: (EQS) /EQUATIONS V1 = 30*V F1 + E1; V2 = 25*V *F1 + E2; V3 = 16*V *F1 + E3; V4 = 10*V F2 + E4; V5 = 19*V99
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1 : (EQS) /EQUATIONS V1 = 30*V F1 + E1; V2 = 25*V *F1 + E2; V3 = 16*V *F1 + E3; V4 = 10*V F2 + E4; V5 = 19*V *F2 + E5; V6 = 17*V *F2 + E6; CALIS (latent curve model) ( ) ( ) AMOS EQS 12 CALIS 1 2 McArdle(1988) Meredith-Tisak(1990) Duncan et. al.(1999) (2000, 12 )
2 ( ) ( ) 3 (1999) (T 1,T 2,T 3 ) n = 363 (T 1,T 2,T 3 ) (X 1,X 2,X 3 ) 1.36, 2.12, 3.18 ( ) ( ) 3 (X 4 ) (X 5 =1, =0 ) (X 6 ) : (n=363) X1 X2 X3 X4 X5 X6 T T T ( 1, 0) Curran(2000)
3 : ( ) 7.1: ( ) X 4 : X 5 : X 6 : X 4 X 5 : X 6 : ( ) X 4, X 5, X 6 2 (HLM, Hierarchical Linear Model) MLM(MultiLevel Model). 5 run 5 Raudenbush et. al. (2000) HLM5. Bryk-Raudenbush(1992)
4 t x t t =1, 2, 3. 6 x t β 0, β 1 x t = β 0 +(t 1)β 1 + e t (t =1, 2, 3) (7.1). 7 e t x (i) t = β (i) 0 +(t 1)β (i) 1 + e (i) t (t =1, 2, 3; i =1,, 363) β 0, β (7.1) (7.1) β 0, β 1 3 x 1 = β 0 +0 β 1 + e 1 x 2 = β 0 +1 β 1 + e 2 x 3 = β 0 +2 β 1 + e 3 x " x 2 = x 3 β 0 β 1 # + e 1 e 2 e 3 (7.2) [β 0, β 1 ] 0 0, 1, 2 6 t =1, 4, 5 7 x t = β 0 + tβ 1 + e t (t =0, 1, 2) X 1,X 2 (0 )1 7.3: 1 ( ) (7.2) 7.3 β 0 β 1 ( ) 4.2 ( ) ( ) (T 1 ) (T 1 )
5 EQS 7.5 ( ) 7.90, β 0, β E(β 0 ) (T 1 ) E(β 1 ) (1 ) E(β 0 ) E(β 1 ) 7.3 (6.2 ) 7.5: 1 7.4: , 1, p.168 (7.3) EQS CALIS (CONSTANT) Intercept Factor(β 0 ) Linear Growth Factor(β 1 ) CONSTANT 1.36, T 1 (X 1 ) 1.36 T 2 T =2.24, = , 3.18 ( ) 7.90 Var(e 1 ) X T 1 (X 1 )
6 ± = 0.88 ± = 0.10 T 1 e 1 e 3 e EQS ( ) (X 4 X 6 ) /INEQUALITY <(E1,E1);. 11 e 1 z-.586,.746,.785 e 1 z- e 1 9 d Var(e1 )= = AMOS, CALIS 11 (*.eqx) Inequality (E1,E1) 7.6: ( ) Lower Range Create
7 ( ) ( ) (T 1 ) β 0 β 1 1 α 0, α 1 13 E[ ] ( β 0 = α 0 + γ 0 X 4 + d 1 β 1 = α 1 + γ 1 X 4 + d 2 X : X 4 =0( ) X 4 =1( ) E(β 0 ) α 0 α 0 + γ 0 E(β 1 ) α 1 α 1 + γ 1 α 0, α 1 γ 0 γ 1 γ 0 6=0 γ 1 6=0 α 0 =1, α 1 =1; γ 0 =4, γ 1 = d 1 d 2 β 0 β 1 7.8: 3 ( ) 7.7: β 0 β 1 β 0 7.6
8 232 7 γ γ 1 =0 3 ( 7.8) : 2 p GFI CFI RMSEA T 1 ( ) ( ) 1. T ( ) 2. T (0.69) T e d e e d 14 γ 1 =0 E(β 1 ) 7.2. AMOS, EQS, CALIS 233 (Var(e i )) (Var(d i )) ( ) x t = β 0 +(t 1)β 1 +(t 1) 2 β 2 + e t (t =1, 2, 3) β 0, β 1, β 2 3 x 3 x 1 = β 0 +0 β 1 +0 β 2 + e 1 x 2 = β 0 +1 β 1 +1 β 2 + e 2 x 3 = β 0 +2 β 1 +4 β 2 + e 3 x x 2 = β 0 β 1 β e 1 e 2 e AMOS, EQS, CALIS 1 ( ) 15 (2000)
9 AMOS, EQS, CALIS : AMOS MS-Excel : AMOS Growth Curve Model (Number of time points 3) ,1,1, 0,1,2 7.11: X 1,X 2,X 3 T 1,T 2,T (ICEPT) (SLOPE) 0 AMOS 7.12 Var(e d 1 )=.59 AMOS 7.4 Var(e 1 ) Var(e 1 ) 0 AMOS Var(e 1 )=0 e 1
10 AMOS, EQS, CALIS 237 ( df=1) 7.12: (7.3) 7.4 p AMOS df=2, p =.387 Var(e 1 ) 7.13: 1 7.4: e (M=1) ICEPT SLOPE ( )d 1 d
11 238 7 (df=4 ) EQS 7.2. AMOS, EQS, CALIS 239 Line for this measurement 3 Continue Latent Growth Curve Model (Step 2 of 2) ( 7.15) EQS 1 ( ) 2 EQS 7.1 alcohol.ess 7.15: Latent Growth Curve Model (Step 2 of 2) 7.14: Latent Growth Curve Model (Step 1 of 2) New Model Helper 3 Latent Growth Curve Model Latent Growth Curve Model (Step 1 of 2) ( 7.14) Variable List V 1 V 3 > Variable Deployed Time Initial Status Model 3 Linear Quadratic 2 Spline Linear Quadratic 2 gwlinear.eds 7.16 Draw Covariances
12 AMOS, EQS, CALIS : : Layout Break Group V V 4,V 5,V File Save As EQS Build EQS Title/Specifications EQS Model Specification OK 18 View Labels 19 View Labels Type of Analysis Structural Mean Analysis gwlinear.eqx EQS Build EQS Run EQS alcohol.eqx gwlinear.out Window gwlinear.eds CALIS CALIS 1 ( 7.3) SAS 7.6 µ(θ) CALIS E[XX 0 ]=µ(θ)µ(θ) 0 + Σ(θ) 20 EQS
13 AMOS, EQS, CALIS : 1 /TITLE Latent Curve Model with Independent Variables Created by EQS 6 for Windows /SPECIFICATIONS DATA= alcohol.ess ; VARIABLES=6; CASES=363; METHODS=ML; MATRIX=CORRELATION; ANALYSIS=MOMENT; /LABELS V1=T1; V2=T2; V3=T3; V4=AGE; V5=SEX; V6=ALC; /EQUATIONS V1 = 1F1 + 0F2 + 1E1; V2 = 1F1 + 1F2 + 1E2; V3 = 1F1 + 2F2 + 1E3; V4 = *V E4; V5 = *V E5; V6 = *V E6; F1 = *V4 + *V5 + *V6 + *V D1; F2 = *V4 + *V5 + *V6 + *V D2; /VARIANCES V999 = 1.00; E1 TO E6 = *; D1 TO D2 = *; /COVARIANCES E4 TO E6 = *; D2, D1 = *; /PRINT FIT=ALL; TABLE=EQUATION; /OUTPUT PARAMETER ESTIMATES; STANDARD ERRORS; RSQUARE; LISTING; /END McDonald(1980) 2 McDonald 2 (covariance matrix for uncorrected for the mean) UCOV 7.6: 1 SAS DATA alcohol(type=corr); INPUT _TYPE_ $ _NAME_ $ t1 t2 t3 age sex alc; CARDS; N CORR t CORR t CORR t CORR age CORR sex CORR alc MEAN STD ; PROC CALIS UCOV AUG DATA=alcohol; LINEQS t1 = 1 f_icept + 0 f_slope + e1, t2 = 1 f_icept + 1 f_slope + e2, t3 = 1 f_icept + 2 f_slope + e3, f_icept = alpha_1 INTERCEP + d1, f_slope = alpha_2 INTERCEP + d2; STD e1-e3 = del1-del3, d1-d2 = psi1-psi2; COV d1-d2 = psi21; RUN; 1 LINEQS INTERCEP AUG. 21 f_icept f_slope d1 d2 f_icept f_slope f_icept 21 Augmented covariance matrix McDonald
14 244 7 f_slope d1 d2 f_icept f_slope e 1 t Value ( < 1.96) 7.7: Var(e d 1 ) WARNING: The central parameter matrix _PHI_ has probably 1 negative eigenvalue(s). Variances of Exogenous Variables Standard Variable Parameter Estimate Error t Value E1 DEL Var(4 1 ) 0 RUN; BOUNDS del1 >=0; 7.8 CALIS Var(e 1 ) 0 Var(e d 1 )=0 Var(e 1 ) Var(e 1 )= SAS (PROC ) Var(e 1 ) : 1 CALIS Manifest Variable Equations T1 = F_ICEPT E1 T2 = F_ICEPT F_SLOPE E2 T3 = F_ICEPT F_SLOPE E3 Latent Variable Equations F_ICEPT = *INTERCEP D1 Std Err ALPHA_1 t Value F_SLOPE = *INTERCEP D2 Std Err ALPHA_2 t Value Variances of Exogenous Variables Standard Variable Parameter Estimate Error t Value INTERCEP E1 DEL E2 DEL E3 DEL D1 PSI D2 PSI
15 : 1 PROC CALIS UCOV AUG DATA=alcohol; LINEQS t1 = 1 f_icept + 0 f_slope + e1, t2 = 1 f_icept + 1 f_slope + e2, t3 = 1 f_icept + 2 f_slope + e3, f_icept = alpha_1 INTERCEP + gamma_11 age + gamma_12 sex + gamma_13 ALC + d1, f_slope = alpha_2 INTERCEP + gamma_21 age + gamma_22 sex + gamma_23 alc + d2, age = m4 INTERCEP + e4, sex = m5 INTERCEP + e5, alc = m6 INTERCEP + e6; STD e1-e6 = del1-del6, d1-d2 = psi1-psi2; COV d1-d2 = psi21, e4-e6 = del54 del64 del65; BOUNDS del1 >=0; RUN; 1 (latent growth model) (latent growth curve model) (growth curve model) ( ) (e.g., ) ( ) ( ) HLM Neale Mx Mx ( ) URL :
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Title 講義のーと : データ解析のための統計モデリング Author(s) 久保, 拓弥 Issue Date 2008 Doc URL http://hdl.handle.net/2115/49477 Type learningobject Note この講義資料は, 著者のホームページ http://hosho.ees.hokudai.ac.jp/~kub ードできます Note(URL)http://hosho.ees.hokudai.ac.jp/~kubo/ce/EesLecture20
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