HIERARCHICAL LINEAR MODELS PUBLICWEB2 Hosted Sites分层线性模型publicweb2主办网站.ppt

HIERARCHICAL LINEARMODELS NESTED DESIGNS A factor A is said to be nested in factor B if the levels of A are divided among the levels of B. This is given the notation A(B). We have encountered nesting before, since Subjects are typically nested in Treatment, S(T), in the randomized two group experiment. NESTED DESIGNS NESTED DESIGNS ANOVA TABLE ESTIMATING VARIANCES ?2C = (MSC – MSP )/p Conceptually this is = (?2? +p?2c - ?2?)/p TESTING CONTRASTS Thus, if one wanted to compare School 1 to School 2, the contrast would be C12 = [ Xschool 1 - Xschool 2 ] Since the school mean is equal to overall mean + school 1 effect + error of school: Xschool 1 = ? ...+ ?1. + e1. , TESTING CONTRASTS the variance of School 1 is VAR(Xschool 1 ) = { ?2? + ?2S }/s = { MS(P(C(S))) + [MS(S) - MS(C(S)]/cp} / s Then t = C12 /{ 2[MS(P(C(S)))+[MS(S)-MS(C(S)]/cp]/s} which is t-distributed with 1, df= Satterthwaite approximation Satterthwaite approximation df= { cpMS(P(C(S)))/s + [MS(S) - MS(C(S)]/s }2 {cpMS(P(C(S)))/s }2 + {[MS(S)}2 + {MS(C(S)]/s }2 (p-1)cs cp(s-1) p(c-1) HLM - GLM differences GLM uses incorrect error terms in HLM designs Multiple comparisons using GLM estimates will be incorrect in many designs HLM uses estimates of all variances associated with an effect to calculate error terms Repeated Measures Multiple measurements on the same individual Time series Identically scaled variables Measurements on related individuals or units Siblings (youngest to oldest among trios of brothers) Spatially ordered observations along a dimension WITHIN-GROUP DESIGNS Within group designs We encountered a repeated measures design in Chapter Six in the guise of the dependent t-test design. : _ _ t = x1. – x2. / sd where sd = [ ( s21 + s22 – 2 r12 s1s2 )/n ]1/2 WITHIN-GROUP DESIGNSMODEL y ij = ? + ?i + ?j + eij where y ij = score of person i at time j, ? = mean of all persons over all occasions, ?i =