Lecture 5 - Latent Variables: Spirits in the Material World or Ghost in the Machine?

1. Lecture 5 - Latent Variables: Spirits in the Material World or Ghost in the Machine? Karen Bandeen-Roche Hurley-Dorrier Professor and Chair of Biostatistics Johns Hopkins University Introduction to Statistical Measurement and Modeling Nanjing University July 15, 2011

2. Johns Hopkins Claude D. Pepper Older Americans Independence Center • The National Institutes of Health • The Brookdale National Foundation

3. Objectivesfor you to leave here knowing… • What is a latent variable? • What are some common latent variable models? • What is the role of assumptions in latent variable models? • Why should I consider using—or decide against using—latent variable models?

7. ε . Ordinary Linear RegressionResidual as Latent Variable . Y . ε X Y . . . . . . . . . . . . X

8. Mixed effect / Multi-level modelsRandom effects as Latent Variables . . . β0 + β1 . . . . . vital . . . β2+ β3 . . . . . . β0 . . . . . . non-vital . . β2 . . . time 0

9. Mixed effect / Multi-level modelsRandom effects as Latent Variables • b0i = random intercept b2i = random slope (could define more) • Population heterogeneity captured by spread in intercepts, slopes +b0i slope: -|b2i| . . . β0 + β1 . . . . . vital . . . β2+ β3 . . . . . . β0 . . . . . . non-vital . . β2 . . . time 0

10. Mixed effect / Multi-level modelsRandom effects as Latent Variables +b0i slope: -|b2i| . . . β0 + β1 . . . . . vital . . ε . β2+ β3 X Y . . . . . . β0 . . . . b . t . non-vital . . β2 . . . time 0

11. Frailty Latent Variable Illustration e1 Y1 … Adverse outcomes Frailty ep Yp Determinants

13. Why do people use latent variable models? • The complexity of my problem demands it • NIH wants me to be sophisticated • Reveal underlying truth (e.g. “discover” latent types) • Operationalize and test theory • Sensitivity analyses • Acknowledge, study issues with measurement; correct attenuation; etc.

14. Well-used latent variable models General software: MPlus, Latent Gold, WinBugs (Bayesian), NLMIXED (SAS), glmm

15. Tailored software: AMOS, LISREL, CALIS (SAS)

16. Example: Theory Infusion • Inflammation: central in cellular repair • Hypothesis: dysregulation=key in accel. aging • Muscle wasting (Ferrucci et al., JAGS 50:1947-54; Cappola et al, J Clin Endocrinol Metab 88:2019-25) • Receptor inhibition: erythropoetin production / anemia (Ershler, JAGS 51:S18-21) up-regulation Stimulus (e.g. muscle damage) IL-1# TNF IL-6 CRP inhibition # Difficult to measure. IL-1RA = proxy

17. Frailty Latent Variable Illustration Measurement Theory informs relations (arrows) e1 ς Y1 λ1 Inflam. regulation … Adverse outcomes ep Yp λp Determinants Structural

18. Theory infusionInCHIANTI data (Ferrucci et al., JAGS, 48:1618-25) • LV method: factor analysis model • two independent underlying variables • down-regulation IL-1RA path=0 • conditional independence .36 -.59 IL-6 . 59 IL-1RA -.40 . 45 Inflammation 1 Up-reg. Inflammation 2 Down-reg. CRP . 31 IL-18 .20 . 31 TNFα Bandeen-Roche et al., Rejuv Res, 2009

19. Interlude • What is mind-body dualism? To whom does the idea owe? • Rene Descartes • To whom does the title of my talk owe? • The Police • Ghost in the Machine: Gilbert Ryle

20. ANOTHER WELL-USED LATENT VARIABLE MODELMotivation: Self-reported Visual functioning • Questionnaires have proliferated • This talk: Activities of Daily Vision5 (ADV) • “Far vision” subscale: How much difficulty with reading signs (night, day); seeing steps (day, dim light); watching TV = Y1,...,Y5 • Question of interest: What aspects of vision determine “far vision” function • One point of view on such “function”: Latent subpopulations

21. Analysis of underlying subpopulationsLatent class analysis / regression POPULATION Ci Xi … P1 PJ ∏11 ∏1M ∏J1 ∏JM … … Y1 YM Y1 YM 19-Goodman, 1974; 27-McCutcheon, 1987

22. Analysis of underlying subpopulations Method: Latent class analysis/ regression • Seeks homogeneous subpopulations • Features that characterize latent groups • Prevalence in overall population • Proportion reporting each symptom • Number of them • Assumption:reporting heterogeneity unrelated to measured or unmeasured characteristics • conditional independence, non differential measurement by covariates of responses within latent groups : partially determine features

23. no x

24. LCR: Self-reported Visual functioning • Study: Salisbury Eye Evaluation (SEE; West et al. 19976) • Representative of community-dwelling elders • n=2520; 1/4 African American • This talk: 1643 night drivers • Analyses control for potential confounders: • Demographic: age (years), sex(1{female}), race(1{nonwhite}), education (years) • Cognition: Mini-Mental State Exam score (MMSE; 30-0 points) • Depression: GHQ subscale score (0-6) • Disease burden: # reported comorbidities

25. Aspects of vision • Visual acuity: .3 logMAR (about 2 lines) • Contrast sensitivity: 6 letters • Glare sensitivity: 6 letters • Stereoacuity: .3 log arc seconds • Visual field: root-2 central points missed • Latter two: span approximately .60 IQR

31. MODEL CHECKING IS POSSIBLE!

32. Observed (solid) and Predicted (dash) Item Prevalence vs Acuity Plots

43. One last issueIdentifiability • Models can be too big / complex • A model is non-identifiable if distinct parameterizations lead to identical data distributions • i.e. analysis not grounded in data • Weak identifiability is common too: • Analysis only indirectly grounded in data (via the model)

44. Identifiability strong model analysis data (ground)

45. Identifiability weak model analysis data (ground)

46. Identifiability non model analysis data (ground)

47. Objectivesfor you to leave here knowing… • What is a latent variable? • What are some common latent variable models? • What is the role of assumptions in latent variable models? • Why should I consider using—or decide against using—latent variable models?

49. Postlude • “Where does the answer lie? … it’s something we can’t buy” • Have a great career