Title: Measurement Models: Exploratory and Confirmatory Factor Analysis
1Measurement Models Exploratory and Confirmatory
Factor Analysis
- James G. Anderson, Ph.D.
- Purdue University
2Conceptual Nature of Latent Variables
- Latent variables correspond to some type of
hypothetical construct - Requires a specific operational definition
- Indicators of the construct need to be selected
- Data from the indicators must be consistent with
certain predictions (e.g., moderately correlated
with one another)
3Multi-Indicator Approach
- A multiple-indicator approach reduces the overall
effect of measurement error of any individual
observed variable on the accuracy of the results - A distinction is made between observed variables
(indicators) and underlying latent variables
(constructs) - Together the observed variables and the latent
variables make up the measurement model
4Principles of Measurement
- Reliability is concerned with random error
- Validity is concerned with random and systematic
error
5Measurement Reliability
- Test-Retest
- Alternate Forms
- Split-Half/Internal Consistency
- Inter-rater
- Coefficient
- 0.90 Excellent
- 0.80 Very Good
- 0.70 Adequate
- 0.50 Poor
6Measurement Validity
- Content ( (whether an indicators items are
representative of the domain of the construct) - Criterion-Related (whether a measure relates to
an external standard against which it can be
evaluated) - Concurrent (when scores on the predictor and
criterion are collected at the same time) - Predictive (when scores on the predictor and
criterion are collected at different times) - Convergent (items that measure the same
construct are correlated with one another) - Discriminant (items that measure different
constructs are not correlated highly with one
another)
7Types of Measurement Models
- Exploratory (EFA)
- Confirmatory (CFA)
- Multitrait-Multimethod (MTMM)
- Hierarchical CFA
8An Exploratory Factor Model
9EFA Features
- The potential number of factors ranges from one
up to the number of observed variables - All of the observed variables in EFA are allowed
to correlate with every factor - An EFA solution usually requires rotation to make
the factors more interpretable. Rotation changes
the correlations between the factors and the
indicators so the pattern of values is more
distinct
10A Confirmatory Factor Model
11CFA Features
- The number of factors and the observed variables
(indicators) that load on each construct (factor
or latent variable) are specified in advance of
the analysis - Generally indicators load on only one construct
(factor) - Each indicator is represented as having two
causes, a single factor that it is suppose to
measure and all other unique sources of variance
represented by measurement error
12CFA Features
- The measurement error terms are independent of
each other and of the factors - All associations between factors are unanalyzed
13A Covariance Structure Model
14A Structural Model of the Dimensions of Teacher
Stress
- Survey of teacher stress, job satisfaction and
career commitment - 710 primary school teachers in the U.K.
15Methods
- 20-Item survey of teacher stress
- EFA (N355)
- CFA (N375)
- 1-Item overall self-rating of stress
- SEM (N710)
16Table1 An oblique five factor pattern solution
(N170)
17Factor Patterns
18EFA Results
- 5 Factor solution
- 4 Items deleted
- Fit Statistics
- Chi Square 156.94
- df 70
- AGFI 0.906
- RMR 0.053
19Confirmatory Factor Analysis
20Covariances between exogenous latent traits
21CFA Results
- 5 Factor solution
- 2 Items deleted
- Fit Statistics
- Chi Square 171.14
- df 70
- AGFI 0.911
- RMR 0.057
22Structural Equation Models
- True Null Model - Hypothesizes no significant
covariances among the observed variables - Structural Null Model - Hypothesizes no
significant structural or correlational relations
among the latent variables - Non-Recursive Model
- Mediated Model
- Regression Model
23Non-recursive model
24Regression Model
25Comparison of Fit Indices
26Results
- Two major contributors to teacher stress
- Work load
- Student Misbehavior
27Confirmatory Factor Analysis with SIMPLIS