Title: **Strong Convergence of Reliability Estimators for Multiple-Component Measuring Instruments in the Behavioral, Educational and Social Sciences**

Speaker: Prof. Tenko Raykov (Michigan State University)

When: Tuesday, December 17, 2019, 16:30

Where: M / E21

This talk shows that in general the popular coefficient alpha estimator for reliability of multicomponent measuring instruments converges almost surely to a quantity that is not equal to the population reliability coefficient. This convergence with probability 1 is a stronger statement than convergence in probability and convergence in distribution for the alpha estimator, which have been studied in the past. In the special case of congeneric measures with uncorrelated errors and equal loadings on the common true score, the alpha estimator converges almost surely to the population reliability coefficient that equals population alpha, which implies its consistency as a reliability estimator. When the loadings are unequal but sufficiently high and similar, the alpha estimator converges also almost surely to population alpha that is essentially indistinguishable from the reliability coefficient, which implies alpha’s approximate consistency then. For the general case, the results entail that the alpha estimator is not a consistent estimator of reliability. The findings add (i) to the critical literature on coefficient alpha in the general case, as well as (ii) to the justification of its use as a dependable measuring instrument reliability estimator in special cases and settings resulting under appropriate restrictive conditions. The discussion is illustrated using a numerical example.

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