lecture13_s10 GM1 - General structural model Part 1:...

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General structural model – Part 1: comparing groups, missing values, partitioning of effects Psychology 588: Covariance structure and factor models Mar 12, 2010
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Comparing groups 2 • All modeling so far considered a single group --- multiple group analysis fits a model simultaneously to several groups, typically with some equality constraints across groups (how different from modeling with a covariate for grouping?) • Testing for group invariance built on the additive nature of chi- square distribution: • Levels of comparability ¾ Model form --- comparison mostly qualitative or best fitting model derived per group ¾ Hierarchy of invariance --- given the same model form, sort out parameters, primary vs. secondary, observed vs. latent 22 11 , GG T g T g gg df df χχ ==
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Testing hierarchy: path modeling part 3 • There is no golden rule for order of invariance testing • Any ordering effect is not arbitrary since the LR test is conditional to what’s already imposed (i.e., common part for both the compared models) • For strict invariance/equivalence, lower-level invariance necessary for higher-level invariance form B B B : same form, 1,. .., :, , : , gT g T g T g T g T g T Hg G H H H Γ ΓΨ ΓΨΦ = == = = = BB ΓΓ ΨΨ ΦΦ
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Testing hierarchy: measurement part 4 • Same hierarchy, but regression weights are factor loadings instead of latent path coefficients form () : same form, 1,. .., : :, , x x x gT xx g T g T g T Hg G H H H δ δδ Λ ΛΘ ΛΘΦ = = == === ΛΛ ΘΘ ΦΦ • For y-measurement models, invariance on Φ irrelevant since covariances between η ’s are model as functions instead of model parameters • Any artifact in fixing LV scales when considered across groups?
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Invariance in mean structure 5 • When structural equations include mean-structure, there is more flexibility in testing order of different kinds of parameters
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This note was uploaded on 06/11/2010 for the course PSYC 588 taught by Professor Sunjinghong during the Spring '10 term at University of Illinois at Urbana–Champaign.

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lecture13_s10 GM1 - General structural model Part 1:...

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