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Latent Variable Modeling Summary / Final Thoughts

This summary presents the key concepts, features, and reasons for using latent variable (LV) models in data analysis. It covers common LV models, hierarchical components, fitting methods, and advanced topics like differential measurement and novel fitting methods. By exploring these models, researchers can gain insights into measurement properties, study designs, and improved measurement strategies. The closing thoughts discuss the philosophy behind utilizing LV models and the importance of proper use in research. Key textbooks for further reading are also recommended.

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Latent Variable Modeling Summary / Final Thoughts

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  1. Latent Variable ModelingSummary / 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 General software: MPlus, Latent Gold, WinBugs (Bayesian), NLMIXED (SAS) gllamm (Stata)

  8. Well-used latent variable models

  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 • 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, 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

  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 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.

  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.

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