1. Factor Analysis
Video lecture 1, Factor Analysis
1.1 Introduction Factor Analysis
Purpose of Factor Analysis
- Estimate a model which explains variance/covariance between a set of observed variables
(in a population) by a set of (fewer) unobserved factors & weightings
o How do sets interrelate with each other → understand how unobserved factors play
a role in the dataset of observed factors.
Example
Collect data
Now you’re interested in how these 6 sets (1-3 = fair grading / 4-6 = satisfaction) relate to each other
- How do G1-2-3 together form the perception of fair grading
- How do S1-2-3 form the perception of satisfaction
➔ Factor analysis
What is factor analysis?
- Interdependence technique → how different items interrelate with each other (not yet
prediction)
- Define structure among variables → define structure among observed variables in dataset
and find out how they relate to each other
- Interrelationships among large number of variables to identify underlying dimensions →
underlying dimensions = factors
- 2 purposes → Data summarization and reduction
,Recap: Measurement model
Underlying items (X1 – 2- 3) → construct
- S1, S2, S3 form perception of satisfaction
Also interested in measurement errors → systematic biases
In total
Why doing Multi-item measurement?
- Increases reliability and validity of measures
- Allows measurement assessment
o Measurement error
o Reliability
o Validity
- Two forms of measurement models
o Formative (emerging = more items who emerge as construct) & reflective (latent =
items reflect construct)
▪ We will see reflective the most → factor analysis
,Reliability and Validity
Reliable → nicely cluster Nicely on target Spread out and
together. Not valid → not but not not on target
on target clustered
together
Reflective measurement models
- Direction of causality is from construct to measure
- Correlated indicators = items correlate with each other and these are used to explain
dimensions
- Takes measurements error into account at item level
- Validity of items is usually tested with FACTOR ANALYSIS.
X1 = factor loading * construct + measurement error
This is what we do with factor analysis
Applications
- Assess the validity of construct measurements
- Practice
o Market segmentation (analyze market according to variables and see how different
customers react to these);
o Product research (how benefit attributes of new products score);
o Price management (how price sensitive)
- So… anything where you would like to asses higher-order dimensions
, 1.2 Conducting a Factor Analysis
Process → from problem formulation to model fit (always the same)
Analysis Process
1. Formulate the problem
2. Construct the correlation matrix
3. Selection extraction method
4. Determining number of factors
5. Rotating factors
6. Interpreting factors → what does this variations tell
7. Using factors in other analyses
8. Determining model fit
Problem Formulation
- The objectives of factor analysis should be identified
o Data summarization
o Data reduction
- Which variables are going to be measured, criteria:
o Based on past research, theory and judgment of the researcher3
o Measurement properties (must be ratio, interval)
o Sample size (4-5 * N per variable) → too low = not enough power
▪ 4 to 5 items per number of respondent per variable
Distinguish between
- Exploratory Factor Analysis
o Exploration of data = finding an underlying structure
o Assumptions that superior factors cause correlations between variables (don’t know
yet what these factors could be)
o Reveal interrelationships.
o Generation of hypotheses
- Confirmatory Factor Analysis
o A priori ideas of underlying factors, derived from theory
o Relationships between variables and factors before conducting the factor analysis
▪ You have expectations
o Testing of hypotheses
Example:
➔ Imagine you want to conduct a research among consumers on their perceptions on
toothpaste
- First you collect data
- How do these items relate and whether they provide you with higher order dimensions