A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters

The Savage–Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an effect on the dependent variable. However, the Savage–Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition is violated for multiple regression models with a Jeffreys–Zellner–Siow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage–Dickey ratio is especially relevant when analytical solutions for the Bayes factor are not available. This is the case for generalized linear models, non-linear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage–Dickey density ratio.     

A tutorial on Bayes factor estimation with the product space method

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial to implement. In this tutorial, we explain and illustrate the use of one such procedure, known as the product space method (Carlin & Chib, 1995). This is a transdimensional Markov chain Monte Carlo method requiring the construction of a “supermodel” encompassing the models under consideration. A model index measures the proportion of times that either model is visited to account for the observed data. This proportion can then be transformed to yield a Bayes factor. We discuss the theory behind the product space method and illustrate, by means of applied examples from psychological research, how the method can be implemented in practice.     

The learnability of abstract syntactic principles

Children acquiring language infer the correct form of syntactic constructions for which they appear to have little or no direct evidence, avoiding simple but incorrect generalizations that would be consistent with the data they receive. These generalizations must be guided by some inductive bias – some abstract knowledge – that leads them to prefer the correct hypotheses even in the absence of directly supporting evidence. What form do these inductive constraints take? It is often argued or assumed that they reflect innately specified knowledge of language. A classic example of such an argument moves from the phenomenon of auxiliary fronting in English interrogatives to the conclusion that children must innately know that syntactic rules are defined over hierarchical phrase structures rather than linear sequences of words (e.g., [Chomsky, 1965] , [Chomsky, 1971] , [Chomsky, 1980] and [Crain and Nakayama, 1987] ). Here we use a Bayesian framework for grammar induction to address a version of this argument and show that, given typical child-directed speech and certain innate domain-general capacities, an ideal learner could recognize the hierarchical phrase structure of language without having this knowledge innately specified as part of the language faculty. We discuss the implications of this analysis for accounts of human language acquisition.     

Bayes factors for the linear ballistic accumulator model of decision-making

Evidence accumulation models of decision-making have led to advances in several different areas of psychology. These models provide a way to integrate response time and accuracy data, and to describe performance in terms of latent cognitive processes. Testing important psychological hypotheses using cognitive models requires a method to make inferences about different versions of the models which assume different parameters to cause observed effects. The task of model-based inference using noisy data is difficult, and has proven especially problematic with current model selection methods based on parameter estimation. We provide a method for computing Bayes factors through Monte-Carlo integration for the linear ballistic accumulator (LBA; Brown and Heathcote, 2008), a widely used evidence accumulation model. Bayes factors are used frequently for inference with simpler statistical models, and they do not require parameter estimation. In order to overcome the computational burden of estimating Bayes factors via brute force integration, we exploit general purpose graphical processing units; we provide free code for this. This approach allows estimation of Bayes factors via Monte-Carlo integration within a practical time frame. We demonstrate the method using both simulated and real data. We investigate the stability of the Monte-Carlo approximation, and the LBA’s inferential properties, in simulation studies.     

The role of the ventral and dorsal pathways in reading Chinese characters and English words

Previous literature in alphabetic languages suggests that the occipital-temporal region (the ventral pathway) is specialized for automatic parallel word recognition, whereas the parietal region (the dorsal pathway) is specialized for serial letter-by-letter reading ( [Cohen et al., 2008] and [Ho et al., 2002] ). However, few studies have directly examined the role of the ventral and dorsal pathways in Chinese reading compared to English reading. To investigate this issue, we adopted the degraded word processing paradigm used by Cohen et al. (2008) and compared brain regions involved in the processing of degraded Chinese characters and English words during lexical decision, using functional magnetic resonance imaging (fMRI). The degraded characters/words were created by inserting blank spaces between radicals of Chinese characters or syllables of English polysyllabic words. Generally, the current study replicated the effects of Cohen et al. (2008), showing that in Chinese – like in alphabetic languages – character spacing modulates both ventral (bilateral cuneus, left middle occipital gyrus) and dorsal (left superior parietal lobule and middle frontal gyrus) pathways. In addition, the current study showed greater activation in bilateral cuneus and right lingual gyrus for Chinese versus English when comparing spaced to normal stimuli, suggesting that Chinese character recognition relies more on ventral visual-spatial processing than English word recognition. Interestingly, bilateral cuneus showed monotonic patterns in response to increasing spacing, while the rest of the regions of interest showed non-monotonic patterns, indicating different profiles for these regions in visual-spatial processing.     

Theory and tests of the conjoint commutativity axiom for additive conjoint measurement

The empirical study of the axioms underlying additive conjoint measurement initially focused mostly on the double cancellation axiom. That axiom was shown to exhibit redundant features that made its statistical evaluation a major challenge. The special case of double cancellation where inequalities are replaced by indifferences–the Thomsen condition–turned out in the full axiomatic context to be equivalent to the double cancellation property but without exhibiting the redundancies of double cancellation. However, it too has some undesirable features when it comes to its empirical evaluation, the chief among them being a certain statistical asymmetry in estimates used to evaluate it, namely two interlocked hypotheses and a single conclusion. Nevertheless, thinking we had no choice, we evaluated the Thomsen condition for both loudness and brightness and, in agreement with other lines of research, we found more support for conjoint additivity than not. However, we commented on the difficulties we had encountered in evaluating it. Thus we sought a more symmetric replacement, which as Gigerenzer and Strube (1983) first noted, is found in the conjoint commutativity axiom proposed by Falmagne (1976, who called it the “commutative rule”). It turns out that, in the presence of the usual structural and other necessary assumptions of additive conjoint measurement, we can show that conjoint commutativity is equivalent to the Thomsen condition, a result that seems to have been overlooked in the literature. We subjected this property to empirical evaluation for both loudness and brightness. In contrast to Gigerenzer and Strube (1983), our data show support for the conjoint commutativity in both domains and thus for conjoint additivity.     

Motivational climate interventions in physical education: A meta-analysis

Objective

The purpose of this study was to synthesize findings from motivational climate interventions employing [Ames, 1992a] and [Ames, 1992b] and [Epstein, 1988] and [Epstein, 1989] TARGET framework within school-based physical education contexts.

Design

The present study employed a quantitative research synthesis design. Meta-analysis uses empirical studies to summarize past research by drawing overall conclusions from separate investigations. This research design highlights important and unsolved issues related to motivational climate interventions within physical education.

Methods

Standard meta-analytic procedures incorporating inclusion and exclusion criteria, literature search, coding procedures, and statistical methods were used to identify and synthesize 22 studies with 24 independent samples. Cohen’s (1988) criteria for effect sizes were used to interpret and evaluate results.

Results

There was an overall small positive treatment effect (g = 0.103) for groups exposed to mastery motivational climates. Outcome analyses identified the most consistent and largest overall treatment effects for behavioral outcomes (g = 0.39–0.49) followed by affective outcomes (g = −0.27 to 0.59) and cognitive outcomes (g = −0.25 to 0.32). Moderator analyses were directed by study heterogeneity and identified several trends in intervention features and study features with the most substantial trend for participant features as elementary students had the largest overall treatment effect (g = 0.41).

Conclusions

Outcome and moderator analyses identified several trends in methodological features, participant features, and study features that should be addressed in future physical education motivational climate interventions.     

Family mastery enhances work engagement in Chinese nurses: A cross-lagged analysis

Based on Greenhaus and Powell's (2006) theory of work–family enrichment and the job demands-resources (JD-R) model of work engagement (Bakker & Demerouti, 2008), this study focused on the family-to-work enrichment process by investigating the effect of family mastery on work engagement in a Chinese context. A sample of 279 Chinese female nurses completed questionnaires in a two-wave longitudinal survey. With a cross–lagged analysis, the results indicated that family mastery at Time 1 had a significant positive effect on work engagement at Time 2. Furthermore, the relationship between family mastery and work engagement was stronger in a context of high (vs. low) job demand. These findings suggested that resource generated in family could directly help people stay engaged in the workplace, particularly under stressful working conditions. Our findings have expanded the JD-R model of work engagement and bridged it with theory of work–family enrichment. Implications for theory and practices are discussed.     

Further evidence of the Narcissistic Personality Inventory’s validity problems: A meta-analytic investigation—Response to Miller, Maples, and Campbell (this issue)

Miller, Maples, and Campbell (this issue) present evidence that Rosenthal and Hooley’s (2010) concerns regarding the Narcissistic Personality Inventory’s (NPI) relation to psychological health may be unwarranted. To resolve this issue empirically, we conducted a meta-analysis (k = 54, N = 38,932). Meta-analytic results revealed that a subset of NPI items were indeed problematic; items that function poorly at differentiating narcissists from non-narcissists accounted entirely for the NPI’s connection to psychological health. These items were also strongly associated with self-esteem, but unrelated to aggression/anger. In contrast, the remaining NPI items were unrelated to psychological health, but associated with aggression/anger. We conclude that although the NPI measures narcissism, its poorest functioning items also link it to outcomes unrelated to narcissism.     

Bayesian inference for psychology,part IV: parameter estimation and Bayes factors

In the psychological literature, there are two seemingly different approaches to inference: that from estimation of posterior intervals and that from Bayes factors. We provide an overview of each method and show that a salient difference is the choice of models. The two approaches as commonly practiced can be unified with a certain model specification, now popular in the statistics literature, called spike-and-slab priors. A spike-and-slab prior is a mixture of a null model, the spike, with an effect model, the slab. The estimate of the effect size here is a function of the Bayes factor, showing that estimation and model comparison can be unified. The salient difference is that common Bayes factor approaches provide for privileged consideration of theoretically useful parameter values, such as the value corresponding to the null hypothesis, while estimation approaches do not. Both approaches, either privileging the null or not, are useful depending on the goals of the analyst.     

Cultural influences on preference consistency: Consistency at the individual and collective levels

Previous research has shown that there are cultural differences in self-concept consistency across situations. However, little is known about cultural differences in preference consistency over time. The present research examined whether Americans are more consistent in their preferences over time than are Japanese. As hypothesized, there were cultural differences in self-reported ( and ) and actual ( and ) preference consistency over time. Further, cultural differences in preference consistency at the individual level (Study 1) were found to aggregate into collective level differences ( and ) in the consistency of preference trends, such as the popularity of baby names. Implications and future directions are discussed.     

Schémas cognitifs, croyances addictives et défenses dans la consommation et l’addiction au cannabis de jeunes adultes

Theoretical background

Integrating the cognitive approaches based on the model of Beck et al. (1993) information treatment, the Young (1994) model of maladapted schemas, the integrative approach of Plutchik (1995) and the clinical approach based on defense mechanisms (Bond, 1995), this study aimed at investigating: (a) the role of the hyperactivated maladapted schemas, (b) the addictive beliefs, (c) the suractivation of the conscious derives of defensive mechanisms and (d) the relationships between these cognitive and defensive variables, in young people's cannabis intensity addiction.

Method

Forty-four young adults, 25 females and 19 males, have completed a self-reported questionnaire estimating: (a) the intensity of cannabis addiction (Décamps et al., 2008), (b) the Rusinek (2006) adaptation of Young's maladapted schemas and (c) the questionnaire of addictive beliefs of Tison and Hautekeete (1998) and the defensive styles questionnaire of Bond et al. (1983) and Bond (1995). Non-parametric statistical analysis has been conducted on three subject's groups (“non-users”, “users non addicted”, “users-addicted”) to test the implications and the links between hypothesized psychological factors (e.g., schemas, beliefs and defences) in cannabis use intensity.

Results and discussion

The intensity of cannabis addiction is correlated significantly with: (a) an hyperactivation of three maladapted schemas: inadequate autocontrol, dependence and fear of lose the control, (b) a hyperactivation of permissive, anticipatory and relief oriented beliefs and (c) a higher activation of the defence “sublimation” and a lower activation of the “displacement”. “sublimation” is correlated with the global activation of 13 schemas that are correlated with the positive relief-oriented beliefs, which are correlated with the “displacement” defence, which is correlated with the anticipatory beliefs. The results showed that the permissive beliefs have the power to differentiate the “non-consumption”, the “consumption without addiction” and “the addiction” to cannabis. Our interpretation displays that greater attention to the dysfunctional beliefs will be required in future researches and should be essential targets in cognitive therapy of this substance use disorder.     

How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

We propose a sampling-based Bayesian t test that allows researchers to quantify the statistical evidence in favor of the null hypothesis. This Savage—Dickey (SD) t test is inspired by the Jeffreys—Zellner—Siow (JZS) t test recently proposed by Rouder, Speckman, Sun, Morey, and Iverson (2009). The SD test retains the key concepts of the JZS test but is applicable to a wider range of statistical problems. The SD test allows researchers to test order restrictions and applies to two-sample situations in which the different groups do not share the same variance.     

Bayesian t tests for accepting and rejecting the null hypothesis

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.     

Default “Gunel and Dickey” Bayes factors for contingency tables

The analysis of R×C contingency tables usually features a test for independence between row and column counts. Throughout the social sciences, the adequacy of the independence hypothesis is generally evaluated by the outcome of a classical p-value null-hypothesis significance test. Unfortunately, however, the classical p-value comes with a number of well-documented drawbacks. Here we outline an alternative, Bayes factor method to quantify the evidence for and against the hypothesis of independence in R×C contingency tables. First we describe different sampling models for contingency tables and provide the corresponding default Bayes factors as originally developed by Gunel and Dickey (Biometrika, 61(3):545–557 (1974)). We then illustrate the properties and advantages of a Bayes factor analysis of contingency tables through simulations and practical examples. Computer code is available online and has been incorporated in the “BayesFactor” R package and the JASP program (jasp-stats.org).     

Passion and burnout in elite junior soccer players: The mediating role of self-determined motivation

Objectives

The purpose of the study was to examine the relationship between forms of passion (harmonious and obsessive; Vallerand et al., 2003) and athlete burnout, and whether these relationships are mediated by self-determined motivation. The proposed model posited that because harmonious passion originates from an authentic self, it will be positively associated with self-determined regulation. Conversely, because obsessive passion originates from ego-invested structures within the self, it will be negatively associated with self-determined regulation. In turn, consistent with research examining the relationship between motivation regulation and athlete burnout, self-determined regulation was expected to be negatively associated with athlete burnout.

Design

Cross-sectional survey.

Method

This model was tested in 149 (M age = 16.2, s = 2.0, range = 12–21) male junior athletes who attended soccer academies in the UK. Participants completed the Passion Scale (Vallerand et al., 2003), the Sport Motivation Scale (Pelletier et al., 1995), and the Athlete Burnout Questionnaire (Raedeke & Smith, 2001).

Results

Harmonious passion was negatively related to a latent athlete burnout factor, whereas obsessive passion was unrelated to a latent athlete burnout factor. The relationship between harmonious passion and burnout was fully mediated by self-determined regulation.

Conclusions

The results suggest that harmonious passion may offer some protection from burnout for athletes due to higher levels of self-determined motivation.     

Phasic auditory alerting improves visual conscious perception

Attention is often conceived as a gateway to consciousness (Posner, 1994). Although endogenous spatial attention may be independent of conscious perception (CP) (Koch Tsuchiya, 2007), exogenous spatial orienting seems instead to be an important modulator of CP ( [Chica et al., 2010] and Chica, Lasaponara, et al., 2011). Here, we investigate the role of auditory alerting in CP in normal observers. We used a behavioral task in which phasic alerting tones were presented either at unpredictable or at predictable time intervals prior to the occurrence of a near-threshold visual target. We find, for the first time in neurologically intact observers, that phasic alertness increases CP, both objectively and subjectively. This result is consistent with evidence showing that phasic alerting can ameliorate the spatial bias exhibited by visual neglect patients (Robertson, Mattingley, Rorden, & Driver, 1998). The alerting network may increase the activity of fronto-parietal networks involved in top-down amplification required to bring a stimulus into consciousness (Dehaene, Changeux, Naccache, Sackur, & Sergent, 2006).     

How to use the diffusion model: Parameter recovery of three methods: EZ, fast-dm, and DMAT

Parameter recovery of three different implementations of the Ratcliff diffusion model was investigated: the EZ model (Wagenmakers, van der Maas, & Grasman, 2007), fast-dm (Voss & Voss, 2007), and DMAT (Vandekerckhove & Tuerlinckx, 2007). Their capacity to recover both the mean structure and individual differences in parameter values was explored. The three methods were applied to simulated data generated by the diffusion model, by the leaky, competing accumulator (LCA) model (Usher & McClelland, 2001) and by the linear ballistic accumulator (LBA) model (Brown & Heathcote, 2008). Results show that EZ and DMAT are better capable than fast-dm in recovering experimental effects on parameters. EZ was best in recovering individual differences in parameter values. When data were generated by the LCA model, the diffusion model estimates obtained with all three methods correlated well with corresponding LCA model parameters. No such one-on-one correspondence could be established between parameters of the LBA model and the diffusion model.     

“I Feel Your Pain”: The effects of observing ostracism on the ostracism detection system

Ostracism—being ignored and excluded—is a painful experience with negative psychological consequences. Social psychologists ( [Kerr and Levine, 2008] and [Spoor and Williams, 2007] ) argue humans have an evolved system for automatically detecting cues of ostracism and exclusion. Detection elicits pain and threats to fundamental needs. We hypothesize simply observing ostracism will cause negative affect and need threat in the observer. Participants observed a three-player Cyberball game; a target player was included or ostracized, and participants were either instructed to take the perspective of this player or given no such instructions. Participants observing ostracism reported negative affect and need threat. Our results indicate that ostracism detection is even more powerful than previously suggested, because vicariously, we feel the pain of others’ ostracism as our own.     

Happy today, happy tomorrow: The (non-)effect of temporal distance on judgments of Life Satisfaction

Construal Level Theory (CLT; Trope &; Liberman, 2003) posits that everyday life predictions, evaluations, and choices are influenced by how near or distant in time the event is. However, judgments of Life Satisfaction (LS) are relatively weakly influenced by situational factors and relatively strongly influenced by personality factors. Moreover, the constructive episodic simulation hypothesis ( [Schacter and Addis, 2007] and [Schacter and Addis, 2007] ) implies that memory of past events provides details for simulations of future novel experiences. Undergraduate students (N = 127) were randomly asked for how desirable LS was and for actual judgements of LS in the near- or distant-future. The results show that LS was more desirable in the distant-future. Thus, indicating that LS is abstractly assessed and judgments of LS should therefore be influenced by temporal distance as predicted by CLT. However, no significant differences in actual LS were found between conditions. Implications for theory development are discussed.