Yarkoni argues that researchers making broad inferences often use impoverished statistical models that fail to include important sources of variation as random effects. We argue, however, that for many common study designs, random effects are inappropriate and insufficient to draw general inferences, as the source of variation is not random, but systematic.

Cross-classified random effects models have been developed for appropriately analyzing data with a cross-classified structure. Despite its flexibility and the prevalence of cross-classified data in social and behavioral research, CCREMs have been under-utilized in applied research. In this article, we present CCREMs as a general and flexible modeling framework, and present a wide range of existing models designed for different purposes as special instances of CCREMs. We also introduce several less well-known applications of CCREMs. The flexibility of CCREMs (...) allows these models to be easily extended to address substantive questions. We use the free R package PLmixed to illustrate the estimation of these models, and show how the general language of the CCREM framework can be translated into specific modeling contexts. (shrink)

This study examined the influence of the executive board of directors’ gender diversity on the financial performance of listed companies on the Bucharest Stock Exchange, for the period 2011 to 2019. The analysis of the composition and different characteristics of the board and the executive directors proved to be effective tools for corporate governance in countries with an emerging capital market. Therefore, a disclosure index on directors’ characteristics was used to moderate the interaction between gender diversity and financial performance, based (...) on the theoretical framework provided by upper echelon theory. The study contributes to the enrichment of the literature both by using the composite indicator built by applying the multiway PCA method on panel data to express financial performance and by designing the ten EGLS panel models involving five financial indicators and two proxies for gender diversity. The results showed that there is a positive impact of the proportion of women on the executive board of directors on financial performance, measured through the composite index, ROA, ROE, and SOL. A statistically significant impact of gender diversity on financial performance was found only for SOL, in the case of the Blau index. Also, using the random-effects model to perform the panel data analysis, the results showed that a higher executive board size can be associated with better financial performance measured through the composite index, ROA, ROE, and EPS. Practical implications are significant for the board of executives’ composition, the complexity of the relationship with the board, and reshaping governance practices. (shrink)

We show that if a real x2ω is strongly Hausdorff -random, where h is a dimension function corresponding to a convex order, then it is also random for a continuous probability measure μ such that the μ-measure of the basic open cylinders shrinks according to h. The proof uses a new method to construct measures, based on effective continuous transformations and a basis theorem for -classes applied to closed sets of probability measures. We use the main result to (...) derive a collapse of randomness notions for Hausdorff measures, and to provide a characterization of effective Hausdorff dimension similar to Frostman’s Theorem. (shrink)

Many psychological studies have shown that human‐generated sequences are hardly ever random in the strict mathematical sense. However, what remains an open question is the degree to which this (in)ability varies between people and is affected by contextual factors. Herein, we investigated this problem. In two studies, we used a modern, robust measure of randomness based on algorithmic information theory to assess human‐generated series. In Study 1 (), in a factorial design with task description as a between‐subjects variable, we (...) tested the effects of context and mental fatigue on human‐generated randomness. In Study 2 (), in online research, in experimental design, we further investigated the effect of mental fatigue on the randomness of human‐generated series and the relationship between the need for cognition (NFC) and the ability to produce random‐like series. Results of Study 1 show that the activation of the ability to produce random‐like series depends on the relevance of the contextual cues (), whether they activate known representations of a random series generator and consequently help to avoid the production of trivial sequences. Our findings from both studies on the effect of mental fatigue (Study 1 – ; Study 2 – ) and cognitive motivation () demonstrate that regardless of the context or task's novelty people quickly lose interest in the random series generation. Therefore, their performance decreases over time. However, people high in the NFC can maintain the cognitive motivation for a longer period and consequently on average generate more random series. In general, our results suggest that when contextual cues and intrinsic constraints are in optimal interaction people can temporarily escape the structured and trivial patterns and produce more random‐like sequences. (shrink)

We study randomness beyond${\rm{\Pi }}_1^1$-randomness and its Martin-Löf type variant, which was introduced in [16] and further studied in [3]. Here we focus on a class strictly between${\rm{\Pi }}_1^1$and${\rm{\Sigma }}_2^1$that is given by the infinite time Turing machines introduced by Hamkins and Kidder. The main results show that the randomness notions associated with this class have several desirable properties, which resemble those of classical random notions such as Martin-Löf randomness and randomness notions defined via effective descriptive set theory such (...) as${\rm{\Pi }}_1^1$-randomness. For instance, mutual randoms do not share information and a version of van Lambalgen’s theorem holds.Towards these results, we prove the following analogue to a theorem of Sacks. If a real is infinite time Turing computable relative to all reals in some given set of reals with positive Lebesgue measure, then it is already infinite time Turing computable. As a technical tool towards this result, we prove facts of independent interest about random forcing over increasing unions of admissible sets, which allow efficient proofs of some classical results about hyperarithmetic sets. (shrink)

This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an n such (...) that n,2n,…,kn shifts of the point all end up in P. We consider multiple recurrence into closed sets that possess various degrees of effectiveness: clopen, Π10 with computable measure, and Π10. The notions of Kurtz, Schnorr, and Martin-Löf randomness, respectively, turn out to be sufficient. We obtain similar results for multiple recurrence with respect to the k commuting shift operators on {0,1}Nk. (shrink)

In this paper, we study the power and limitations of computing effectively generic sequences using effectively random oracles. Previously, it was known that every 2-random sequence computes a 1-generic sequence and every 2-random sequence forms a minimal pair in the Turing degrees with every 2-generic sequence. We strengthen these results by showing that every Demuth random sequence computes a 1-generic sequence and that every Demuth random sequence forms a minimal pair with every pb-generic sequence. Moreover, (...) we prove that for every comeager${\cal G} \subseteq {2^\omega }$, there is some weakly 2-random sequenceXthat computes some$Y \in {\cal G}$, a result that allows us to provide a fairly complete classification as to how various notions of effective randomness interact in the Turing degrees with various notions of effective genericity. (shrink)

We present a comparatively simple way to construct Martin-Löf random and rec-random sets with certain additional properties, which works by diagonalizing against appropriate martingales. Reviewing the result of Gács and Kučera, for any given set X we construct a Martin-Löf random set from which X can be decoded effectively. By a variant of the basic construction we obtain a rec-random set that is weak truth-table autoreducible and we observe that there are Martin-Löf random sets that (...) are computably enumerable self-reducible. The two latter results complement the known facts that no rec-random set is truth-table autoreducible and that no Martin-Löf random set is Turing-autoreducible [8, 24]. (shrink)

We study inversions of the jump operator on ${\mathrm{\Pi }}_{1}^{0}$ classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random. Both of the classes coincide with the degrees above 0′ (...) which are not 0′-dominated. A further application is the complete solution of [24, Problem 3.6.9]: one direction of van Lambalgen's theorem holds for weak 2-randomness, while the other fails. Finally we discuss various techniques for coding information into incomplete randoms. Using these techniques we give a negative answer to [24, Problem 8.2.14]: not all weakly 2-random sets are array computable. In fact, given any oracle X, there is a weakly 2-random which is not array computable relative to X. This contrasts with the fact that all 2-random sets are array computable. (shrink)

We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

The essential role of creativity has been highlighted in several human knowledge areas. Regarding the neural underpinnings of creativity, there is evidence about the role of left dorsolateral prefrontal cortex (DLPFC) and left inferior frontal gyrus (IFG) on divergent thinking (DT) and convergent thinking (CT). Transcranial stimulation studies suggest that the left DLPFC is associated with both DT and CT, whereas left IFG is more related to DT. However, none of the previous studies have targeted both hubs simultaneously and compared (...) transcranial direct current stimulation (tDCS) and random noise stimulation (tRNS). Additionally, given the relationship between cognitive flexibility and creativity, we included it in order to check if the improvement in creativity may be mediated by cognitive flexibility. In this double-blind, between-subjects study, 66 healthy participants were randomly assigned to one of three groups (N = 22) that received a transcranial direct current stimulation (tDCS), transcranial random noise stimulation (tRNS), or sham for 20 min. The tDCS group received 1.5 mA with the anode over the left DLPFC and cathode over the left IFG. Locations in tRNS group were the same and they received 1.5 mA of high frequency tRNS (100–500 Hz). Divergent thinking was assessed before (baseline) and during stimulation with unusual uses (UU) and picture completion (PC) subtests from Torrance Creative thinking Test, whereas convergent thinking was evaluated with the remote association test (RAT). Stroop test was included to assess cognitive flexibility. ANCOVA results of performance under stimulation (controlling for baseline performance) showed that there were significant differences in PC (F = 3.35, p = 0.042, np2 = 0.10) but not in UU (F = 0.61, p = 0.546) and RAT (F = 2.65, p = 0.079) scores. Post-hoc analyses showed that tRNS group had significantly higher scores compared to sham (p = 0.004) in PC. More specifically, tRNS showed higher performance in fluency (p = 0.012) and originality (p = 0.021) dimensions of PC compared to sham. Regarding cognitive flexibility, we did not find any significant effect of any of the stimulation groups (F = 0.34, p = 0.711). Therefore, no further mediation analyses were performed. Finally, the group that received tDCS reported more adverse effects than sham group (F = 3.46, p = 0.035). Altogether, these results suggest that tRNS may have some advantages over tDCS in DT. (shrink)

A widely accepted tenet of evolutionary biology is that spontaneous mutations occur randomly with regard to their fitness effect. However, since the mutation rate varies along a genome and this variation can be subject to selection, organisms might evolve lower mutation rates at loci where mutations are most deleterious or increased rates where mutations are most needed. In fact, mechanisms of targeted hypermutation are known in organisms ranging from bacteria to humans. Here we review the main forces driving the evolution (...) of local mutation rates and identify the main limiting factors. Both targeted hyper‐ and hypomutation can evolve, although the former is restricted to loci under very frequent positive selection and the latter is severely limited by genetic drift. Nevertheless, we show how an association of repair with transcription or chromatin‐associated proteins could overcome the drift limit and lead to non‐random hypomutation along the genome in most organisms.Editor's suggested further reading in BioEssays Stress‐induced mutation via DNA breaks in Escherichia coli: A molecular mechanism with implications for evolution and medicine Abstract. (shrink)

We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness (...) notions going back to the work of Kurtz [73], Kautz [61], and Solovay [125]; and other calibrations of randomness based on definitions along the lines of Schnorr [117].These notions have complex interrelationships, and connections to classical notions from computability theory such as relative computability and enumerability. Computability figures in obvious ways in definitions of effective randomness, but there are also applications of notions related to randomness in computability theory. For instance, an exciting by-product of the program we describe is a more-or-less naturalrequirement-freesolution to Post's Problem, much along the lines of the Dekker deficiency set. (shrink)

A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Löf randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a positive answer to which would (...) also have yielded a reasonable randomness notion for left-c.e. semimeasures. Unfortunately, though, we find a negative answer, except for some special cases. (shrink)

The multimedia technology and computer technology supported by the development of modern science and technology provide an important platform for the development of college physical education teaching activities. To better play the role of network auxiliary teaching platform in college sports teaching and improve the effectiveness of college sports teaching, the construction method of multimedia auxiliary teaching effect evaluation model based on the random number forest algorithm is proposed. Through the specification of the random forest algorithm and the (...) optimization of the teaching quality evaluation index, the auxiliary teaching level of the college physical education network is analyzed, and the evaluation of the multimedia auxiliary teaching effect of the physical education courses is completed. The experimental results verify the effectiveness of the evaluation model designed in this article, with a user satisfaction of 72%. Teachers and students can use the evaluation model to improve the teaching quality and teaching efficiency, improve the management work, and promote the scientific, standardization, and specialization of physical education teaching management in colleges and universities. (shrink)

An emergent body of literature examined why some firms apply some environmental initiatives while other firms do not take responsibility for their natural environment? Thus, firm environmental orientation (responsiveness and performance) are linked in the literature to several variables. Unfortunately, the relationship between firm environmental orientation and either available resources or firm size showed mixed results and inconclusive evidence. Therefore, the aim of this paper is to show empirically how available resources and firm size can explain differences in firm environmental (...) responsiveness and environmental performance. Econometric results of environmental responsiveness using the logistic regression model demonstrated that firm size does appear to add something unique in explaining differences in environmental responsiveness while available resource can be safely dropped from the model. However, econometric analysis of environmental performance using the maximum-likelihood random effects model showed strong evidence that available resources and firm size are significant predictors of firm environmental performance. (shrink)

How realistic is it to adopt a quantum random walk model to account for decisions involving two choices? Here, we discuss the neural plausibility and the effect of initial state and boundary thresholds on such a model and contrast it with various features of the classical random walk model of decision making.

Historically, one of the most controversial aspects of Darwinian evolution has been the prominent role that randomness and random change play in it. Most biologists agree that mutations in DNA have random effects on fitness. However, fitness is a highly simplified scalar representation of an enormously complex phenotype. Challenges to Darwinian thinking have focused on such complex phenotypes. Whether mutations affect such complex phenotypes randomly is ill understood. Here I discuss three very different classes of well-studied molecular (...) phenotypes in which mutations cause nonrandom changes, based on our current knowledge. What is more, this nonrandomness facilitates evolutionary adaptation. Thus, living beings may translate DNA change into nonrandom phenotypic change that facilitates Darwinian evolution. (shrink)

We formalise the notion of those infinite binary sequences z that admit a single program P which expresses the entire algorithmical structure of z. Such a program P minimizes the information which must be used in a relative computation for z. We propose two concepts with different strength for this notion, the learnable and the super-learnable sequences. We establish three different equivalent characterizations of learnable (super-learnable, resp.) sequences. In particular, we prove that a sequences z is learnable (super-learnable, resp.) if (...) and only if there is a computable probability measure p such that p is Schnorr (Martin-Lof, resp.) p-random. There is a recursively enumerable sequence which is not learnable. The learnable sequences are invariant with respect to all total and effective transformations of infinite binary sequences. (shrink)

Examinations form part of the assessment processes that constitute the basis for benchmarking individual educational progress, and must consequently fulfill credibility, reliability, and transparency standards in order to promote learning outcomes and ensure academic integrity. A randomly selected question examination is considered to be an effective solution to mitigate sharing of questions between students by addressing replicated inter-examination questions that compromise examination integrity and sequential intra- examination questions that compromise examination comprehensivity. In this study, a Monte Carlo approach was used (...) to design six examination schemes for the purpose of generating and evaluating 600 RSQEs in order to investigate the effects of RSQE design on replicated inter-examination and sequential and intra-examination questions. Results revealed that the number of randomly selected questions from the pool and the number of sub-pools inversely affected the replication and sequencing of the examination questions. Thus, by designing the RSQE in many sub-pools, in equivalence to the number of examination questions and selecting only one question from each sub-pool, and updating the sub-pools after each examination, the passing of information can be prevented, ensuring the integrity of the examinations. (shrink)