Estimation of the predictive power of the model in mixed‐effects meta‐regression: A simulation study

Several methods are available to estimate the total and residual amount of heterogeneity in meta‐analysis, leading to different alternatives when estimating the predictive power in mixed‐effects meta‐regression models using the formula proposed by Raudenbush (1994, 2009). In this paper, a simulation study was conducted to compare the performance of seven estimators of these parameters under various realistic scenarios in psychology and related fields. Our results suggest that the number of studies (k) exerts the most important influence on the accuracy of the results, and that precise estimates of the heterogeneity variances and the model predictive power can only be expected with at least 20 and 40 studies, respectively. Increases in the average within‐study sample size () also improved the results for all estimators. Some differences among the accuracy of the estimators were observed, especially under adverse (small k and ) conditions, while the results for the different methods tended to convergence for more optimal scenarios.     

Development of the Two‐Dimensional Mood Scale for self‐monitoring and self‐regulation of momentary mood states

The purpose of this study was to develop a measure for self‐monitoring and self‐regulation of momentary mood states. The Two‐Dimensional Mood Scale (TDMS), consisting of eight words selected on the basis of pleasure and arousal, was created as an efficient measure of self‐monitoring. In Study 1, the validity and reliability of the TDMS were examined by administering the measure to 904 university students. Structural equation modeling revealed that mood states were constructed of two components, arousal and pleasure, and factor analysis found two factors, vitality and stability. In Study 2, differences between two mood manipulations, activation (exercise) and relaxation techniques were examined in 224 university students. The results showed that exercise induced higher vitality (, ) but no change in stability (, ), while relaxation resulted in an increase in stability (, ) but no change in vitality (, ). The TDMS can be combined with various mood manipulations to enable individuals to self‐regulate and alter negative psychological states.     

Functions of Nonsuicidal Self‐Injury Are Differentially Associated with Suicide Ideation and Past Attempts among Childhood Trauma Survivors

Research into factors for suicide has revealed relations between trauma exposure and suicidality (e.g., Bridge, Goldstein, & Brent, 2006 ; Joiner, Sachs‐Ericson, Wingate, Brown, Anestis, & Selby, 2007 ) wherein painful and provocative experiences (e.g., nonsuicidal self‐injury [NSSI]) are an important link (e.g., Van Orden, Witte, Cukrowicz, Braithwaite, Selby, & Joiner, 2010 ; Smith, 2013 ). No prior research has assessed the relationship between functions of NSSI and suicidality among childhood trauma survivors. Participants who endorsed childhood trauma exposure (N = 121; M_age = 18.69, range 18–22) completed measures of posttraumatic stress disorder (PTSD) symptoms, NSSI, and suicidality. Multiple regressions assessing whether the four functions of NSSI predicted suicide ideation and past attempts after controlling for PTSD symptom severity found that only social negative reinforcement was associated with SI ( = .304, SE = .243, t = 2.23, p = .028), while only automatic negative reinforcement was associated with past attempts ( = .470, SE = .066, t = 2.25, p = .028). Findings highlight the importance of assessing NSSI functions when assessing suicidality among trauma survivors.     

Testing the difficulty theory of the SON‐R –17, a non‐verbal test of intelligence

Fischer's (1973) linear logistic test model can be used to test hypotheses regarding the effect of covariates on item difficulty and to predict the difficulty of newly constructed test items. However, its assumptions of equal discriminatory power across items and a perfect prediction of item difficulty are never absolutely met. The amount of misfit in an application of a Bayesian version of the model to two subtests of the SON‐R –17 is investigated by means of item fit statistics in the framework of posterior predictive checks and by means of a comparison with a model that allows for residual (co)variance in the item parameters. The effect of the degree of residual (co)variance on the robustness of inferences is investigated in a simulation study.     

Notes on attribution functions

Let be the knowledge space derived from an attribution function σ on Q. Under an assumption for σ, this paper gives some necessary and sufficient conditions such that is discriminative. It also discusses the resolubility of σ when Q is an infinite set. More precisely, this paper proves that σ is not resoluble if Q is uncountable, and gives a necessary and sufficient condition such that σ is resoluble when is -well-graded. By way of applications of these results, discriminativeness and resolubility are discussed around the merge of skill multimaps and the meshing of the delineated knowledge spaces.     

Comparing two independent groups: A test based on a one‐step M‐estimator and bootstrap‐t

A new test is proposed for the problem of comparing two independent groups in terms of some measure of location. The proposed test () uses a one‐step M‐estimator and a bootstrap‐t method with the procedure proposed by Özdemir and Kurt (2006) . Eight methods were compared in terms of actual Type I error and power when the underlying distributions differ in skewness and kurtosis under heterogeneity of variances. For the 21 theoretical distributions, the Yuen test with the bootstrap‐t method was the most favourable, followed by test. For the five real data sets, the proposed test and percentile bootstrap method with the one‐step M‐estimator performed best.     

Individual Differences in Risky Decision Making: A Meta‐analysis of Sensation Seeking and Impulsivity with the Balloon Analogue Risk Task

To represent the state‐of‐the‐art in an effort to understand the relation between personality and risk taking, we selected a popular decision task with characteristics that parallel risk taking in the real world and two personality traits commonly believed to influence risk taking. A meta‐analysis is presented based on 22 studies of the Balloon Analogue Risk Task from which correlations with sensation seeking and impulsivity assessments could be obtained. Results calculated on a total of 2120 participants showed that effect size for the relation of sensation seeking with risk taking was in the small–moderate range ( = .14), whereas the effect size for impulsivity was just around the small effect size threshold ( = .10). Although we considered participants' demographics as moderators, we found only significantly larger effect sizes for the older adolescents and young adults compared with other ages. The findings of the present review supported the view that inconsistencies in personality–risk research were mostly due to random fluctuations of specific effect sizes, rather than to lack of theoretical ties or to measurement unreliability. It is also concluded that studies aimed at relating individual differences in personality to performance in experimental decision tasks need an appropriate sample size to achieve the power to produce significant results. Copyright © 2013 John Wiley & Sons, Ltd.     

“Do Unto Others”: Effects of Priming the Golden Rule on Buddhists’ and Christians’ Attitudes Toward Gay People

The Golden Rule, a core precept of many religions, emphasizes the importance of treating others with compassion. We examined whether priming Golden Rule messages would influence Buddhists’ and Christians’ attitudes toward gay people and perceptions that homosexuality is a choice. In a priming task, participants filled in missing words for popular quotations including two Golden Rule messages that were attributed to either Buddha or Jesus. Christians ( N = 585) in the Buddha‐attributed Golden Rule condition showed stronger explicit anti‐gay attitudes and were more likely to agree that homosexuality is a choice than Christians in the Jesus‐attributed or control conditions, = .012, = .035, even after controlling for political orientation and religiosity. Buddhists ( = 394) showed no variation in attitudes across priming conditions, = .001, = .78. Our results suggest that although the Golden Rule has an important influence on believers, its message of compassion may produce more prejudice if it comes from an outgroup source compared to an ingroup source.     

Limited‐information goodness‐of‐fit testing of diagnostic classification item response models

Despite the growing popularity of diagnostic classification models (e.g., Rupp et al., 2010, Diagnostic measurement: theory, methods, and applications, Guilford Press, New York, NY) in educational and psychological measurement, methods for testing their absolute goodness of fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full‐information test statistics such as Pearson's X² and the likelihood ratio statistic G² suffer from sparseness in the underlying contingency table from which they are computed. Recently, limited‐information fit statistics such as Maydeu‐Olivares and Joe's (2006, Psychometrika, 71, 713) M₂ have been found to be quite useful in testing the overall goodness of fit of item response theory models. In this study, we applied Maydeu‐Olivares and Joe's (2006, Psychometrika, 71, 713) M₂ statistic to diagnostic classification models. Through a series of simulation studies, we found that M₂ is well calibrated across a wide range of diagnostic model structures and was sensitive to certain misspecifications of the item model (e.g., fitting disjunctive models to data generated according to a conjunctive model), errors in the Q‐matrix (adding or omitting paths, omitting a latent variable), and violations of local item independence due to unmodelled testlet effects. On the other hand, M₂ was largely insensitive to misspecifications in the distribution of higher‐order latent dimensions and to the specification of an extraneous attribute. To complement the analyses of the overall model goodness of fit using M₂, we investigated the utility of the Chen and Thissen (1997, J. Educ. Behav. Stat., 22, 265) local dependence statistic $X_{\mathrm{LD}}^2$ for characterizing sources of misfit, an important aspect of model appraisal often overlooked in favour of overall statements. The $X_{\mathrm{LD}}^2$ statistic was found to be slightly conservative (with Type I error rates consistently below the nominal level) but still useful in pinpointing the sources of misfit. Patterns of local dependence arising due to specific model misspecifications are illustrated. Finally, we used the M₂ and $X_{\mathrm{LD}}^2$ statistics to evaluate a diagnostic model fit to data from the Trends in Mathematics and Science Study, drawing upon analyses previously conducted by Lee et al., (2011, IJT, 11, 144).     

IN PRAISE OF A LOGIC OF DEFINITIONS THAT TOLERATES Ω‐INCONSISTENCY

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, , under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of to the theory of truth.     

How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like , is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers (specifically, the radicands of radical expressions) as natural numbers. Strategy self‐reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task‐specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.     

Early access to abstract representations in developing readers: evidence from masked priming

A commonly shared assumption in the field of visual‐word recognition is that retinotopic representations are rapidly converted into abstract representations. Here we examine the role of visual form vs. abstract representations during the early stages of word processing – as measured by masked priming – in young children (3rd and 6th Graders) and adult readers. To maximize the chances of detecting an effect of visual form, we employed a language with a very intricate orthography, Arabic. If visual form plays a role in the early stages of processing, greater benefit would be expected from related primes that have the same visual form (in terms of the ligation pattern between a word's letters) as the target word (e.g.– [ktz b–ktA b] – note that the three initial letters are connected in prime and target) than for those that do not (– [ktxb–ktA b]). Results showed that the magnitude of priming effect relative to an unrelated condition (e.g. –) was remarkably similar for both types of prime. Thus, despite the visual complexity of Arabic orthography, there is fast access to the abstract letter representations not only in adult readers by also in developing readers.     

Statistical Learning Is Not Affected by a Prior Bout of Physical Exercise

This study examined the effect of a prior bout of exercise on implicit cognition. Specifically, we examined whether a prior bout of moderate intensity exercise affected performance on a statistical learning task in healthy adults. A total of 42 participants were allocated to one of three conditions—a control group, a group that exercised for 15 min prior to the statistical learning task, and a group that exercised for 30 min prior to the statistical learning task. The participants in the exercise groups cycled at 60% of their respective O₂max. Each group demonstrated significant statistical learning, with similar levels of learning among the three groups. Contrary to previous research that has shown that a prior bout of exercise can affect performance on explicit cognitive tasks, the results of the current study suggest that the physiological stress induced by moderate‐intensity exercise does not affect implicit cognition as measured by statistical learning.     

Can we disregard the whole model? Omnibus non-inferiority testing for R2 in multi-variable linear regression and in ANOVA

Determining a lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model (i.e., to confirm the lack of a meaningful association between an outcome and predictors). Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper introduces non-inferiority tests for ANOVA and linear regression analyses, which correspond to the standard widely used F test for and R², respectively. A simulation study is conducted to examine the Type I error rates and statistical power of the tests, and a comparison is made with an alternative Bayesian testing approach. The results indicate that the proposed non-inferiority test is a potentially useful tool for ‘testing the null’.     

The empowering effect of punishment on forgiveness

We examined the process by which punishment enables forgiveness, testing the proposition that punishment restores a sense of justice to victims, an experience that is empowering. In Study 1 (N = 69), university students received insulting feedback and were given the opportunity (or not) to sanction the offender. In Study 2 (N = 91), participants imagined having the opportunity (or not) to recommend punishment for a person who had vandalized their house. A two‐step mediation model (punishment justice restoration empowerment forgiveness) was supported in these two studies. In Study 3 (N = 227), punishment options were expanded to test the role of victim voice in the context of third‐party and personal retributive and restorative justice responses to workplace bullying, as well as taking into account revenge as an alternative to justice restoration. When victims had voice, empowerment again played a central indirect role in relations between punishment and forgiveness.     

A meta‐analytic review of tipping compensation practices: An agency theory perspective

Tipping represents a form of compensation valued at over $50 billion a year in the United States alone. Tipping can be used as an incentive mechanism to reduce a principal–agent problem. An agency problem occurs when the interests of a principal and agent are misaligned, and it is challenging for the principal to monitor or control the activities of the agent. However, past research has been limited in the investigation of the extent to which tipping is effective at addressing this problem. Following an examination of 74 independent studies with 12,271 individuals, meta‐analytic results indicate that there is a small, positive relation between service quality and percentage of a bill tipped ( = .15 without outliers). Yet, in support of the idea behind tipping, relative weights analyses illustrate that service quality was a stronger predictor of percentage of the bill tipped than food quality, frequency of patronage, and dining party size. Evidence also suggests that racial minority servers tend to be tipped less than White servers (Cohen's d = .17), and women tend to be tipped more than men (Cohen's d = .15). Still, given the magnitude of the effect, one might question if tipping is an effective compensation practice to reduce the principal–agent problem. We discuss theoretical and practical implications for future research.     

Modelling monotonic effects of ordinal predictors in Bayesian regression models

Ordinal predictors are commonly used in regression models. They are often incorrectly treated as either nominal or metric, thus under- or overestimating the information contained. Such practices may lead to worse inference and predictions compared to methods which are specifically designed for this purpose. We propose a new method for modelling ordinal predictors that applies in situations in which it is reasonable to assume their effects to be monotonic. The parameterization of such monotonic effects is realized in terms of a scale parameter b representing the direction and size of the effect and a simplex parameter modelling the normalized differences between categories. This ensures that predictions increase or decrease monotonically, while changes between adjacent categories may vary across categories. This formulation generalizes to interaction terms as well as multilevel structures. Monotonic effects may be applied not only to ordinal predictors, but also to other discrete variables for which a monotonic relationship is plausible. In simulation studies we show that the model is well calibrated and, if there is monotonicity present, exhibits predictive performance similar to or even better than other approaches designed to handle ordinal predictors. Using Stan, we developed a Bayesian estimation method for monotonic effects which allows us to incorporate prior information and to check the assumption of monotonicity. We have implemented this method in the R package brms, so that fitting monotonic effects in a fully Bayesian framework is now straightforward.     

Two simple approximations to the distributions of quadratic forms

Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to with z_i being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the λ_i and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the λ_i is small, the rescaled statistic is also adequate for practical model inference. But comparing T_R against will inflate type I errors when substantial differences exist among the λ_i, especially, when d is also large.     

The Effects of Assisted Housing on Child Well‐Being

The most rigorous research on the causal effects of assisted housing on children's outcomes finds no such effects. The present study uses rich longitudinal data from the Panel Study of Income Dynamics, augmented with Census, American Community Survey and U.S. Department of Housing and Urban Development administrative data, to unpack these nil effects. Analyses include 194 children ( age = 6.2 years) living in assisted housing in 1995 or later who were 13–17 years old in 2002 or 2007, and an unassisted comparison group of 215 children who were income‐eligible for, but never received, housing assistance. Results suggested no mean effects of living in assisted housing during childhood on adolescent cognitive, behavior, and health outcomes, addressing selection through propensity score matching and instrumental variables. However, quantile regressions suggest assisted housing provides an added boost for children with the best cognitive performance and fewest behavior problems but has opposite effects on children with the lowest cognitive scores and most behavior problems. Further tests indicate that these differences are not explained either by neighborhood effects or housing quality. A potentially fruitful avenue for future research investigates differences in how parents take advantage of the housing affordability provided by assisted housing to benefit their children.