Latent Variable ModelingSummary / Final Thoughts Karen Bandeen-Roche Qian-Li Xue October 28, 2016
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?
Objectives • What is a latent variable (LV)?
“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
Objectives • What is a latent variable (LV)? • Measurement is strongest when model linking observables to underlying variables is informed by scientific theory
Objectives • What are some common LV models?
Well-used latent variable models General software: MPlus, Latent Gold, WinBugs (Bayesian), NLMIXED (SAS) gllamm (Stata)
Objectives • What are major features of LV modeling? • Hierarchical: structural and measurement components • Fitting • Evaluating fit • Predictions • Identifiability
Objectives • Why should I consider using—or decide against using—LV models? • Perhaps the highest reason: measurement properties (reliability, validity)
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
Advanced topics • Differential measurement • Implications for scoring / prediction • Study designs • Ramifications for risk factor analysis • Translation of findings into improved measurement strategies
Advanced topics • Novel fitting methods • Big data • 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
Advanced topics • Novel scoring methods • Latent class outcome scoring • “Error” correction Croon, LatVar & LatStruct Model, 2002 • Bartlett-like method Petersen et al., Psychometrika, 2012 • Estimating equations approaches Sanchez et al., Ann Appl Stat, 2009 Vermunt, Political Analysis, 2010
Advanced topics • Beyond model checking / identifiability • Characterization of model family consistent with one’s data • Sensitivity analysis
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
Proper use oflatent 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.
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.