Under the general common factor model, the reliabilities of factor score estimators might be of more interest than the reliability of the total score (the unweighted sum of item scores). In this paper, lower bounds to the reliabilities of Thurstone’s factor score estimators, Bartlett’s factor score estimators, and McDonald’s factor score estimators are derived and conditions are given under which these lower bounds are equal. The relative performance of the derived lower bounds is studied using classic example data sets. The results show that estimates of the lower bounds to the reliabilities of Thurstone’s factor score estimators are greater than or equal to the estimates of the lower bounds to the reliabilities of Bartlett’s and McDonald’s factor score estimators.

We construct a double common factor model for projecting the mortality of a population using as a reference the minimum death rate at each age among a large number of countries. In particular, the female and male minimum death rates, described as best-performance or best-practice rates, are first modelled by a common factor model structure with both common and sex-specific parameters. The differences between the death rates of the population under study and the best-performance rates are then modelled by another common factor model structure. An important result of using our proposed model is that the projected death rates of the population being considered are coherent with the projected best-performance rates in the long term, the latter of which serves as a very useful reference for the projection based on the collective experience of multiple countries. Our out-of-sample analysis shows that the new model has potential to outperform some conventional approaches in mortality projection.