Frequently Asked Questions
What is the difference between PC and PAF?
- Principle Axis Factoring (PAF) analyzes only the variance in the items
that is shared with other items. That's why the
communalities will be less than 1 (they represent the proportion of
variance in an item explained by the other items). PAF is
generally considered best for exploring the underlying factors for
theoretical purposes For example, PAF is usually driven by questions
- "How many factors?"
- "What are the factors?"
- "What is the relationship amongst the factors?"
- Principal Components (PC) analyzes all the variance in the items.
That's why the communalities are all 1 (representing 100% of the
variance of each item being included in the analysis). PC is generally considered the best method for
the pragmatic purposes of data reduction.
Data reduction means that the goal is to simplify, by summarising the
variance associated with, say, 30 items
down to, say, 5 factors. The goal is to capture the lion's share
of the variance in the 30 items using a smaller number of factors.
PC is most common used in the process of
- mental test development and for
- developing composite scores for subsequent analyses (e.g., using ANOVA
What is a Simple or Clean Factor Structure?
- A simple or clean factor structure is evident when each item in a factor
analysis loads highly on one factor and lowly on other factors.
- Note that the 'appearance' of a simple factor structure can occur by
suppressing loadings below (typically) .1, .2., .3, etc. Suppression of
factor loadings should always be indicated in a table note.