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.     

Effects of modelling on children''s pretend play

The effects of modelling on pretend play were studied in children between 2.6 and 3.6 years of age by examining changes both in the action and language-based expressions of pretending. Three modelled scenes were demonstrated with the same realistic toys used by the child in the pre-modelling phase. The results gave support to the idea of the effectiveness of modelling. The effects of the modelled scenes were clearest among children whose pre-modelling play consisted of object-centred actions including few of pretending. The post-modelling play of this subgroup showed better quality of action and language categories and integration measures. Among the decentred players no significant action benefit could be achieved. This might have been an outcome of the contextual limits of the toy material and of the drop of play motivation caused by the model interruption. However, these children expressed verbal pretending revealing significant pre-post effects for inventive utterances.     

Heterogeneous heterogeneity by default: Testing categorical moderators in mixed-effects meta-analysis

Categorical moderators are often included in mixed-effects meta-analysis to explain heterogeneity in effect sizes. An assumption in tests of categorical moderator effects is that of a constant between-study variance across all levels of the moderator. Although it rarely receives serious thought, there can be statistical ramifications to upholding this assumption. We propose that researchers should instead default to assuming unequal between-study variances when analysing categorical moderators. To achieve this, we suggest using a mixed-effects location-scale model (MELSM) to allow group-specific estimates for the between-study variance. In two extensive simulation studies, we show that in terms of Type I error and statistical power, little is lost by using the MELSM for moderator tests, but there can be serious costs when an equal variance mixed-effects model (MEM) is used. Most notably, in scenarios with balanced sample sizes or equal between-study variance, the Type I error and power rates are nearly identical between the MEM and the MELSM. On the other hand, with imbalanced sample sizes and unequal variances, the Type I error rate under the MEM can be grossly inflated or overly conservative, whereas the MELSM does comparatively well in controlling the Type I error across the majority of cases. A notable exception where the MELSM did not clearly outperform the MEM was in the case of few studies (e.g., 5). With respect to power, the MELSM had similar or higher power than the MEM in conditions where the latter produced non-inflated Type 1 error rates. Together, our results support the idea that assuming unequal between-study variances is preferred as a default strategy when testing categorical moderators.     

The use of latent class models for assessing prerequisite relations and transference among traits

This paper presents a strategy for pairwise assessment which may be used to evaluate the nature of both prerequisite and transference relations existing among a set of traits. This strategy is appropriate for use both within a confirmatory context, in which an attempt is made to establish the validity of some specified set of relations among traits, as well as within an exploratory context, in which a search is made for unconjectured prerequisite and transference relations existing between pairs of traits. Both uses of this strategy are based on a variety of latent class models which are representative of various possible relational states existing between pairs of traits. Thus, the nature of trait relations may be investigated through the use of statistical assessments of both absolute and relative fit attained by these models. An application is presented to exemplify how this strategy may be used within the exploratory context.The author is obliged to Clifford Clogg, C. Mitchell, Dayton, and William Schafer for helpful comments made regarding a previous draft of this paper as well as to Mary Papageorgiou who provided access to the data which was considered in this study.     

Effects of peer social initiations on the behavior of withdrawn preschool children

Social approach to peers was evaluated as an intervention for isolate preschoolers. During baseline, confederate peers made few social approaches to the target subjects. Confederates greatly increased their rate of social approaches during the first intervention, decreased social approaches during a second baseline, and increased social approaches again in a second intervention phase. Increases in confederate social initiations immediately increased the frequency of subjects' positive social behavior. Additionally, five of six subjects showed an increase in their own positive social initiations during intervention periods. The results suggest that: (a) peers may be programmed to increase the positive social behaviors of their isolate classmates, and (b) remediating social deficits requires assessment and intervention specifically tailored to the individual child.     

EFFECTS OF DIRECT,INTERMITTENT, AND VICARIOUS REINFORCEMENT PROCEDURES ON THE DEVELOPMENT AND MAINTENANCE OF INSTRUCTION-FOLLOWING BEHAVIORS IN A GROUP OF YOUNG CHILDREN1

A group of young children (mean age: 2.5 yr) were instructed to follow different requests by a teacher in a day-care setting. Experiment I verified that mean group instruction following was low (10%) despite the opportunity for “observational learning”, i.e., the group of 12 children could watch a nonreinforced adult comply with the teacher's request. In Experiment II, when positive consequences were provided contingent on the adult model's behavior, mean group instruction following was relatively unaffected (14%). When direct reinforcement was given to four peer models, each for several sessions, the individual performances of three of the four peer models was elevated (from 50% to 80%); however, the mean performance of the remaining nonreinforced children (N = 7) was only moderately affected (21%). When reinforcement contingencies were again changed, so that each group member was provided direct, but intermittent reinforcement, mean group performance increased substantially to levels of over 70%. Once instruction following was high, presentation of reinforcement only to one peer model sufficed to maintain performance whereas earlier, this same vicarious reinforcement procedure had failed to establish group compliance. The maintenance of instruction-following behavior when reinforcement was applied solely to one child was interpreted mainly in terms of a high resistance to extinction following a history of intermittent reinforcement rather than a “vicarious”- or “self”-reinforcement mechanism. Finally, removal and re-introduction of group intermittent reinforcement, respectively, lowered performance (to levels of 40%) and elevated (to levels of 65%) the group's performance.     

The effects of instructions, incentive, and feedback on a community problem: dormitory noise

A reinforcement system utilizing instructions, modelling, feedback, and group reinforcement was employed in an attempt to reduce disruptive noise on three university residence halls. A fourth hall received the same treatment program without the reinforcement component. Noise scores were determined by recording the number of discrete noise occurrences over a criterion decibel level. On all four residential floors, noise scores during treatment conditions were lower than initial and final baseline levels. Additionally, periods of noise reduction corresponded to the changing criterion multiple-baseline and reversal designs utilized. Pre- and posttreatment questionnaire responses from the three reinforcement floors paralleled changes in objective noise data. At posttreatment, residents reported less noise disturbance of study and sleep and more control over the noise situation and floor problems in general. These results indicated that a comprehensive behavior-modification treatment package was effective in reducing disruptive noise in university residence halls. Difficulties in data collection and anomalies in the data are discussed. Future directions for field-based behavior-modification research are outlined.     

The impacts of ignoring individual mobility across clusters in estimating a piecewise growth model

A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models.     

Preference structures and threshold models

Preferences are often represented in terms of a function, in the deterministic case as well as in the probabilistic case. In the present paper we develop a new numerical representation of preference structures for which the strict preference relation (P) is without circuit but not necessarily transitive. Moreover, we investigate the consequences of the representation for the usual preference structures. In particular, we propose new formulations for the numerical representation of the interval order structure.