  Reliability is an essential measure of how closely observed scores represent
latent scores (reflecting constructs), assuming some latent variable
measurement model. We present a general theoretical framework of reliability,
placing emphasis on measuring association between latent and observed scores.
This framework was inspired by McDonald's (2011) regression framework, which
highlighted the coefficient of determination as a measure of reliability. We
extend McDonald's (2011) framework beyond coefficients of determination and
introduce four desiderata for reliability measures (estimability,
normalization, symmetry, and invariance). We also present theoretical examples
to illustrate distinct measures of reliability and report on a numerical study
that demonstrates the behavior of different reliability measures. We conclude
with a discussion on the use of reliability coefficients and outline future
avenues of research.
