Confidence interval-based sample size determination formulas and some mathematical properties for hierarchical data

The use of hierarchical data (also called multilevel data or clustered data) is common in behavioural and psychological research when data of lower-level units (e.g., students, clients, repeated measures) are nested within clusters or higher-level units (e.g., classes, hospitals, individuals). Over the past 25 years we have seen great advances in methods for computing the sample sizes needed to obtain the desired statistical properties for such data in experimental evaluations. The present research provides closed-form and iterative formulas for sample size determination that can be used to ensure the desired width of confidence intervals for hierarchical data. Formulas are provided for a four-level hierarchical linear model that assumes slope variances and inclusion of covariates under both balanced and unbalanced designs. In addition, we address several mathematical properties relating to sample size determination for hierarchical data via the standard errors of experimental effect estimates. These include the relative impact of several indices (e.g., random intercept or slope variance at each level) on standard errors, asymptotic standard errors, minimum required values at the highest level, and generalized expressions of standard errors for designs with any-level randomization under any number of levels. In particular, information on the minimum required values will help researchers to minimize the risk of conducting experiments that are statistically unlikely to show the presence of an experimental effect.     

What Makes for a Good Life? A Four-Nation Study

How do we assess the value of our lives? What makes the life we live a good or worthy one in our own eyes? What are its aims? The answers to these questions are implicit in the often unarticulated commitments by which people define their selves, purposes, and actions. These commitments structure the moral framework that guides our everyday qualitative distinctions and positions us within a unified narrative of continuity and change. The substantive conception of a good life, we argue, presupposes but is not reducible to a set of basic values. As an initial exploration of cultural variation, Canadian, Chinese, Indian, and Japanese university students were compared on what they held to be most important for assessing the worth of their lives. The results revealed considerable commonality of content with notable differences consistent with the cultural ethos of each group.     

On the Mathematical Relationship Between Latent Change Score and Autoregressive Cross-Lagged Factor Approaches: Cautions for Inferring Causal Relationship Between Variables

The present paper focuses on the relationship between latent change score (LCS) and autoregressive cross-lagged (ARCL) factor models in longitudinal designs. These models originated from different theoretical traditions for different analytic purposes, yet they share similar mathematical forms. In this paper, we elucidate the mathematical relationship between these models and show that the LCS model is reduced to the ARCL model when fixed effects are assumed in the slope factor scores. Additionally, we provide an applied example using height and weight data from a gerontological study. Throughout the example, we emphasize caution in choosing which model (ARCL or LCS) to apply due to the risk of obtaining misleading results concerning the presence and direction of causal precedence between two variables. We suggest approaching model specification not only by comparing estimates and fit indices between the LCS and ARCL models (as well as other models) but also by giving appropriate weight to substantive and theoretical considerations, such as assessing the justifiability of the assumption of random effects in the slope factor scores.     

Time-specific Errors in Growth Curve Modeling: Type-1 Error Inflation and a Possible Solution with Mixed-Effects Models

Growth curve modeling (GCM) has been one of the most popular statistical methods to examine participants’ growth trajectories using longitudinal data. In spite of the popularity of GCM, little attention has been paid to the possible influence of time-specific errors, which influence all participants at each timepoint. In this article, we demonstrate that the failure to take into account such time-specific errors in GCM produces considerable inflation of type-1 error rates in statistical tests of fixed effects (e.g., coefficients for the linear and quadratic terms). We propose a GCM that appropriately incorporates time-specific errors using mixed-effects models to address the problem. We also provide an applied example to illustrate that GCM with and without time-specific errors would lead to different substantive conclusions about the true growth trajectories. Comparisons with other models in longitudinal data analysis and potential issues of model misspecification are discussed.     

Constrained k‐means on cluster proportion and distances among clusters for longitudinal data analysis

Clustering individuals by measures of similarity or dissimilarity at trajectories of changes in longitudinal data enables determination of typical patterns of development and growth. The present research proposes a new constrained k‐means method with lower bound constraints on cluster proportions and distances among clusters at focused variables and time points to fulfill various needs in clustering longitudinal data. The method assumes a large number of clusters at the onset and iteratively deletes and combines clusters according to these constraints. An additional property of the proposed constrained k‐means includes direct estimation of the unknown number of clusters. Simulation results clearly show the usefulness of the method for extracting clusters in plausible, real‐life analysis including non‐normality within clusters, and the proposed algorithm works well and convergence of the estimates is satisfactory. An actual example using Japanese longitudinal data regarding sleep habits and mental health is presented to verify the utility of the proposed constrained k‐means.     

Accelerating heterogeneous nucleation to increase hardness and electrical conductivity by deformation prior to ageing for Cu-4 at.% Ti alloy

ABSTRACT

Deformation bands, especially shear bands were intentionally formed in supersaturated Cu-4 at.% Ti alloy by groove-rolling with 75% area reduction. Cold deformation prior to the ageing process changed the precipitation behaviour of the alloy. The deformed structure with shear bands was maintained, without showing recovery and recrystallisation, even after prolonged ageing at 450°C for more than one day. The thermally stable shear bands act as nucleation initiation sites and prevent the expansion of discontinuous cellular precipitates. The hardness reached a value of 305?Hv and an electrical conductivity of 15% IACS (IACS?=?International Annealed Copper Standard. 100% IACS is defined as the conductivity corresponding to a volume resistivity at 20°C of 17.241?nΩ), compared to 283?Hv and 13% IACS for conventional solid-solutioned and peak-hardened alloy. In addition, the ageing time to reach the highest hardness was shortened from 720 to 180?min at 450°C.     

Happy People Become Happier through Kindness: A Counting Kindnesses Intervention

We examined the relationship between the character strength of kindness and subjective happiness (Study 1), and the effects of a counting kindnesses intervention on subjective happiness (Study 2). In Study 1, participants were 175 Japanese undergraduate students and in Study 2, participants were 119 Japanese women (71 in the intervention group and 48 in the control group). Results showed that: (a) Happy people scored higher on their motivation to perform, and their recognition and enactment of kind behaviors. (b) Happy people have more happy memories in daily life in terms of both quantity and quality. (c) Subjective happiness was increased simply by counting one’s own acts of kindness for one week. (d) Happy people became more kind and grateful through the counting kindnesses intervention. Discussion centers on the importance of kindness in producing subjective happiness.     

Reducing Inappropriate Bicycle Parking Through Persuasive Communication

In this study, the effectiveness of persuasive communication in reducing inappropriate bicycle parking was investigated. We hypothesized that persuasive communication aimed at promoting behavioral intention with respect to reducing the frequency of inappropriate bicycle parking would not actually achieve its objective, but that persuasive communication aimed at promoting implementation intention, as well as behavioral intention, would be successful. We conducted a field experiment using 99 participants who were daily bicycle users. They were randomly assigned to a control group and to 3 experimental groups. The results indicated that participants in the with-advice group and planning group had stronger implementation intentions, and thus reduced their incidence of inappropriate bicycle parking, than did the control and the without-advice groups. However, there were no differences in behavioral intention.     

Right hemispheric dominance in processing of unconscious negative emotion

Right hemispheric dominance in unconscious emotional processing has been suggested, but remains controversial. This issue was investigated using the subliminal affective priming paradigm combined with unilateral visual presentation in 40 normal subjects. In either left or right visual fields, angry facial expressions, happy facial expressions, or plain gray images were briefly presented as negative, positive, and control primes, followed by a mosaic mask. Then nonsense target ideographs were presented, and the subjects evaluated their partiality toward the targets. When the stimuli were presented in the left, but not the right, visual fields, the negative primes reduced the subjects' liking for the targets, relative to the case of the positive or control primes. These results provided behavioral evidence supporting the hypothesis that the right hemisphere is dominant for unconscious negative emotional processing.     

Postsaccadic processing of the retinal image during picture scanning

Eye movements were monitored while observers inspected photographs of natural scenes. At the end of each saccade (i.e., at the beginning of each period of steady fixation), the stimulus was replaced for a certain period of time by a uniform field (Experiment 1) or a blurred version of the stimulus scene (Experiment 2). Total fixation duration was measured as a function of the duration of the initial uniform field or the blurred image that followed the saccade. It was found that fixation duration increased proportionally with the duration of the initial replacement field, even for durations as short as 25 msec. These results suggest that the visual system uses information on the retina right after each saccade is completed and that the blurred, low-resolution information used in Experiment 2 (cutoff frequency of 0.8 cpd) is not sufficient for the requirements of picture processing in this task.