A Comparative Investigation of Confidence Intervals for IndependentVariables in Linear Regression

In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.     

Dealing with Multiple Solutions in Structural Vector Autoregressive Models

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.     

Modeling Clustered Data with Very Few Clusters

Small-sample inference with clustered data has received increased attention recently in the methodological literature, with several simulation studies being presented on the small-sample behavior of many methods. However, nearly all previous studies focus on a single class of methods (e.g., only multilevel models, only corrections to sandwich estimators), and the differential performance of various methods that can be implemented to accommodate clustered data with very few clusters is largely unknown, potentially due to the rigid disciplinary preferences. Furthermore, a majority of these studies focus on scenarios with 15 or more clusters and feature unrealistically simple data-generation models with very few predictors. This article, motivated by an applied educational psychology cluster randomized trial, presents a simulation study that simultaneously addresses the extreme small sample and differential performance (estimation bias, Type I error rates, and relative power) of 12 methods to account for clustered data with a model that features a more realistic number of predictors. The motivating data are then modeled with each method, and results are compared. Results show that generalized estimating equations perform poorly; the choice of Bayesian prior distributions affects performance; and fixed effect models perform quite well. Limitations and implications for applications are also discussed.     

Élaboration et validation du Test d’Orientation Temporelle (TOT)

Temporal orientation is an essential data of the human psyche that modulates how we relied to the times of life. This survey describes the creation of a psychometric measure of temporal orientation in young French adults. Starting with the observation that temporal orientation is difficult for youngsters, a team of psychologists developed a preliminary version of the instrument. The psychometric validity of the test has been analyzed. The data have been collected on 507 high school students and academic students in the region of Nantes. An exploratory factorial analysis shows four dimensions: “short-term”, “immediately”, “anticipation” and “long-term”. The internal consistency is generally satisfactory and the measure of convergence confirms the external validity. The weak interrelationships between dimensions indicate distinct psychological constructs. A validated version composed of 30 items of the Temporal Orientation Test (TOT) is proposed.     

Le momentum psychologique en sport : vers une perspective complexe et dynamique

Psychological momentum (PM) is a social phenomenon that has triggered the curiosity of sport psychologists since the early 1980s. From early to recent conceptualizations, PM has been considered as a complex construct, inherently related to variations in sport performance. Over the past 30 years, several models have been proposed to untangle how PM is triggered, which psychological changes are involved in PM experiences, and how PM relates to performance. While linear (causal) models have dominated past research on PM, researchers have recently found that PM can change nonlinearly, depending on the performance history of the competition. This systematic review aims to provide an overview of different PM models that have been proposed in the past to increase insights into the complexity of PM, including the transition from linear causal models to nonlinear dynamical models. Moreover, based on the current state of affairs, perspectives for future research are provided.     

Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach.     

Nesselroade and Molenaar's Measurement Concerns and Proposals: An Introduction

In this special section Nesselroade and Molenaar (N & M) propose a provocative new approach to measurement invariance. When measures are collected repeatedly over time (e.g., daily diary studies), a potentially unique measurement model relating the items to the underlying construct can be created for each individual. If hypothesized causal paths specified between constructs (e.g., frustration → aggression) can be constrained to be equal across the individuals, a model with idiographic measurement of the constructs, but with nomothetic structural relationships can be specified. Three commentaries react to N & M's proposal. Revelle and Wilt challenge the priority given by N & M to unique individual measurement structures, arguing that between subjects differences in structural relationships are empirically important and meaningful. Markus's uses David Hume's framework to raise philosophy of science challenges for N & M's approach. Maydeu-Olivares challenges the incremental validity of N & M's approach, arguing that N & M's approach is unlikely to improve the prediction of between subjects criteria. Finally, N & M present a rejoinder to the three commentaries.     

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

The Irony of Social Trust: Individual‐level and Contextual‐level Links with Protest Intention and Radical Right Support in Switzerland

This research examines how social trust translates into dynamics of mobilisation for inclusion or exclusion in Swiss cantons by studying how social trust is linked to equality‐directed protest intention versus radical right support, comparing individual‐level and contextual‐level relationships. The study is based on data from the Swiss Household Panel collected between 2002 and 2008. The impact of individual‐level and contextual‐level social trust is analysed in three‐level regression models of repeated observations, nested in individuals who are nested in cantons. The results indicate complex patterns that depend on the level at which social trust is assessed and confirm the need for a contextualised view of social trust and social capital. For individuals, higher social trust is associated with higher protest intention and lower radical right support. However, in cantons characterised by higher rates of social trust, individuals are less likely to engage in protest actions and more likely to support the radical right. Further analyses show that canton‐level social trust is intertwined with other contextual factors, suggesting that in certain configurations, that is, combined with low levels of cultural and social diversity, climates of social trust may be linked to more restricted forms of solidarity and the persistence of inequality. Copyright © 2015 John Wiley & Sons, Ltd.