Latent variables are useful constructs for modeling states that cannot be directly observed, such as skills, attitudes and health states. Tests designed to measure latent scores often take the form of questionnaires. The developer of such a test aims to assemble a set of items that measures a latent state with good precision. A challenge is that the best set of items depends on the respondent’s true latent score, so a test optimized to give good precision for some respondents may be less precise for others. This dissertation explores statistical methods to optimize the measuring instrument through simulation studies and empirical applications to diverse populations.

The papers included here evaluate adaptive methods that select items based on current knowledge about the respondent. Paper 1 proposes an adaptive method for selecting one item at a time in a Voting Advice Application. With a test that continuously selects the most informative next item, the respondent can conclude the session without answering all items and still get a result that is sufficiently accurate. The proposed method relies on Item Response Theory and a multidimensional latent construct.

In Paper 2, we explored an adaptive model to measure the health states of patients evaluated for symptoms of Parkinson's disease. We compared this adaptive model to optimized static item sets designed for good population-average precision. The Parkinson's dataset consisted of repeated measurements across multiple timepoints, which required a longitudinal approach. In both Papers 1 and 2, the purpose of the methods was to enable more time-efficient versions of tests to increase usage.

Papers 3 and 4 evaluate methods for tracking abilities that change over time. Unlike the Parkinson's scenario with a full test repeated at multiple timepoints, here we have only one observation per time point. In these settings, it is common to abandon traditional statistical models and instead rely on computationally inexpensive algorithms. Of these algorithms, the Elo rating system stands out as the most prominent. This rating system, developed to rate chess players, now has widespread use in many competitive sports and also in education.

We identified limitations associated with the Elo method, and proposed extensions to remedy these. In Paper 3, we developed a hybrid approach that combines standard Elo with statistical modeling to incorporate group-level information. In Paper 4, we demonstrated that in a closed system in which students improve in ability, and where item difficulties are estimated in real time, the Elo method produces increasingly deflated ability estimates. We proposed a method to quantify and offset this system-level deflation.