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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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Appendix 2.B Item Reliability

Reliability refers to the consistency or repeatability of measurement. It is defined as the extent to which the variance of an observed variable is explained by the true score that the variable is designed to measure. In other words, the reliability is defined as the ratio of the true score variance to the total variance of the observed measure. Let us define img where img is the true score that y is to measure and img is the measurement error. The reliability of variable y is defined as the ratio of variance explained by the true score to the variance to the observed variance of y:

(2.10) equation

where img and img are variance of the true score and variance of measurement error; respectively, and img is the factor loading. Note that the reliability defined in Equation (2.10) is in fact ...

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