1. Latent Variable Modeling Summary / Final Thoughts
Karen Bandeen-Roche
Qian-Li Xue
October 28, 2016

2. Objectives What is a latent variable (LV)?
What are some common LV models?
What are major features of LV modeling?
Hierarchical: structural and measurement components
Fitting
Evaluating fit
Predictions
Identifiability
Why should I consider using—or decide against using—LV models?

3. Objectives
What is a latent variable (LV)?

4. “LATENT”
“…concepts in their purest form… unobserved or unmeasured … hypothetical”
Bollen KA, Structural Equations with Latent Variables, p. 11, 1989
“…in principle or practice, cannot be observed”
Bartholomew DJ, The Statistical Approach to Social Measurement, p. 12
“Underlying: not directly measurable. Existing in hidden form but capable of being measured indirectly by observables.”
Bandeen-Roche K, Synthesis, 2006

5. Objectives What is a latent variable (LV)?
Measurement is strongest when model linking observables to underlying variables is informed by scientific theory

6. Objectives
What are some common LV models?

7. Well-used latent variable models
Latent variable scale
Observed variable scale
Continuous
Discrete
Factor analysis
LISREL
Discrete FA
IRT (item response)
Latent profile
Growth mixture
Latent class analysis, regression
General software: MPlus, Latent Gold, WinBugs (Bayesian), NLMIXED (SAS)
gllamm (Stata)

8. Well-used latent variable models
Latent variable scale
Observed variable scale
Continuous
Discrete
Factor analysis
LISREL
Discrete FA
IRT (item response)
Latent profile
Growth mixture
Latent class analysis, regression

9. Objectives What are major features of LV modeling?
Hierarchical: structural and measurement components
Fitting
Evaluating fit
Predictions
Identifiability

10. Objectives
Why should I consider using—or decide against using—LV models?
Perhaps the highest reason: measurement properties (reliability, validity)

11. Advanced topics More models Many of them!
Hybrids (ex/ Factor mixture model)
Lubke & Muthen, Psych Methods, 2005
Specialties (ex/ latent class logit model for discrete choice data)
Greene & Henscher, Transportation Res B, 2003
Scientifically relevant models

12. Advanced topics Differential measurement
Implications for scoring / prediction
Study designs
Ramifications for risk factor analysis
Translation of findings into improved measurement strategies

13. Advanced topics Novel fitting methods Big data Flexible models
Penalized models
Houseman, Coull, Betensky, Biometrics, 2006
Leoutsakos et al., Statist Med, 2011
Flexible models
Methods that merge model based (latent variable) and data descriptive (robust) features

14. Advanced topics Novel scoring methods Latent class outcome scoring
“Error” correction
Croon, Lat Var & Lat Struct Model, 2002
Bartlett-like method
Petersen et al., Psychometrika, 2012
Estimating equations approaches
Sanchez et al., Ann Appl Stat, 2009
Vermunt, Political Analysis, 2010

15. Advanced topics Beyond model checking / identifiability
Characterization of model family consistent with one’s data
Sensitivity analysis

16. Closing thought: Philosophy
Why?
To operationalize / test theory
To learn about measurement errors, differential reporting
They summarize multiple measures parsimoniously
To describe population heterogeneity
Popperian learning
Why not?
Their modeling assumptions may determine scientific conclusions
Their interpretation may be ambiguous
Nature of latent variables?
Uniqueness (identifiability)
What if very different models fit comparably? (estimability)
Seeing is believing
Import: They are widely used

17. Proper use of latent variable models?
The complexity of my problem demands it
NIH wants me to be sophisticated
Reveal underlying truth
Operationalize and test theory
Model checking is crucial
Sensitivity analyses
Acknowledge, study issues with measurement; correct attenuation; etc.

18. Thank you!

19. Three Excellent Textbooks
Bartholomew D, Knott M & Moustaki I. Latent Variable Models and Factor Analysis: A Unified Approach, 3d. Edition. Wiley: London, 2011.
Bollen KA. Structural Equations with Latent Variables. Wiley: New York, 1989.
Skrondal A, Rabe-Hesketh S. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equations Models. Chapman & Hall: Boca Raton, 2004.