Representation of Game Algebras

We prove that every abstractly defined game algebra can be represented as an algebra of consistent pairs of monotone outcome relations over a game board. As a corollary we obtain Goranko's result that van Benthem's conjectured axiomatization for equivalent game terms is indeed complete.     

Some Supervaluation-based Consequence Relations

In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim–Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation.     

Testing the Physical Activity Self-Definition Model among low-active adults participating in a physical activity intervention

Seeing oneself as a physically active person is one of the strongest predictors of physical activity behaviour and self-regulatory strategies. Determining whether and how physical activity self-perceptions can be stimulated may help low-active individuals who do not see themselves as a physically active person become more active. Cross-sectional research has tested the Physical Activity Self-Definition (PASD) model among active samples; longitudinal studies among low-active adults have yet to be done. The purpose of this study was to test the predictive power of the PASD model among low-active adults over a 16-week physical activity intervention. Participants completed surveys of validated questionnaires in-person at baseline (pre-intervention) and at 16-weeks (end of intervention) at one of two primary care facilities. The final sample included 119 low-active adults. Partial least squares-structural equation modeling indicated that the original model had small-medium predictive power (Q² = 0.22; SRMR = 0.13 [0.05, 0.07]; RMSE = 1.13; MAE = 0.9; BIC = 1348.40). Two paths were added in the revised model (perceived wanting—PASD; perceived ability—perceived commitment), which explained an additional 4% and 5% of the variance in perceived commitment (R² = 0.62 [0.48, 0.72]) and PASD (R² = 0.74 [0.64, 0.80]; all p’s < 0.001), respectively. The revised model had medium predictive power (Q² = 0.25; SRMR = 0.11 [0.05, 0.06]; RMSE = 1.1; MAE = 0.87; BIC = 1332.84) All path coefficients remained positive and significant at p ≤ .001. Among low-active adults, perceived wanting and perceived ability may be more salient when engaging in physical activity and regarding themselves as a physically active person. Findings may support practitioners and health care professionals in designing physical activity interventions to foster PASD among low-active adult populations.     

Back to the basics: Rethinking partial correlation network methodology

The Gaussian graphical model (GGM) is an increasingly popular technique used in psychology to characterize relationships among observed variables. These relationships are represented as elements in the precision matrix. Standardizing the precision matrix and reversing the sign yields corresponding partial correlations that imply pairwise dependencies in which the effects of all other variables have been controlled for. The graphical lasso (glasso) has emerged as the default estimation method, which uses ℓ₁-based regularization. The glasso was developed and optimized for high-dimensional settings where the number of variables (p) exceeds the number of observations (n), which is uncommon in psychological applications. Here we propose to go ‘back to the basics’, wherein the precision matrix is first estimated with non-regularized maximum likelihood and then Fisher Z transformed confidence intervals are used to determine non-zero relationships. We first show the exact correspondence between the confidence level and specificity, which is due to 1 minus specificity denoting the false positive rate (i.e., α). With simulations in low-dimensional settings (p ≪ n), we then demonstrate superior performance compared to the glasso for detecting the non-zero effects. Further, our results indicate that the glasso is inconsistent for the purpose of model selection and does not control the false discovery rate, whereas the proposed method converges on the true model and directly controls error rates. We end by discussing implications for estimating GGMs in psychology.     

Holistic face processing is penetrable … depending on the composite design

Holistic processing (HP) of faces is usually measured by the composite effect. While Weston and Perfect [2005. Effects of processing bias on the recognition of composite face halves. Psychonomic Bulletin & Review, 12, 1038–1042. doi:10.3758/BF03206440] found that priming at the local level speeded recognition of components of faces, Gao et al. [2011. Priming global and local processing of composite faces: Revisiting the processing-bias effect on face perception. Attention Perception & Psychophysics, 73, 1477–1486. doi:10.3758/s13414-011-0109-7] found that only global priming had an effect on HP of faces. The two studies used different versions of the composite task (the partial design, which is considered to be prone on bias, and the complete design). However, the two studies also differed in other respects and it is difficult to know to what extent issues with the partial design contributed to the differing conclusions. In the present study, the HP indexed by the complete design measure was augmented by global priming. In contrast, no effect was observed in the partial design index. We claim that the partial design index reflects other factors besides HP, including response bias, and conclude that HP can be understood within the context of domain-general attentional processes.     

Replies to comments on "Which method delivers greater signal-to-noise ratio: Structural equation modelling or regression analysis with weighted composites?" by Yuan and Fang (2023)

Observational data typically contain measurement errors. Covariance-based structural equation modelling (CB-SEM) is capable of modelling measurement errors and yields consistent parameter estimates. In contrast, methods of regression analysis using weighted composites as well as a partial least squares approach to SEM facilitate the prediction and diagnosis of individuals/participants. But regression analysis with weighted composites has been known to yield attenuated regression coefficients when predictors contain errors. Contrary to the common belief that CB-SEM is the preferred method for the analysis of observational data, this article shows that regression analysis via weighted composites yields parameter estimates with much smaller standard errors, and thus corresponds to greater values of the signal-to-noise ratio (SNR). In particular, the SNR for the regression coefficient via the least squares (LS) method with equally weighted composites is mathematically greater than that by CB-SEM if the items for each factor are parallel, even when the SEM model is correctly specified and estimated by an efficient method. Analytical, numerical and empirical results also show that LS regression using weighted composites performs as well as or better than the normal maximum likelihood method for CB-SEM under many conditions even when the population distribution is multivariate normal. Results also show that the LS regression coefficients become more efficient when considering the sampling errors in the weights of composites than those that are conditional on weights.