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2. 2 3. 3 Q & A 4. 4 Growth Change 5. 5 Cross-sectional vs. Longitudinal () () 1. 2. ( Multilevel analysis) 3. 4. (Panel & Cohort studies) 6. 6 vs. 7. 7 () 88 8. 8 (Latent Growth Modeling, LGM) Latent Curve Models Latent Growth Curve Models Latent Change Analysis Latent Trajectory Models Multilevel Analysis (Hierarchical Linear Model, HLM) Mixed Effects Models Random Effect Models 9. 9 IM ean,IV ar ICEPT S M ean,S V ar SLOPE 0 X1 1 0 0 X2 1 1 0 X3 1 2 0 X4 1 3 0 X5 1 4 0, Var E1 1 0, Var E2 1 0, Var E3 1 0, Var E4 1 0, Var E5 1 CovIS 10. 10 SEM() (Kline, 2006) 1.(y) 2. 3. 4. 0 5 10 15 20 25 30 0 2 4 6 8 10 Time Outcome 11. 11 LGMSEM Kline (2005)pn p:n=1:101:20 (Jackson, 2003) 12. 12 Kline (2005, p49~50) kurtosis=3 ( 3kurtosis=0 skew=0) 2 8 skew>3 kurtosis>20 13. 13 LGC () () (0) 14. 14 (INTERCEPT) 1 (SLOPE) ( ) 1.10 2.21 3.34 15. 15 y1 y2 y3 y4 y5 e1 e2 e3 e4 e5 Intercept 1 1 1 1 1 Mean Var. 5 1 (); 16. 16 0,1,2,3,4 0,1,2,3,4 1(y1) (=0) 1,2,3,4 1 y1 y2 y3 y4 y5 e1 e2 e3 e4 e5 Slope 0 1 2 3 4 Mean Var. 17. 17 (Y3) 0,1,3,4 612 24 0,1,2,4 (e.g., quadratic) 0,1,2,3,4 0,1,4,9,16 18. 18 19. 19 1 2 3 X1 1 0 0 -3 X2 1 1 2 -2 X3 1 2 4 -1 X4 1 3 6 0 20. 20 0 () 21. 21 () () 22. 22 () 23. 23 0 2 4 6 8 10 12 14 16 18 1 2 3 4 5 6 Time Outcome Cov Cov Cov 24. 24 () () 25. 25 200620072008 567 200220042008 26. 26 LGM (T = 3) = T(T + 1)/2+T 4 4 64 14 2 2 T 1 ICEPT SLOPE 0 y1 1 0 0 y2 1 1 0 y3 1 2 0 y4 1 3 0, var E1 1 0, var E2 1 0, var E3 1 0, var E4 1 27. 27 T(T + 1)/2 + T P0 T: P: T = 3, df = 9 8 = 1 T = 4, df = 14 9 = 5 T = 5, df = 20 10= 10 T = 6, df = 27 -11= 18 T = 7, df = 35 -12= 23 ICEPT SLOPE 0 y1 1 0 0 y2 1 1 0 y3 1 2 0 y4 1 3 0, var E1 1 0, var E2 1 0, var E3 1 0, var E4 1 28. 28 1. 2. SEM likelihood ratio chi-square test (2) comparative fit index (CFI) root mean-square error of approximation (RMSEA) 3. 4. 5. / 29. 29 (IS-Model) ICEPT SLOPE 0 y1 1 0 0 y2 1 1 0 y3 1 2 0 y4 1 3 0, var E1 1 0, var E2 1 0, var E3 1 0, var E4 1 time1 time2 time3 time4 30. 30 31. 31 1. 0 5 10 15 20 25 30 35 8 years 10 years 12 years 14 yesrs 20 21 22 23 24 25 26 27 8 years 10 years 12 years 14 yesrs 32. 32 0 5 10 15 20 25 30 8 years 10 years 12 years 14 yesrs 33. 33 i0 s Vari Vars() Covis:() () 34. 34 2. 35. 35 3. Imean 8 21.989 *** Smean 6 1.362 *** Ivar 8 3.146 0.013 Svar 6 0.335 0.113 IScov 8 0.143 0.679 Level 1 E1 8 2.108 0.027 E2 10 1.462 0.007 E3 12 2.313 0.003 E4 14 .309 0.710 36. 36 3. 21.99 61.36 68% 21.991.77 668% 1.360.579 37. 37 4. 38. 38 Picecwise LGM Period 1 Period 2 39. 39 (Piecewise LGM) time1 time2 time3 time4 time5 Phase 1 Phase 2 40. 40 41. 41 rmsea>0.08 42. 42 (additive LGM) time1 time2 time3 time4 time5 Phase 1 Phase 2 43. 43 44. 44 45. 45 rmsea=0.104NNFICFI 0.9 46. 46 (non-linear LGM) IM ean,IVarICEPT 0 X1 1 0 X2 1 0 X3 1 0 X4 1 0, Var E1 1 0, Var E2 1 0, Var E3 1 0, Var E4 1 Q M ean,Q Var QUAD 0 1 4 9 CovIQ IM ean,IVar ICEPT SM ean,SVar SLOPE 0 X1 1 0 0 X2 1 1 0 X3 1 2 0 X4 1 3 0, Var E1 1 0, Var E2 1 0, Var E3 1 0, Var E4 1 CovIS Q M ean,Q Var QUAD 0 1 4 9 CovSQ CovIQ 47. 47 (non-linear LGM) time1 time2 time3 time4time1 time2 time3 time4 time1 time2 time3 time4 time1 time2 time3 time4 logit 48. 48 (non-linear LGM) time1 time2 time3 time4 49. 49 50. 50 rmsea=0 51. 51 (Conditional LGM) 52. 52 (Conditional LGM) 53. 53 ? 54. 54 55. 55 56. 56 57. 57 (Multivariate LGM) 58. 58 59. 59 () () 1. 2. 3. (e1 e2 e3) 4. 60. 60