Reliability of a Longitudinal Sequence of Scale Ratings

Reliability captures the influence of error on a measurement and, in the classical setting, is defined as one minus the ratio of the error variance to the total variance. Laenen, Alonso, and Molenberghs (Psychometrika 73:443-448, 2007) proposed an axiomatic definition of reliability and introduced the R (T) coefficient, a measure of reliability extending the classical approach to a more general longitudinal scenario. The R (T) coefficient can be interpreted as the average reliability over different time points and can also be calculated for each time point separately. In this paper, we introduce a new and complementary measure, the so-called R (I >) , which implies a new way of thinking about reliability. In a longitudinal context, each measurement brings additional knowledge and leads to more reliable information. The R (I >) captures this intuitive idea and expresses the reliability of the entire longitudinal sequence, in contrast to an average or occasion-specific measure. We study the measure's properties using both theoretical arguments and simulations, establish its connections with previous proposals, and elucidate its performance in a real case study.