lecture7_s10 CFA - Confirmatory Factor Analysis:...

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Confirmatory Factor Analysis: measurement models Psychology 588: Covariance structure and factor models Feb 17, 2010
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Few things on measurement theory 2 • Measurement may be defined as assigning numbers to observational units (“subjects”) so as to indicate the magnitude (and direction if bipolar) on an intended concept (construct, latent variable) • A measurement model quantitatively defines the relationships between observed phenomena (items, indicators, measures, manifest variables) and unobservable concepts (factors, latent variables) ¾ e.g., Spearman’s single factor model, 2-parameter logistic model, graded response model, etc. ¾ We will only consider linear relationships in SEM (in the classical form, while generalized SEM allows nonlinear relationships)
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Spearman’s single factor model 3 • A set of measures are modeled to linearly relate to a single common factor as: ii i x λ ξδ ξ =+ = + x λδ • With means included: ( ) () ,, 0 iii i i xE E ν λξ δ κ + = = + x νλ δ • Rescaling does (and should) not affect measurement structure --- though it’s not trivial to find right rescaling, e.g., in multiple group analysis
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Convergent & discriminant validity 4 • According to construct validity, a properly measured latent variable should covary high with an item that is theoretically believed to highly relate with; and should covary low with one that is theoretically believed to relate not so much with • MTMM (multitrait-multimethod) procedure is one modeling technique to verify a type of convergent and discriminant validity (Fig 6.4 in p.192; also see Tables 6.2 and 6.3) 13 34 12 11 31 13 34 13 23 11 22 xx ξξ ρ λλ λλρ =+ x1 d1 x2 d2 x3 d3 x4 d4 T1 T2 M4 M3 r12 l 1 3 4 l42 r34 2 l11
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• (Construct, criterion, convergent-divergent, etc.) validity is typically assessed by bivariate correlations of observed variables --- possibly misleading due to measurement errors • Alternatively, validity of a measure
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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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lecture7_s10 CFA - Confirmatory Factor Analysis:...

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