智者必怀仁？智慧与美德的关系辨析

智慧与美德是独立但相互作用的心理结构。针对其关系,以往哲学家与心理学家基于个人经验和文化观念进行了大量规范性层面的理论思辨,但仍存在理论分歧（线性论、阈值论、从属论）,且缺少以定量方法为主的描述性层面的实证研究,尤其缺乏基于实验的关于“智”与“仁”双向因果关系的探索。未来研究可以借鉴实验伦理学的范式,着眼于研究特定领域、特定情境下智慧与美德之间的双向因果关系,加强中国文化背景下的智慧与美德关系的研究,并探索其潜在的认知神经机制。如何统一智慧与美德关系的“应然”与“实然”的研究,是接下来需要面临的挑战。     

Bouts of responding: the relation between bout rate and the rate of variable-interval reinforcement

By nose poking a lighted key, rats obtained food pellets on either a variable-interval schedule of reinforcement or a schedule that required an average of four additional responses after the end of tile variable-interval component (a tandem variable-interval variable-ratio 4 schedule). With both schedule types, the mean variable interval was varied between blocks of sessions from 16 min to 0.25 min. Total rate of key poking increased similarly as a function of the reinforcer rate for the two schedule types, but response rate was higher with than without the four-response requirement. Analysis of log survivor plots of interresponse times showed that key poking occurred in bouts. The rate of initiating bouts increased as a function of reinforcer rate but was either unaffected or was decreased by adding the four-response requirement. Within-bout response rate was insensitive to reinforcer rate and only inconsistently affected by the four-response requirement. For both kinds of schedule, the ratio of bout time to between-bout pause time was approximately a power function of reinforcer rate, with exponents above and below 1.0.     

Geometric representation of association between categories

Categories can be counted, rated, or ranked, but they cannot be measured. Likewise, persons or individuals can be counted, rated, or ranked, but they cannot be measured either. Nevertheless, psychology has realized early on that it can take an indirect road to measurement: What can be measured is the strength of association between categories in samples or populations, and what can be quantitatively compared are counts, ratings, or rankings made under different circumstances, or originating from different persons. The strong demand for quantitative analysis of categorical data has thus created a variety of statistical methods, with substantial contributions from psychometrics and sociometrics. What is the common basis of these methods dealing with categories? The basic element they share is that the sample space has a special geometry, in which categories (or persons) are point masses forming a simplex, while distributions of counts or profiles of ratings are centers of gravity, which are also point masses. Rankings form a discrete subset in the interior of the simplex, known as the permutation polytope, and paired comparisons form another subset on the edges of the simplex. Distances between point masses form the basic tool of analysis. The paper gives some history of major concepts, which naturally leads to a new concept: the shadow point. It is then shown how loglinear models, Luce and Rasch models, unfolding models, correspondence analysis and homogeneity analysis, forced classification and classification trees, as well as other models and methods, fit into this particular geometrical framework.     

Should we rely on the Kenward–Roger approximation when using linear mixed models if the groups have different distributions?

The study explores the robustness to violations of normality and sphericity of linear mixed models when they are used with the Kenward–Roger procedure (KR) in split‐plot designs in which the groups have different distributions and sample sizes are small. The focus is on examining the effect of skewness and kurtosis. To this end, a Monte Carlo simulation study was carried out, involving a split‐plot design with three levels of the between‐subjects grouping factor and four levels of the within‐subjects factor. The results show that: (1) the violation of the sphericity assumption did not affect KR robustness when the assumption of normality was not fulfilled; (2) the robustness of the KR procedure decreased as skewness in the distributions increased, there being no strong effect of kurtosis; and (3) the type of pairing between kurtosis and group size was shown to be a relevant variable to consider when using this procedure, especially when pairing is positive (i.e., when the largest group is associated with the largest value of the kurtosis coefficient and the smallest group with its smallest value). The KR procedure can be a good option for analysing repeated‐measures data when the groups have different distributions, provided the total sample sizes are 45 or larger and the data are not highly or extremely skewed.