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This note is concerned with a validity-related limitation of the widely available and routinely used index 'alpha if item deleted' in the process of construction and development of multiple-component measuring instruments. Attention is drawn to the fact that this statistic can suggest dispensing with such scale components, whose removal leads to loss of criterion validity while maximizing the popular coefficient alpha. As an alternative, a latent variable modelling approach is discussed that can be used for point and interval estimation of composite criterion validity (as well as reliability) after deletion of single components. The method can also be utilized to test conventional or minimum level hypotheses about associated population change in measurement quality indices.
Tenko Raykov (Sat,) studied this question.