Where Have the Persons Gone? – An Illustration of Individual Score Methods in Autoregressive Panel Models

Abstract

Much effort has been made to develop models for longitudinal data analysis, but comparably less attention has been paid to the use of individual specific values on latent variables in longitudinal models. In a tutorial style, this article introduces the reader to four common approaches to obtain individual scoresindividual mean score, Bartlett method, regression method, Kalman filterand reviews criteria commonly used to evaluate their performance. By means of simulated data, we mimic realistic scenarios and investigate in how far analytic results on the asymptotic performance of individual scores translate into practical situations. We end this article with a discussion of the use and usefulness of individual scores.

Robustness of Individual Score Methods against Model Misspecification in Autoregressive Panel Models

“…The same is true for the Kalman filter (Kalman, 1960), which is an inherently longitudinal approach and considered to be an optimal method for online individual score estimation (e. g., Hardt et al, 2019;Oud et al, 1990) in a longitudinal context. The Kalman filter involves two steps: in the first step (prediction step), the individual scoref KF j;tjtÀ1 at time point t is predicted by the individual score at the previous time point t À 1 yieldinĝ…”

“…Note that the index for the time point in the Kalman filtering approach goes from t ¼ 2 to T, where T denotes the total number of measurement occasions. At t ¼ 1, the Kalman filter can be initialized completely "uninformative" for instance by setting f KF j;1j1 and P KF 1j1 to arbitrary values or "informative" by choosing individual score estimates obtained by another individual score method (e. g., the Bartlett method or the regression method, see Oud, Jansen, Van Leeuwe, Aarnoutse, & Voeten, 1999;Hardt et al, 2019; for more comprehensive research on the initial condition specification, see Losardo, 2012).…”

“…For the purpose of the present paper and in line with Hardt, Hecht, Oud, and Voelkle (2019), we consider an individual score as a realization of a normally distributed random latent variable that conceptually represents a psychological construct. Let any construct (e. g., intelligence, depression, positive/negative affect, etc.)…”

Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation – An Illustration and Tutorial

“…Only parameters that are not of interest from a substantive point of view are suitable for being integrated out. However, even if person parameters are of interest, the proposed nuisance-free implementations can still be used and person parameters might then be estimated in a further step using individual score methods (see, e.g., Hardt, Hecht, Oud, & Voelkle, 2019;Hardt, Hecht, & Voelkle, in press). (6) JAGS was used because it is a popular and stable multi-purpose Bayesian software.…”

A Computationally More Efficient Bayesian Approach for Estimating Continuous-Time Models

“…However, this is also the case in the frequentist likelihood approaches for estimating structural equation models many users are accustomed to. Moreover, as in SEM, individual score methods (e.g., Hardt, Hecht, Oud, & Voelkle, 2019; can be used to estimate person parameters if there is substantive interest in them, for instance, for individual diagnostic purposes. Another issue is that the distributional forms of the sample scatter matrix and the sample mean vector need to be known and Bayesian samplers for these distributions need to be provided.…”