2009 KAMS/KSMA Fall International Confernece 274 <Abstract> Usual and Unusual Mistakes in the Use of SEM Seong-Keon Lee ) - Concept of SEM - Types of Linear SEM - Softwares of SEM - Measurement Model and Structural Model - Tips in drawing path diagram - Error terms - Parameters -> Regression weight - Unidentification - Parameters -> Variance - Measurement unit of potential variable - Relationships among external variables - Model fitting index Measures based on the sample discrepancy Measures based on the population discrepancy Information-theoretic measures Comparisons to a baseline model Parsimony Adjusted Measures GFI and related measures Miscellaneous measures Selection of one of several a prori specified models Keywords: SEM, Linear SEM, Measurement Model, Structural Model, Parameters ) Sungshin Women's University
2009 KAMS/KSMA Fall International Confernece 275 Usual and Unusual Mistakes in the Use of SEM 구조방정식모형의이해 - 흔히범하는오류 Lee, Seong-Keon Department of Statistics, Sungshin Women s Univ. 이성건성신여자대학교통계학과
2009 KAMS/KSMA Fall International Confernece 276 선형구조방정식모형 l Linear Structural Equation Model 연구영역속에있는인과변수들간의관계를일련의선형방정식들 로표현한모형. 변수들간의공분산 (covariance) 구조를분석하며, 계량경제및행 동과학분야의연구에서중요한통계적도구로사용됨. ü 다중 (multiple) 또는다변량 (multivariate) 회귀분석 ü 선형측정오차 (measurement-error) 모형 ü 경로분석 (path analysis) 및인과모형 (causal model) ü 탐색적 (exploratory), 확증적 (confirmatory) 인자분석 ü 정준상관분석 (canonical correlation analysis)
2009 KAMS/KSMA Fall International Confernece 277 선형구조방정식모형의표현 l l l l LISREL (Linear Structural relationship) model - Joreskog & Sorbom (974, 989, 993) COSAN (Covariance Structural Analysis) model - McDonald (978, 980) RAM (Reticular Action) model - McArdle (980), McArdle & McDonald (984) LINEQS (Linear Equations) model - Bentler & Weeks (980) ü 구조방정식모형을분석하기위한소프트웨어 LISREL : www.ssicentral.com, www.philscience.com AMOS/SPSS : www.spss.com, www.spss.co.kr CALIS/SAS : www.sas.com, www.sas.com/~korea EQS, EzPATH, LINCS, LISCOMP
2009 KAMS/KSMA Fall International Confernece 278 구조방정식모형 (Structural Equation Model) 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 언어능력 x 수리능력 x 2 대학의학습능력 (h 2 ) 입학시학습능력 (h ) 전공성적 y 2 교양성적 y 3 수능성적 y IQ 점수 x 5 지능 x 3 내생잠재변수 (endogenous latent variables): h, h 2 외생잠재변수 (exogenous latent variables): x, x 2, x 3
2009 KAMS/KSMA Fall International Confernece 279 측정모형과구조모형 l 측정모형 (Measurement Model) 잠재변수 (latent variable) 들과관찰변수 (observable variable) 들간 의연관 ( 측정 ) 관계를규정하는모형으로써, 관찰된변수들의측정에 관련된특성들 ( 신뢰도와타당도 ) 을묘사하는데사용되며측정과정에 서불가피하게수반되는오류를반영한다. l 구조모형 (Structural Model) 잠재변수 (latent variable) 들간의연관및인과관계에의해가설화된 구조를규정하는모형으로써, 인과의효과들과이를통해설명되어 지지않은모형오차의변이를묘사하는부분이포함된다.
2009 KAMS/KSMA Fall International Confernece 280 경로도작성시주의해야할사항 l l l l l 오차변수오차변수의계수를 로고정하기단일지시자문제잠재변수의측정단위규정외생변수들간의연관성
2009 KAMS/KSMA Fall International Confernece 28 () 오차변수 δ δ 2 δ 3 δ 4 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 언어능력 x 수리능력 x 2 z 2 대학의학습능력 (h 2 ) 입학시학습능력 (h ) 전공성적 y 2 교양성적 y 3 수능성적 y ε 2 ε 3 ε δ 5 IQ 점수 x 5 지능 x 3 오차변수는일종의잠재변수로서외생변수임 ( 모든내생변수는오차변수를가짐 ). 각오차변수는분산 (variance) 을가지고있음. 일반적으로오차변수들은서로상관되어있지않은것으로가정됨. z
참조 : 오차변수들간의연관성 2009 KAMS/KSMA Fall International Confernece 282
Warning (Error) Message 2009 KAMS/KSMA Fall International Confernece 283
2009 KAMS/KSMA Fall International Confernece 284 (2) 오차변수의계수를 로고정하기 δ δ 2 δ 3 δ 4 δ 5 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 IQ 점수 x 5 언어능력 x 수리능력 x 2 지능 x 3 z 2 대학의학습능력 (h 2 ) 입학시학습 능력 (h ) z 전공성적 y 2 교양성적 y 3 수능성적 y ε 2 ε 3 ε x x = l x x + d 2 = l x 2x + d 2
Parameters Regression weight 2009 KAMS/KSMA Fall International Confernece 285
Unidentification ( 식별불능 ) 2009 KAMS/KSMA Fall International Confernece 286
2009 KAMS/KSMA Fall International Confernece 287 (3) 단일지시자문제 δ δ 2 δ 3 δ 4 δ 5 0 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 IQ 점수 x 5 언어능력 x 수리능력 x 2 지능 x 3 x 5 = l x 53x3 + d y = l y h + e 5 (0) (0) z 2 대학의학습능력 (h 2 ) 입학시학습능력 (h ) z 전공성적 y 2 교양성적 y 3 수능성적 y ε 2 ε 3 ε 0
Parameters Variance 2009 KAMS/KSMA Fall International Confernece 288
2009 KAMS/KSMA Fall International Confernece 289 (4) 잠재변수의측정단위규정 δ δ 2 δ 3 δ 4 δ 5 0 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 IQ 점수 x 5 언어능력 x 수리능력 x 2 지능 x 3 z 2 대학의학습능력 (h 2 ) 입학시학습능력 (h ) z 전공성적 y 2 교양성적 y 3 수능성적 y 잠재변수와인과변수들간의관계를적절히파악하기위해특히모수행렬들의원소들이가지는의미를해석, 비교하기위해서는잠재변수들에대한측정단위가규정되어야할필요가있음. ε 2 ε 3 ε 0
Parameters Regression weight 2009 KAMS/KSMA Fall International Confernece 290
2009 KAMS/KSMA Fall International Confernece 29 (5) 외생변수들간의연관성 δ δ 2 δ 3 δ 4 δ 5 0 국어점수 x 영어점수 x 2 수학점수 x 3 과학점수 x 4 IQ 점수 x 5 언어능력 x f f 2 3 수리능력 x 2 지능 x 3 f 32 z 2 대학의학습능력 (h 2 ) 입학시학습능력 (h ) z 전공성적 y 2 교양성적 y 3 수능성적 y ε 2 ε 3 ε 0 일반적으로내생변수들간에는서로상관되어있는것으로가정됨. f 2 = cov( x2, x)
Warning (Error) Message 2009 KAMS/KSMA Fall International Confernece 292
2009 KAMS/KSMA Fall International Confernece 293 모형의평가 - 적합도지수 l l l Measures based on the Sample Discrepancy ü FMIN (minimum fit function value) 작을수록우수 ü CMIN ( 카이제곱값 ) : (N-)ⅹF min 작을수록우수 ü CMIN/df 2( 또는 3) 이하이면우수 Measures based on the Population Discrepancy ü NCP (non-centrtrality parameter) : CMIN-df 작을수록우수 ü RMSEA (root mean square error of...) 0.05( 또는 0.0) 이하이면우수 Information-theoretic Measures ü AIC (Akaike information criterion) : CMIN + 2q 작을수록우수 ü BCC (Browne-Cudeck (989) criterion) 작을수록우수 ü BIC (Bayes information criterion) : CMIN + q ln(n) 작을수록우수 ü CAIC (consistent AIC) : CMIN + q (ln(n)+) 작을수록우수 ü ECVI (expected cross-validation index) : AIC/n 작을수록우수 ü MECVI : BCC/n 작을수록우수
2009 KAMS/KSMA Fall International Confernece 294... 적합도지수 l l l Comparisons to a Baseline Model ü NFI (normed fit index) 0.9 이상이면우수 ü RFI (relative fit index) 0.9 이상이면우수 ü IFI (incremental fit index) 0.9 이상이면우수 ü TLI (Tucker-Lewis coefficient, NNFI) 0.9 이상이면우수 ü CFI (comparative fit index) 0.9 이상이면우수 Parsimony Adjusted Measures ü PNFI (parsimony adjusted NFI) 0.5( 또는 0.6) 이상이면우수 ü PCFI (parsimony adjusted CFI) 0.5( 또는 0.6) 이상이면우수 GFI and related Measures ü GFI (goodness-of-fit index) 0.9 이상이면우수 ü AGFI (adjusted goodness-of-fit index) 0.9 이상이면우수 ü PGFI (parsimony GFI) 0.5( 또는 0.6) 이상이면우수 ü RMR (root mean square residual) 작을수록우수 ü SRMR (standadized RMR) 0.05 이하이면우수 ( 참조 ) AMOS 에서 SRMR 의출력방법 - AMOS A to Z 논문작성절차에따른구조방정식모형분석 ( 김대업, 학현사 )
2009 KAMS/KSMA Fall International Confernece 295... 적합도지수 l Miscellaneous Measures ü CN (Hoelter s critical N) 200 이상이면우수 ü RMR (root mean square residual) 작을수록우수 ü SRMR (standadized RMR) 0.05 이하이면우수 ü CVI (cross-validation index) : F(S v,σ m ) (/2n v )k(k+) l Selection of One of Several a priori Specified Models ü Another approach is to compare the models on the basis of some criteria that takes parsimony (in the sense of number of parameters) into account as well as fit. This approach can be used regardless of whether or not the models can be ordered in a nested sequence. Three strongly related criteria have been proposed: the AIC measure of Akaike (974, 987), the CAIC by Bozdogan (987), and the single sample cross-validation index ECVI by Browne & Cudeck (989). ü To apply these measures to the decision problem, one estimates each model, ranks them according to one of these criteria and chooses the model with the smallest value.
2009 KAMS/KSMA Fall International Confernece 296 <Abstract> How to Get the Moderating and Mediating Effect in SEM Hyuncheol Kang ) - Mediating effect - Direct effect, indirect effect and total effect - Moderating effect Discrete moderating variable Continuous moderating variable Keywords: Mediating effect, Direct effect, Indirect effect, Total effect, Discrete moderating variable, Continuous moderating variable ) Hoseo University
2009 KAMS/KSMA Fall International Confernece 297 How to get the moderating and mediating effect in SEM 2009.. 2. 강현철 호서대학교정보통계학과
2009 KAMS/KSMA Fall International Confernece 298 매개효과 (Mediating Effect) l 매개변수 (Mediator Variable) ü 외생변수와내생변수의인과관계에서중간에개입하는변수. ü 매개변수에의한간접효과가 0이아닐때매개효과가있다고한다. ( 부분매개, 완전매개 ) 근무년수 a e 호감 z 3 b 지지도 z 2 나이 d f c 복종심 z
2009 KAMS/KSMA Fall International Confernece 299 직접효과, 간접효과, 총효과 l 직접효과 (Direct Effect) ü 외생변수가내생변수에직접적으로미치는효과. 예 ) 나이 지지도 의직접효과 : b 복종심 호감 의직접효과 : f l 간접효과 (Direct Effect) ü 외생변수가매개변수들을통해내생변수에간접적으로미치는효과예 ) 나이 지지도 의간접효과 : cⅹd 나이 호감 의간접효과 : (bⅹe )+(cⅹdⅹe )+(cⅹf ) l 총효과 (Total Effect) ü 직접효과 + 간접효과 예 ) 나이 지지도 의총효과 : b+(cⅹd )
2009 KAMS/KSMA Fall International Confernece 300 Some Background References Baron, R. M., & Kenny, D. A. (986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 5, 73-82. Kenny, D. A. (200). Mediation. Retrieved from the web May 4, 2002. http://davidakenny. net/cm/mediate.htm MacKinnon, D. P. (2000). Contrasts in multiple mediator models. In J. S. Rose & L. Chassin (Eds.), Multivariate Applications in Substance Use Research: New Methods for New Questions (pp. 4-60). Mahwah, NJ: Erlbaum. MacKinnon, D. P. (2002). Statistical mediation. Retrieved from the web May 4, 2002. http://www.public.asu.edu/~davidpm/ripl/mediate.htm MacKinnon, D. P., et. al. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7, 83-04. Preacher, K. J., & Leonardelli, G. J. (200). Calculation for the Sobel Test. Retrieved from the web June 7, 2002. http://www.unc.edu/~preacher/sobel/sobel.htm Sobel, M. E. (982). Asymptotic confidence intervals for indirect effects in structural equation models. In S Leinhardt (Ed.), Sociological Methodology 982 (pp. 290-32). Washington, DC: American Sociological Association. Sobel, M. E. (986). Some new results on indirect effects and their standard errors in covariance structure models. In N. Tuma (Ed.), Sociological Methodology 986 (pp. 59-86). Washington, DC: American Sociological Association. Kline, R. B. (2005). Principles and practice of structural equation modeling. MacKinnon, D. P. (2008). Introduction to statistical mediation analysis.
2009 KAMS/KSMA Fall International Confernece 30 LISREL & AMOS Output : 직접효과 Y = - 0.087*X2, Errorvar.= 2.96, R2 = 0. (0.09) (.4) -4.65 9.22 Y2 = - 0.280*Y + 0.058*X2, Errorvar.= 8.49, R2 = 0.23 (0.062) (0.06) (0.92) -4.58 3.59 9.22 유의수준 0% t ³.645 5% t ³.960 % t ³2.576 Y3 = - 0.220*Y + 0.850*Y2 + 0.860*X, Errorvar.= 9.45, R2 = 0.39 (0.098) (0.0) (0.340) (2.) -2.23 7.53 2.52 9.22
2009 KAMS/KSMA Fall International Confernece 302 LISREL & AMOS Output : 총효과, 간접효과 TOTAL EFFECTS OF X ON Y X X2 -------- -------- Y - - -0.087 (0.09) -4.650 Y2 - - 0.083 (0.06) 5.35 Y3 0.86 0.089 (0.342) (0.08) 2.58 4.858 INDIRECT EFFECTS OF X ON Y X X2 -------- -------- Y - - - - Y2 - - 0.025 (0.008) 3.265 Y3 - - 0.089 (0.08) 4.858
2009 KAMS/KSMA Fall International Confernece 303 AMOS Output: Bootstrap Estimates - AMOS 매뉴얼 (SPSS Korea 컨설팅팀편역 ) - AMOS A to Z 논문작성절차에따른구조방정식모형분석 ( 김대업, 학현사 )
2009 KAMS/KSMA Fall International Confernece 304 조절효과 (Moderating Effect) l 조절변수 (Moderator Variable) ü 독립변수와종속변수간의관계에서상황적으로유의한영향을미치는변수. ü 조절변수의수준에따라서경로계수의크기가다를때조절효과가있다고한다. 근무년수 a e 호감 z 3 b 지지도 z 2 나이 d f 성별 f f 2? c 복종심 z 성별
2009 KAMS/KSMA Fall International Confernece 305 이산형 vs. 연속형조절변수 l 이산형조절변수 ü 성별, 학년, 지역등과같이이산적인값을갖는조절변수 ü 다중집단분석 [Multiple-Group(Population) Analysis] l 연속형조절변수 ü 지능, 우울감, 자신감등과같이연속적인수치값을갖는조절변수 ü 상호작용효과 (Interaction Effect) 를고려. ü 조절변수를상, 하 ( 혹은상, 중, 하 ) 로구분하여이산형조절변수로취급하기도한다.
2009 KAMS/KSMA Fall International Confernece 306 () 이산형조절변수 l 단계 ü 관찰변수의 ( 분산 ) 공분산행렬에대하여집단간동일성을평가한다. ü 공분산행렬에대한동일성이받아들여지면조절변수의효과에대한분석은의미가없게된다. l 단계 2 ü 연구자의가설모형 (Unconstrained model, Base model, Full model) 에대하여적합도를평가한다. ü 이과정에서적합도가만족스럽지않을경우수정지수등을참조하여모형을수정할필요가있다. l 단계 3 ü 관심모수에대하여동일성의제약을부과한제약모형 (Constrained model, Reduced model) 에대하여적합도를평가한다. ü 기본모형과의적합도 ( 카이제곱값등 ) 의차이를이용하여전체적조절효과를평가한다. l 단계 4 ü 개별모수들에대한조절효과를평가한다. ü CR(Critical Ratio) 값에의한검정등.
2009 KAMS/KSMA Fall International Confernece 307 사례 ) Felson and Bohrnstedt (979) l A nonrecursive model by Felson and Bohrnstedt (979) Gender ü Example 7 in Chapter, Amos TM 7.0 User s Guide
2009 KAMS/KSMA Fall International Confernece 308 단계. 공분산행렬의동일성에대한검정 FnB_979_0_notitle.amw
2009 KAMS/KSMA Fall International Confernece 309... 단계. 공분산행렬의동일성에대한검정
2009 KAMS/KSMA Fall International Confernece 30... 단계. 공분산행렬의동일성에대한검정 Edit Select All Edit Space Vertically
2009 KAMS/KSMA Fall International Confernece 3... 단계. 공분산행렬의동일성에대한검정
2009 KAMS/KSMA Fall International Confernece 32... 단계. 공분산행렬의동일성에대한검정 각집단모두에대하여...
2009 KAMS/KSMA Fall International Confernece 33... 단계. 공분산행렬의동일성에대한검정
2009 KAMS/KSMA Fall International Confernece 34... 단계. 공분산행렬의동일성에대한검정 FnB_979_0.amw
2009 KAMS/KSMA Fall International Confernece 35... 단계. 공분산행렬의동일성에대한검정 (6ⅹ7)/2 = 2 =
2009 KAMS/KSMA Fall International Confernece 36 ( 참조 ) 각집단에대한분석 FnB_979_fem.amw FnB_979_mal.amw
2009 KAMS/KSMA Fall International Confernece 37 단계 2. 기본모형의적합도평가 FnB_979_A.amw
... 단계 2. 기본모형의적합도평가 2009 KAMS/KSMA Fall International Confernece 38
2009 KAMS/KSMA Fall International Confernece 39 단계 3. 제약모형의적합도평가 FnB_979_B.amw
2009 KAMS/KSMA Fall International Confernece 320... 단계 3. 제약모형의적합도평가 Δχ 2 = 9.493 3.83 = 6.30 Δdf = 0 4 = 6 χ 2 0.05(6) = 2.59
2009 KAMS/KSMA Fall International Confernece 32 ( 참조 ) Critical ratios for differences of estimates
2009 KAMS/KSMA Fall International Confernece 322... ( 참조 ) Critical ratios for differences of estimates CR = (θ θ 2 ) / SQRT(SE 2 +SE 22 ) 유의수준 0% t ³.645 5% t ³.960 % t ³2.576
2009 KAMS/KSMA Fall International Confernece 323... ( 참조 ) Critical ratios for differences of estimates 표. 경로계수추정치 Female Male Difference academic GPA 0.023 ( 0.492)* 0.02 ( 0.522)* 0.002 (-0.030) attract height 0.000 ( 0.003) 0.09 ( 0.32) -0.09 (-0.29) attract weight -0.002 (-0.078) -0.003 (-0.7) 0.00 ( 0.093) attract rating 0.76 ( 0.363)* 0.095 ( 0.89) 0.08 ( 0.74) attract academic.607 ( 0.525)*.386 ( 0.453)* 0.22 ( 0.072) academic attract -0.002 (-0.006) 0.063 ( 0.92) -0.065 (-0.98) + ( ) 안의수치는표준화추정치임. * 유의수준 5% 하에서통계적으로유의함을나타냄.
2009 KAMS/KSMA Fall International Confernece 324 (2) 연속형조절변수 X Y e y X3 X2 e x2 X Y e y X3 X2 e x2 X*X3 X2 = a*x + b*x3 + c*x*x3 => X2 = (a+c*x3)*x + b*x3
2009 KAMS/KSMA Fall International Confernece 325 사례 ) 상호작용을이용한조절효과분석 Interaction_0.amw
2009 KAMS/KSMA Fall International Confernece 326... 사례 ) 상호작용을이용한조절효과분석 Interaction_A.amw
2009 KAMS/KSMA Fall International Confernece 327... 사례 ) 상호작용을이용한조절효과분석 Interaction_B.amw
2009 KAMS/KSMA Fall International Confernece 328 Ping(995) 의접근법 ( 참조 ) x2_z2 = (x+x2)*(z+z2) - 구조방정식모델을위한 SIMPLIS 활용과실습 ( 배병렬, 청목출판사 )
2009 KAMS/KSMA Fall International Confernece 329 Joreskog & Yang(996) 의접근법 x_z = x*z ( 참조 ) - 구조방정식모델을위한 SIMPLIS 활용과실습 ( 배병렬, 청목출판사 ) - 구조방정식모델이해와활용 ( 배병렬, 대경 )
Kenny & Judd(984) 의접근법 2009 KAMS/KSMA Fall International Confernece 330
2009 KAMS/KSMA Fall International Confernece 33 <Abstract> Bayesian Inference in SEMs Dong-Hee Lee ) - An Overview of Bayesian Inferences Baysesian theory Baysesian computation - Markov Chain Monte Carlo method The Gibbs sampler Metropolis-Hastings Algorithm - Bayesian Approaches in SEMs Benefits of Bayesian approach Confirmatory factor analysis with a single group Latent class analysis for discrete outcomes Latent variables in panel and clustered data analysis Keywords: Bayesian Inferences, Baysesian theory, Markov Chain Monte Carlo method, The Gibbs sampler, Metropolis-Hastings Algorithm ) Kyonggi University