Mediation with categorical variables compleat

This rejoinder addresses the thoughtful issues raised by the commentators. We hold to the analytical solution of fitting X → M (to obtain a and sa) and X&;M→ (to obtain b and sb) via regression or logistic regression, depending on whether M and Y are continuous or categorical. Then researchers compute za, zb, and ZMediation.     

Informational constraints shape emergent functional behaviours during performance of interceptive actions in team sports

Objectives

This study aimed to explain how defenders intercept the trajectory of a passing ball by understanding how they coupled their actions to critical information sources in a competitive performance setting in team sports.

Design

Time series data on movement displacements of fifteen senior male futsal performers were recorded and digitized during nine competitive futsal games.

Method

Performance was recorded by a digital camera and digitized with TACTO software. The spatial-temporal dynamics of performers during ten intercepted and ten non-intercepted passes were compared. Time to ball interception was calculated by the difference between the time of each defender to an interception point in ball trajectory and the time of the ball’s arrival at the same interception point. Initial distances between defenders and ball and velocity data of defenders and ball over time were also recorded.

Results

Time to ball interception revealed positive values when passes were not intercepted, and negative to zero values when passes were intercepted. At the moment of pass initiation defenders’ distances to the ball constrained their possibilities for successful interception. Analysis of defenders’ adaptations to the environment revealed that continuous changes in the defenders’ velocities constrained their success of the interception.

Conclusions

Intercepted passes seemed to be influenced by the continuous regulation of a defender’s velocity relative to the ball’s trajectory. Time to ball interception is a variable that captured the emergent functional behaviours of players attempting to intercept the trajectory of a pass in the team sport of futsal.     

Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Abstract

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors’ interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.     

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.     

Predictors of treatment outcome for youth receiving intensive residential treatment for obsessive–compulsive disorder (OCD)

ABSTRACT

Little is known about the predictors of outcome from intensive residential treatment of OCD. This study aimed to examine age, gender, and baseline OCD severity, as well as measures of comorbid anxiety and depressive, internalizing/externalizing, and inattention symptoms, as predictors of treatment outcome in adolescents receiving intensive residential treatment for OCD.

The sample comprised 314 adolescents aged 13–17 years with treatment-resistant OCD and a Children’s Yale–Brown Obsessive–Compulsive Scale Self-Report (CY-BOCS-SR) total score ≥16. Bivariate and multiple regression models were used to evaluate the predictors of continuous OCD severity outcome and treatment response.

Results of the bivariate regression analyses of predictors demonstrated that length of treatment, pre-treatment OCD severity, and symptoms of anxiety and depression significantly predicted post-treatment OCD severity, while only symptoms of depression and anxiety predicted treatment response. When including all predictors in the same model, only baseline OCD severity remained a significant predictor of post-treatment OCD severity, and none of the assessed variables significantly predicted treatment response.

Results indicate that low pre-treatment OCD severity predicts lower OCD severity following treatment, although it did not predict treatment response.     

Why are moderators of self-other agreement difficult to establish?

Agreement between the self and other rated personality profiles was studied in two samples involving 11,096 speakers of two languages, Dutch and Estonian, who completed two different personality questionnaires, the NEO-PI-3 and HEXACO-PI-R. An outstanding agreement was achieved in the most occasions: in only 4–6% of dyadic pairs was the correlation between two randomly paired profiles higher than the actually observed correlation between true pairs. As in previous studies, we found that age and sex of participants and length of acquaintance had no significant effect on the level of self-other agreement. However, intimate knowledge helped married and unmarried couples in both samples be more accurate in their personality judgments; family members, in turn, had knowledge that made them more accurate than two people who were just acquaintances or friends. We believe that these outcomes can be explained by the contention that the judgment of another’s personality is a relatively simple task, which is accomplishable for most people most of the time. In other words, because judging another person’s personality is an easy task, we are not able to determine “good targets,” “good judges,” or “good traits.” Perhaps it is only “good information” which determines the closeness of the target-judge relationship, and which has a small but reliable impact on the level of self-other agreement. This explains why it is so difficult to find individual differences in the ability to judge another person’s personality.