Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution

Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors are proposed and evaluated. The methods include (a) distribution checking based on individual growth curve analysis; (b) distribution comparison based on Deviance Information Criterion, and (c) post hoc checking of degrees of freedom estimates for t distributions. The performance of the methods is compared through simulation studies. When the sample size is reasonably large, the method of post hoc checking of degrees of freedom estimates works best. A web interface is developed to ease the use of the 3 methods. Application of the 3 methods is illustrated through growth curve analysis of mathematical ability development using data on the Peabody Individual Achievement Test Mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort (Bureau of Labor Statistics, U.S. Department of Labor, 2005).     

Aggregating and Testing Intra-Individual Correlations: Methods and Comparisons

From a longitudinal study, we have repeatedly measured data from multiple individuals at multiple occasions. For each individual, the relation between 2 variables can be measured by the Pearson’s correlation. The question is how to aggregate the multiple correlations and conduct statistical inference on the aggregated intra-individual correlation. Several methods are proposed to aggregate and test intra-individual correlations: (a) a meta-analysis method based on Fisher’s Z transformed correlations, (b) a meta-analysis method based on the Pearson’s correlations, and (c) a multilevel modeling method using data standardized within each individual. The performance of the methods after bias corrections was compared using simulations with considering factors including numbers of individuals, numbers of time points, population effect sizes, and their distribution forms (homogeneous vs heterogeneous). The results from the simulation studies show that estimation biases were found using the meta-analytic methods and suggestions on when and how to correct biases were provided based on the simulation results. Furthermore, the performance of the 3 methods after necessary bias corrections was found to be comparable and reasonably good, indicating that all 3 methods worked for aggregating and testing intra-individual correlations. An empirical daily diary data set was then used to illustrate the applications of the 3 methods. The assumptions, advantages and disadvantages, and possible extensions of the 3 methods were discussed.     

Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories

A general equadion is presented, covering all arbitrary values for the true population splits, for obtaining the true population phi, given observed cell frequencies for a selected sample, and true population splits. A nongeneral solution is also offered, based on the use of the G Index. Demonstrations with hypothetical data are given.     

Minority goals for interaction with the majority: Seeking distance from the majority and the effect of rejection on identification

Four studies investigated the conditions under which minority group members respond to group‐based discrimination with increased identification with their group. We propose that minorities' interaction goals should serve as a moderator: seeking distance from the majority might keep minority identification alive in the face of perceived discrimination. These predictions were tested correlationally in Study 1 among Chinese immigrants in Australia (sample 1a) and children of rural migrant workers in a Chinese city (sample 1b). In Studies 2 and 3, perceived discrimination was manipulated among Romanian immigrants in France and Polish immigrants in Scotland. In Study 4, both minority goals and perceived discrimination were manipulated among a sample of international students in Australia. Results showed that only for those who were inclined to seek distance from the majority, minority group identification increased when discrimination was high compared with low. Discussion focuses on the way that seeking distance might be an important strategy for coping with discrimination. Copyright © 2012 John Wiley & Sons, Ltd.     

The influence of attentional control on stimulus processing is category specific in Stroop tasks

It is still unclear how attentional control influences stimulus processing. We investigated this issue in four Stroop task experiments utilizing a pretest–training–posttest design. Subjects were given extensive training on the Stroop task using typical incongruent Stroop trials. The rates of color naming and word reading, which reflect the efficiency of stimulus processing, were assessed in pretest and posttest. The difference in rates between posttests and pretests reflects the influence of attentional control, acquired during the training phase, on stimulus processing. In Experiment 1, members of color category were used in the training phase; in Experiment 2, members of color category were used, but not in the training phase; in Experiment 3, they were neither in the color category nor were they used in the training. The results consistently showed that the suppression of word reading and the enhancement of color naming were developed in the training phases and they were not due to general training of color-naming task without conflict but to color-naming training with Stroop conflict (Experiment 4). More importantly, both suppression and enhancement affected the members of color category regardless of whether they were trained or not. The present findings suggest that the influence of attentional control on stimulus processing is category specific. We discuss the implications of the present results in terms of existing research on the locus of attentional control in Stroop tasks.     

Synchronization with competing visual and auditory rhythms: bouncing ball meets metronome

Synchronization of finger taps with periodically flashing visual stimuli is known to be much more variable than synchronization with an auditory metronome. When one of these rhythms is the synchronization target and the other serves as a distracter at various temporal offsets, strong auditory dominance is observed. However, it has recently been shown that visuomotor synchronization improves substantially with moving stimuli such as a continuously bouncing ball. The present study pitted a bouncing ball against an auditory metronome in a target–distracter synchronization paradigm, with the participants being auditory experts (musicians) and visual experts (video gamers and ball players). Synchronization was still less variable with auditory than with visual target stimuli in both groups. For musicians, auditory stimuli tended to be more distracting than visual stimuli, whereas the opposite was the case for the visual experts. Overall, there was no main effect of distracter modality. Thus, a distracting spatiotemporal visual rhythm can be as effective as a distracting auditory rhythm in its capacity to perturb synchronous movement, but its effectiveness also depends on modality-specific expertise.     

Fabrication of opal-like thin films

A process is described for the fabrication of opal-like thin films by controlling a solid–liquid interface moving at an inclined glass substrate. A special airflow is adopted to control solvent evaporation. SEM images and photographs show that the films, composed of polystyrene spheres, are coloured, flat, uniform, packed multilayers, and are well arrayed over a large scale. The ordered domains range in size from 10 to 15?µm. The spheres in suspension crystallized, caused by an intense interaction between the spheres on the boundary between the suspension and the substrate. A wide photonic band gap is observed in the normal-incidence transmission spectra of the films fabricated by this method. Cracks and defects in the films are examined and discussed.     

Electropulsing-induced strengthening of steel at high temperature

Electropulsing usually promotes a metastable phase to evolve towards its equilibrium state. This work reports an alternative case, where electropulsing promotes the decomposition of the stable δ-phase in duplex stainless steel at high temperature. This decomposition enables both the γ-phase and the σ-phase in the steel to survive and hence to strengthen it at high temperature. The hardness of the quenched sample with electropulsing treatment is 49.4% higher than that without electropulsing treatment. A fundamental understanding of the observation is developed.     

A continuum model of deformation-twin dominant crack growth in fcc metals

A continuum model is proposed to address the effects of deformation twinning on ductile versus brittle fracture behaviour of low strain-hardening fcc metals after exhaustion of work hardening. Instead of discrete twin nucleation, a number of partial dislocations ahead of the tip exhibit themselves as twins at the final stage of failure. The crack-tip plasticity is amended for deformation twinning and the constitutive form for the flow strength of arrays of twins of the same sign is expressed as a second gradient of microrotation for their coupling. The twins not only shield the crack tip but also inhibit further dislocation emission to form a dislocation-free zone (DFZ) in the immediate vicinity of the tip. The stress fields induced by deformation twinning lead to fracture branching under Mode I loading. The model is borrowed from the conceptual model presented by Beltz et al. [Acta Mater. 44 3943 (1996)], based on the equivalence of the stresses derived from twin-based crack-tip plasticity, macroscopic plasticity and elasticity on the DFZ boundary. The DFZ size and the crack-tip shielding ratio are obtained, as well as the branching angle. The branching angle is noteworthy for low strain-hardening metals. A strong dependence of the toughness on intrinsic surface energy and hardening index is examined. The toughness reduction due to crack-tip constraints and in the ductile-to-brittle transition (DBT) temperature region is revisited and found to be in agreement with experimental observations and available predictions.     

Thermodynamic fluctuations in magnetic states: Fe3Pt as a prototype

To understand the Invar anomalies, such as negative thermal expansion and spontaneous magnetization, we have applied our recently developed thermodynamic framework for a system with itinerant-electron magnetism to the ordered Fe₃Pt. The framework has coherently predicted the finite temperature intermixing between the fully ferromagnetic (FM) configuration and the spin-flipping configurations (SFCs). We have also discovered a tri-critical point at which a high-temperature second-order phase transition, between the fully ordered FM phase and the paramagnetic phase which is disordered due to SFCs, becomes first order at low temperatures.