Multilevel models in developmental psychological research: Rationales and applications

Effect size measures for longitudinal growth analyses: Extending a framework of multilevel model R-squareds to accommodate heteroscedasticity, autocorrelation, nonlinearity, and alternative centering strategies

Developmental researchers commonly utilize multilevel models (MLMs) to describe and predict individual differences in change over time. In such growth model applications, researchers have been widely encouraged to supplement reporting of statistical significance with measures of effect size, such as R-squareds (R² ) that convey variance explained by terms in the model. An integrative framework for computing R-squareds in MLMs with random intercepts and/or slopes was recently introduced by Rights and Sterba and it subsumed pre-existing MLM R-squareds as special cases. However, this work focused on cross-sectional applications, and hence did not address how the computation and interpretation of MLM R-squareds are affected by modeling considerations typically arising in longitudinal settings: (a) alternative centering choices for time (e.g., centering-at-a-constant vs. person-mean-centering), (b) nonlinear effects of predictors such as time, (c) heteroscedastic level-1 errors and/or (d) autocorrelated level-1 errors. This paper addresses these gaps by extending the Rights and Sterba R-squared framework to longitudinal contexts. We: (a) provide a full framework of total and level-specific R-squared measures for MLMs that utilize any type of centering, and contrast these with Rights and Sterba's measures assuming cluster-mean-centering, (b) explain and derive which measures are applicable for MLMs with nonlinear terms, and extend the R-squared computation to accommodate (c) heteroscedastic and/or (d) autocorrelated errors. Additionally, we show how to use differences in R-squared (ΔR² ) measures between growth models (adding, for instance, time-varying covariates as level-1 predictors or time-invariant covariates as level-2 predictors) to obtain effects sizes for individual terms. We provide R software (r2MLMlong) and a running pedagogical example analyzing growth in adolescent self-efficacy to illustrate these methodological developments. With these developments, researchers will have greater ability to consider effect size when analyzing and predicting change using MLMs.

Developmental changes in the relationship between the infant's attention and emotion during early face-to-face communication: the 2-month transition

Weekly observations documented developmental changes in mother-infant face-to-face communication between birth and 3 months. Developmental trajectories for each dyad of the duration of infant facial expressions showed a change from the dominance of Simple Attention (without other emotion expressions) to active and emotionally positive forms of attention to the mother toward the end of the 2nd month. The results support an overlapping waves model, rather than a stage model, of developmental change. Sequential analysis found developmental changes from cycling between Gaze Elsewhere and Simple Attention to the Mother's Face in the early weeks to a complex sequence of transitions between Concentrated Attention, Smile, and Cooing Expression nested into sequences of positive communication during the 2nd and 3rd months.

Developmental changes in mother-infant face-to-face communication: birth to 3 months

This study documented the growth of the earliest form of face-to-face communication in 16 mother-infant dyads, videotaped weekly during a naturalistic face-to-face interaction, between 1 and 14 weeks, in 2 conditions: with the infant in the mother's arms and with the infant semi-reclined on a sofa. Results showed a curvilinear development of early face-to-face communication, with a significant increase occurring between Week 4 and Week 9 depending on the dyad. After 2 months, trajectories diverged into 2 groups: I whose duration of face-to-face communication continued to increase and I whose duration peaked and then began to decrease. After the 1st month, the duration of face-to-face communication was significantly longer when the infant was on the sofa rather than in the mother's arms. In the latter condition, during the 3rd month, girls spent a significantly longer time than boys in face-to-face communication. These findings suggest that context (infant being held vs. not being held) interacts with the infant's age and sex in affecting mother-infant communication.

Testing Predictive Developmental Hypotheses

Predictive developmental hypotheses play a crucial role in developmental theories. These hypotheses link early developmental behaviors or processes to later developmental outcomes. Empirical tests of predictive developmental hypotheses are generally based on standard regression models. It is argued that hierarchical linear models or longitudinal multilevel models offer a better alternative. A multivariate longitudinal model linking developmental data to a criterion is described and an application is given. The application, derived from attachment theory, pertains to the prediction of infant behavior in the Strange Situation. It is concluded that the proposed approach offers a valuable tool to the developmentalist, both from a theoretical and methodological point of view.

The electronic mood device: design, construction, and application

The electronic mood device (EMD) is designed to help answer questions about the variability and dynamics of emotions. It is a small, portable instrument used for repeated recording of moods and feelings. Both construction and operation of the EMD are described. The EMD can best be conceived of as an electronic mood adjective checklist. Persons using the EMD are signaled at designated (e.g., hourly) or random intervals to register their mood or feelings. Paper and pencil are not required. An application is given. It shows how feelings vary within and between persons and during the day. It is concluded that the EMD offers several advantages over paper-and-pencil instruments. Retrospective use is impossible. Timing and registration are accurate. Data handling is fast. Potential future applications are suggested.

Prematurity, posture and the development of looking behaviour during early communication

This study concerns the developing relationship between motor control and looking behaviour in full term (N = 15) and pre-term (N = 29) infants during face-to-face interaction with the mother at 6, 12 and 18 weeks of corrected age. Infants with inborn errors or major medical complications were excluded. In the pre-term infants the development of head and arm postures during interaction differed from the full term pattern, especially in infants born before 32 weeks and/or small-for-gestational age. The full term infants were more advanced than other infants in the ability to grasp an object. These findings were related to group differences in looking behaviour, suggesting that differences in the development of looking behaviour may be (partly) accounted for by differences in the development of motor control.