A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Multilevel models in developmental psychological research: Rationales and applications

The armoury of statistical techniques has recently been enhanced with the multilevel model for longitudinal data. The present article explains the multilevel model for longitudinal data to the statistically non-sophisticated reader. It shows how the model relates to the five rationales of longitudinal research, as they were put forward by Baltes and Nesselroade (1979). In addition, it shows how the model matches Wohlwill's methodology of developmental functions. To elucidate the model further, three applications are given. The applications pertain to the development of children's sleeping duration during the first 18 months of life, the effects of early hospitalization on the daily frequency of crying, and the developmental relationship between social and solitary play.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

Linear Analogue Self-Assessment and Procrustean Measurement: A Critical Review of Visual Analogue Scaling in Pain Assessment

Visual analogue scales (VASs) are one of the most widely used self-report measures of clinical pain. This article reviews the empirical literature on linear analogue self-assessment (LASA) and critically examines the features that appear to have made it such an attractive measurement option in pain assessment. It is concluded that analogue scaling does not withstand critical scrutiny as a primary measure of either pain intensity or pain affect and that, in most circumstances, the overall clinical utility of VASs is inferior to that of more structured pain indices.     

Exploring the set-theoretical structure of objects by additive trees

Arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set-symmetric distances. The set-symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree. Imperfect versions of these feature arrangements are proposed, which also are indistinguishable by the set-symmetric distance model. The distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree. When dissimilarities are defined by the more general contrast model and a constant may be added to proximity data, then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree. However, in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear.The author is grateful to Mathieu Koppen for detailed comments on an earlier version of this article.     

Dynamic equilibrium on a cyclic-interval schedule with a ramp

Five human subjects pressed a panel for money on a cyclic-interval schedule that arranged recurring periods of linearly increasing reinforcement rates (ramps). Response rate versus time functions for all subjects showed recurring periods of linearly increasing response rates. The responding of four of the five subjects was in phase with the reinforcement input. The remaining subject showed a two-minute phase shift. These results suggest that organisms may act like simple amplifiers on cyclic-interval schedules, that is, the form of the input signal is not changed by the organism, but is returned with amplification. By analogy with the variable-interval case, the controlling variable on cyclic-interval schedules with rate ramps may be the constant reinforcement acceleration that is arranged by the schedule.     

Tests for stability in linear structural equation systems

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. Convergence depends upon the eigenvalues of the structural coefficient matrix. The test for convergence developed by Jöreskog and Sörbom is shown to be only sufficient, not necessary and sufficient.     

A note on the estimation of the level of predictive precision of a fitted linear equation

A procedure that utilizes the sample multiple correlation to form a lower bound for the level of predictive precision of a fitted regression equation is suggested. The procedure is shown to yield probability statements which are true at least 100(1–)% of the time.