Linear Mixed Model 2013 02 16 2 Linear

Linear Mixed Model을 이용한 분석 결과 2013. 02. 16 권순선

2. Linear Mixed Model (LMM) ü 선형회귀모형 where y = dependent variable = residual error X = design matrix for fixed effects = fixed effects parameters R = residual variance matrix ü 선형혼합모형 where y = dependent variable = residual error X = design matrix for fixed effects Z = design matrix for random effects = fixed effects parameters = random effects parameters V = the covariance matrix

3. LMM analysis result • Dependent variable : 밀린 거리 • Independent variable : – Fixed effects : 몸무게, 키, crouch, 미는 힘, 실제 속도, 미는 중간 타이밍(발 위치) – Random effects : subject • Estimated method : Restricted maximum likelihood estimation(REML) – unbiased estimator • Covariance structure : variance components(vc)

3. LMM analysis result Information Criteria Model AIC BIC Fixed effect model 1252. 1 1253. 3 Random intercept model 1202. 8 1205. 1 Random intercept and slope 1204. 8 1208. 4 ü The rule of thumb is smaller is better § Random intercept model이 제일 좋은 모형으로 나타남 • • AIC (Akaike Information Criterion) : = 2 k – 2 ln(L) , k : # of parameters , L : likelihood function for the estimated model BIC (Bayesian Information Criterion) = -2 ln(L) + k ln(n) , n : # of obs.

3. LMM analysis result Type 3 Test of Fixed Effects Effect Num d. f. Den d. f. F-value P-value 몸무게 1 84 1. 23 0. 2697 키 1 84 0. 08 0. 7783 Crouch 3 84 3. 19 0. 0278 미는 힘 1 84 3. 54 0. 0633 실제 속도 1 84 1. 13 0. 2913 미는 중간 타이밍 (발위치) 1 84 7. 43 0. 0078

3. LMM analysis result Least Squares Means Estimate Standard error Crouch 20도 251. 16 14. 89 Crouch 30도 239. 64 15. 05 Crouch 60도 248. 2 15. 13 정상 299. 1 18. 67 Effect