Composite Reliability

Composite reliability
composite reliability is a measure of the overall reliability of a collection of heterogeneous but similar items
individual item reliability (test the reliability of the items using Croinbach Alpha )vs. composite reliability (of the construct, the latent variable)
The factor loadings are simply the correlation of each indicator with the composite
(construct factor), and the factor correlations are oblained by correlating the composites.
calculate composite relaibility for the latent variables, LISREL does not output the "composite reliability" directly. You have to calculate it by hand.
SEM approach for reliability analysis, the reliability estimate from the SEM approach tends to be higher than Cronbach’s α. Structural equation model for estimating
the reliability for the composite consisting of congeneric measures.
Composite reliability--- a measure of scale reliability, Composite reliability assesses the internal consistency of a measure, 2 means square, see Fornell & Larcker (1981)

(sum of standardized loading) 2 / [(sum of standardized loading) 2 + sum of indicator measurement error (the sum of the variance due to random measurement
error for each loading-- 1 minus the square of each loading ]

Let A be the standardized loadings for the indicators for a particular latent variable. Let B be the corresponding error terms, where error is 1 minus the reliability of the indicator; the reliability of the indicator is the square of the indicator's standardized loading.
The reliability of a measure is that part containing no purely random error
(Carmines & Zeller, 1979). In SEM terms, the reliability of an indicator is defined
as the variance in that indicator that is not accounted for by measurement error. It is
commonly represented by the squared standardized multiple correlation coefficient, which
ranges from 0 to 1 (Bollen, 1989; Jöreskog & Sörbom, 1993a). However, because
these coefficients are standardized, they are not useful for comparing reliability
across subpopulations.

composite reliability = [SUM(A)] 2 /[(SUM(A)] 2 + SUM(B).
Example, Suppose I have a construct with three indicators, i1, i2 and i3. When I run this construct in AMOS I get as standardized regression weights: 0.7, 0.8 and 0.9. For computing the composite reliability, I just make:
CR = (sum of standardized loading) 2 / (sum of standardized loading) 2 + sum of indicator measurement error)
CR = (0.7 + 0.8 + 0.9)2 / ((0.7 + 0.8 + 0.9)2 + (1-0.49 + 1-0.64 + 1-0.81)
CR = (5.76)/(5.76 + 1.06)
CR = 0.844
Average variance extracted (AVE), see Fornell & Larcker (1981),
The variance extracted estimate, which measures the amount of variance captured by a construct in relation to the variance due to random measurement error

sum of squared standardized loading / sum of squared standardized loading + sum of indicator measurement error--sum of the variance due to random measurement error in each loading=1 minus the square of each loading )

variance extracted = [(SUM(A 2)]/[(SUM(A 2) + SUM(ei))].
Example,
AVE = (sum of squared standardized loading) / (sum of squared standardized loading + sum of indicator measurement error)
AVE = (0.49 + 0.64 + 0.81)/((0.49 + 0.64 + 0.81) + (1-0.49 + 1-0.64 + 1-0.81) AVE = (1.94)/(1.94+1.06)
AVE = 0.647

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