Determination of the Regression Coefficients and Their Associated Standard Errors in Hierarchical Regression Analysis

Hierarchical regression analysis is potentially a very useful statistical technique for establishing the significance of sets of predictor variables. However, when a hierarchical analysis which is based on theory is performed, some estimation procedures for the regression coefficients and their associated standard errors are potentially inappropriate. Specifically, the hierarchical regression equations, the incremental or hierarchical tests, and the parameter estimation of this procedure may not correspond. This problem is investigated by the development of four approaches (simultaneous, stagewise, orthogonal, and hierarchical) of estimation to the analysis. For each method, regression, coefficient estimators and their standard errors are determined. By comparison of these approaches, the use of orthogonalized sets of predictor variates or a modification to a series of simultaneous analyses are recommended as the most sensible technique for a theory driven hierarchical analysis.     

The integration of visual and functional classifications in concept formation

Summary Simple motor responses of different similarity were assigned to geometric figures of different similarity. Subsequently, subjects had to learn hierarchical classifications of visually similar or dissimilar figures which were associated with either similar or dissimilar responses. In this way, the visual and the functional similarity of the conceptually united figures were orthogonally varied. It was found that visually similar figures are conceptually classified fastest regardless of their functional similarity. In contrast, functional similarity has a considerable impact on the hierarchical classification of visually dissimilar figures. Functionally similar figures are conceptually faster classified than dissimilar ones. From the results we conclude that concepts are autonomously formed as mediating representations in stimulus-response coordinations. The hierarchical organization of concepts is thereby based on the sequential organization of both the visual input and the behavioral output. Further consequences of this approach are discussed.Portions of this research were presented at the International Symposium on Structure and Function of Human Memory, in Memoriam Hermann Ebbinghaus, Berlin, July 1985     

认知控制的层级性：来自任务切换的脑电证据*

认知控制的主要研究范式之一是任务切换。以往研究发现切换代价受到认知控制层级性的调节, 但鲜有研究探索这一调节过程的动态神经机制。本研究通过嵌套的线索-任务切换范式考察不同层级任务切换代价的差异及其神经机制。在实验中, 要求被试完成高低两种层级任务, 低层级任务要求被试判断数字大小(或奇偶); 高层级任务则须先加工数字的某一语义特征(如当前数字是否是偶数), 然后进行大小判断。行为结果表明, 高层级任务切换代价显著大于低层级任务切换代价。线索锁时的脑电结果表明, 层级效应最早出现于P2成分, 切换效应(切换与重复之差)在CNV成分上受到任务层级的调控, 反映了在任务目标重构阶段给予高层级任务更多的选择性注意以及更高的主动性控制。目标锁时的脑电结果表明, 在N2及慢波(SP)成分上, 高层级任务切换与重复的波幅差异相比低层级任务显著更大, 反映了在抑制旧任务集与重构新反应集的过程中增强的反应性控制。这些结果为任务设置重构论和认知控制的层级性提供了新的证据。     

Auditory local bias and reduced global interference in autism

Processing local elements of hierarchical patterns at a superior level and independently from an intact global influence is a well-established characteristic of autistic visual perception. However, whether this confirmed finding has an equivalent in the auditory modality is still unknown. To fill this gap, 18 autistics and 18 typical participants completed a melodic decision task where global and local level information can be congruent or incongruent. While focusing either on the global (melody) or local level (group of notes) of hierarchical auditory stimuli, participants have to decide whether the focused level is rising or falling. Autistics showed intact global processing, a superior performance when processing local elements and a reduced global-to-local interference compared to typical participants. These results are the first to demonstrate that autistic processing of auditory hierarchical stimuli closely parallels processing of visual hierarchical stimuli. When analyzing complex auditory information, autistic participants present a local bias and a more autonomous local processing, but not to the detriment of global processing.     

Hierarchically organized behavior and its neural foundations: a reinforcement learning perspective

Research on human and animal behavior has long emphasized its hierarchical structure—the divisibility of ongoing behavior into discrete tasks, which are comprised of subtask sequences, which in turn are built of simple actions. The hierarchical structure of behavior has also been of enduring interest within neuroscience, where it has been widely considered to reflect prefrontal cortical functions. In this paper, we reexamine behavioral hierarchy and its neural substrates from the point of view of recent developments in computational reinforcement learning. Specifically, we consider a set of approaches known collectively as hierarchical reinforcement learning, which extend the reinforcement learning paradigm by allowing the learning agent to aggregate actions into reusable subroutines or skills. A close look at the components of hierarchical reinforcement learning suggests how they might map onto neural structures, in particular regions within the dorsolateral and orbital prefrontal cortex. It also suggests specific ways in which hierarchical reinforcement learning might provide a complement to existing psychological models of hierarchically structured behavior. A particularly important question that hierarchical reinforcement learning brings to the fore is that of how learning identifies new action routines that are likely to provide useful building blocks in solving a wide range of future problems. Here and at many other points, hierarchical reinforcement learning offers an appealing framework for investigating the computational and neural underpinnings of hierarchically structured behavior.     

Daddy,Why are People so Complex?

The implications of Warren McCulloch's 1945 concept of heterarchy are analyzed in terms of human value and motivational systems. The results demonstrate the near-impossibility of predicting behavior on the basis of any hierarchical scheme, or even which among a set of hierarchical schemes will be selected as the basis of a behavioral choice. Thus, for example, people regularly say one thing and do another.     

Confidence interval-based sample size determination formulas and some mathematical properties for hierarchical data

The use of hierarchical data (also called multilevel data or clustered data) is common in behavioural and psychological research when data of lower-level units (e.g., students, clients, repeated measures) are nested within clusters or higher-level units (e.g., classes, hospitals, individuals). Over the past 25 years we have seen great advances in methods for computing the sample sizes needed to obtain the desired statistical properties for such data in experimental evaluations. The present research provides closed-form and iterative formulas for sample size determination that can be used to ensure the desired width of confidence intervals for hierarchical data. Formulas are provided for a four-level hierarchical linear model that assumes slope variances and inclusion of covariates under both balanced and unbalanced designs. In addition, we address several mathematical properties relating to sample size determination for hierarchical data via the standard errors of experimental effect estimates. These include the relative impact of several indices (e.g., random intercept or slope variance at each level) on standard errors, asymptotic standard errors, minimum required values at the highest level, and generalized expressions of standard errors for designs with any-level randomization under any number of levels. In particular, information on the minimum required values will help researchers to minimize the risk of conducting experiments that are statistically unlikely to show the presence of an experimental effect.     

Global/local processing of hierarchical visual stimuli in a conflict–choice task by capuchin monkeys (<Emphasis Type="Italic">Sapajus</Emphasis> spp.)

In the last two decades, comparative research has addressed the issue of how the global and local levels of structure of visual stimuli are processed by different species, using Navon-type hierarchical figures, i.e. smaller local elements that form larger global configurations. Determining whether or not the variety of procedures adopted to test different species with hierarchical figures are equivalent is of crucial importance to ensure comparability of results. Among non-human species, global/local processing has been extensively studied in tufted capuchin monkeys using matching-to-sample tasks with hierarchical patterns. Local dominance has emerged consistently in these New World primates. In the present study, we assessed capuchins’ processing of hierarchical stimuli with a method frequently adopted in studies of global/local processing in non-primate species: the conflict–choice task. Different from the matching-to-sample procedure, this task involved processing local and global information retained in long-term memory. Capuchins were trained to discriminate between consistent hierarchical stimuli (similar global and local shape) and then tested with inconsistent hierarchical stimuli (different global and local shapes). We found that capuchins preferred the hierarchical stimuli featuring the correct local elements rather than those with the correct global configuration. This finding confirms that capuchins’ local dominance, typically observed using matching-to-sample procedures, is also expressed as a local preference in the conflict–choice task. Our study adds to the growing body of comparative studies on visual grouping functions by demonstrating that the methods most frequently used in the literature on global/local processing produce analogous results irrespective of extent of the involvement of memory processes.     

权力层级与团队绩效关系：权力与地位的一致与背离

本研究致力于探讨在权力与地位不一致的背景下, 权力层级与团队绩效研究的分歧。本研究提出权力层级与团队绩效的关系取决于团队的层级一致性——权力与地位的匹配度。具体地, 当层级一致(权力与地位匹配)时, 权力层级促进团队绩效; 当层级不一致(权力与地位不匹配)时, 权力层级抑制团队绩效。本研究结合问卷、实验和二手数据方法来验证假设, 研究1通过对46个大学生创业实践团队的两阶段问卷调查, 发现层级一致性对权力层级与团队绩效的关系具有调节作用。此后, 研究2通过一项涉及64个团队的实验来揭示因果关系, 发现权力争夺在权力层级和层级一致性的交互与团队绩效的关系中起中介作用。最后研究3通过203个观测值的互联网公司二手数据重复验证了层级一致性的调节作用, 并提升了本研究的生态效度。本研究为权力层级的研究做出了一定的贡献, 并为团队管理提供了启示。     

Subject-Verb Agreement in Children and Adults: Serial or Hierarchical Processing?

Two processes, serial and hierarchical, are generally opposed to account for grammatical encoding in language production. In a developmental perspective, the question addressed here is whether the subject-verb agreement during writing is computed serially, once the words are linearly ordered in the sentence, or hierarchically, as soon as the number features are determined in a hierarchical frame. Adults and children from 3rd to 5th grades were requested to listen to sentences with built-in prepositional phrases or relative clauses and to transcribe them as quickly as possible. A serial hypothesis assumes that subject-verb agreement errors should be equally frequent with both preambles because each has the same length separating the subject head noun and the main verb. Conversely, according to a hierarchical view, errors should be more frequent with a prepositional phrase because the syntactic distance between the subject and the verb is greater than with a relative clause. The results revealed a main effect of the preamble manipulated in 5th graders and adults, but not in 3rd graders. These data were in favor of a hierarchical processing in older writers and a serial one in younger children. However, in 3rd grade, we assumed that the potential serial account was a result of the resource constraint on writing more than of a real serial processing of the agreement.     

Post-traumatic stress disorder symptoms in United Nations peacekeepers: an examination of factor structure in peacekeepers with and without chronic pain

Recent factor analytic investigations of post-traumatic stress disorder in military veterans suggest that symptoms are best described by either a hierarchical 2-factor model or a 4-factor inter-correlated model. Other recent evidence suggests that post-traumatic stress disorder and chronic pain are intricately related; however, the nature of this relationship is not well understood. Factor analysis provides one method for clarifying this relationship. In study 1, we compared competing models of post-traumatic stress disorder symptom structure in a sample of 400 male United Nations peacekeepers using confirmatory factor analysis. Results indicated that both the hierarchical 2-factor and the 4-factor inter-correlated models provided good fit to the data. In study 2, the reliability of these models was assessed in 427 male United Nations peacekeepers with chronic back pain and 341 without. Group comparisons of the confirmatory factor analysis results revealed that the structure of the hierarchical 2-factor and 4-factor inter-correlated models both provided good fit to the data in both the chronic back pain and the group without. However, the structure of the models for the group with chronic back pain group differed in significant ways from that of the group without chronic back pain. Post-traumatic stress disorder symptoms in military veterans can be adequately conceptualized using either a hierarchical 2-factor or 4-factor inter-correlated model. Chronic pain has a minimal influence on overall factor structure. The hierarchical 2-factor model, while parsimonious, does not provide the degree of symptom detail provided by the 4-factor inter-correlated model. Implications for conceptualization of post-traumatic stress disorder symptoms for patients with chronic back pain and significant post-traumatic stress disorder symptomatology are discussed.     

Post-Traumatic Stress Disorder Symptoms in United Nations Peacekeepers: An Examination of Factor Structure in Peacekeepers with and without Chronic Pain

Recent factor analytic investigations of post-traumatic stress disorder in military veterans suggest that symptoms are best described by either a hierarchical 2-factor model or a 4-factor inter-correlated model. Other recent evidence suggests that post-traumatic stress disorder and chronic pain are intricately related; however, the nature of this relationship is not well understood. Factor analysis provides one method for clarifying this relationship. In study 1, we compared competing models of post-traumatic stress disorder symptom structure in a sample of 400 male United Nations peacekeepers using confirmatory factor analysis. Results indicated that both the hierarchical 2-factor and the 4-factor inter-correlated models provided good fit to the data. In study 2, the reliability of these models was assessed in 427 male United Nations peacekeepers with chronic back pain and 341 without. Group comparisons of the confirmatory factor analysis results revealed that the structure of the hierarchical 2-factor and 4-factor inter-correlated models both provided good fit to the data in both the chronic back pain and the group without. However, the structure of the models for the group with chronic back pain group differed in significant ways from that of the group without chronic back pain. Post-traumatic stress disorder symptoms in military veterans can be adequately conceptualized using either a hierarchical 2-factor or 4-factor inter-correlated model. Chronic pain has a minimal influence on overall factor structure. The hierarchical 2-factor model, while parsimonious, does not provide the degree of symptom detail provided by the 4-factor inter-correlated model. Implications for conceptualization of post-traumatic stress disorder symptoms for patients with chronic back pain and significant post-traumatic stress disorder symptomatology are discussed.     

Optimal Hierarchical Learning Path Design With Reinforcement Learning

E-learning systems are capable of providing more adaptive and efficient learning experiences for learners than traditional classroom settings. A key component of such systems is the learning policy. The learning policy is an algorithm that designs the learning paths or rather it selects learning materials for learners based on information such as the learners’ current progresses and skills, learning material contents. In this article, the authors address the problem of finding the optimal learning policy. To this end, a model for learners’ hierarchical skills in the E-learning system is first developed. Based on the hierarchical skill model and the classical cognitive diagnosis model, a framework to model various mastery levels related to hierarchical skills is further developed. The optimal learning path in consideration of the hierarchical structure of skills is found by applying a model-free reinforcement learning method, which does not require any assumption about learners’ learning transition processes. The effectiveness of the proposed framework is demonstrated via simulation studies.     

Syntactic structure and artificial grammar learning: the learnability of embedded hierarchical structures

Embedded hierarchical structures, such as "the rat the cat ate was brown", constitute a core generative property of a natural language theory. Several recent studies have reported learning of hierarchical embeddings in artificial grammar learning (AGL) tasks, and described the functional specificity of Broca's area for processing such structures. In two experiments, we investigated whether alternative strategies can explain the learning success in these studies. We trained participants on hierarchical sequences, and found no evidence for the learning of hierarchical embeddings in test situations identical to those from other studies in the literature. Instead, participants appeared to solve the task by exploiting surface distinctions between legal and illegal sequences, and applying strategies such as counting or repetition detection. We suggest alternative interpretations for the observed activation of Broca's area, in terms of the application of calculation rules or of a differential role of working memory. We claim that the learnability of hierarchical embeddings in AGL tasks remains to be demonstrated.     

Sequential item selection: Optimal and heuristic policies

This paper considers testing in which the goal is to minimize the number of test items required to establish a learner's state of ability. Focus is on optimal or near optimal selection over a well-defined universe of items or stimuli. Selection policies are determined for the case in which the items have hierarchical or partial hierarchical relationships. Derivation of an optimal policy rests upon techniques from dynamic programming. For situations in which an optimal policy may be too costly to compute, two heuristic approximations are offered. One heuristic counts the hypothetical estimates of ability that remain tenable following a response to each item and chooses the item that minimizes the expectation of that number. The other selects the item that maximizes the statistic of information.     

What could be My Next Job? Using Flat Information Structures to Generate Creative Future Career Ideas

In a dynamic labor market, it is important to help people combine information and generate creative solutions to cope with complex career challenges. In the present research, we apply the theory of information structure to creative career idea generation and hypothesize that flat information structures—that is, structures in which the information is disorganized—are more conducive to creativity than hierarchical information structures—that is, structures in which information is organized in higher‐order categories. In two experimental studies, participants had to combine career information related to self and work preferences that was presented either in flat or hierarchical structures. We found that flat information structures, compared with hierarchical information structures, led to future career ideas that were more creative on average. Our results suggest that cognitive flexibility explains the effect of information structure on the creativity of career ideas. Theoretical implications and suggestions for career management practices are discussed.     

A Monte Carlo study of the effects of correlated method variance in moderated multiple regression analysis

It has been suggested that hierarchical regression analysis provides an unambiguous conclusion with regard to the existence of moderator effects (Arnold & Evans, 1979). This paper examines the impact of correlated error among the dependent and independent variables in order to explore whether or not artificial interaction terms can be generated. A Monte Carlo study was performed to investigate the effects of correlated error on noninteraction and interaction models. The results are clear-cut. Artifactual interaction cannot be created; true interactions can be attentuated. Some practical suggestions are provided for drawing inferences from hierarchical regression analysis.     

Hierarchical organisation in perception of orientation

According to Rock [1990, in The Legacy of Solomon Asch (Hillsdale, NJ: Lawrence Erlbaum Associates)], hierarchical organisation of perception describes cases in which the orientation of an object is affected by the immediately surrounding elements in the visual field. Various experiments were performed to study the hierarchical organisation of orientation perception. In most of them the rod-and-frame-illusion (RFI: change of the apparent vertical measured on a central rod surrounded by a tilted frame) was measured in the presence/absence of a second inner frame. The first three experiments showed that, when the inner frame is vertical, the direction and size of the illusion are consistent with expectancies based on the hierarchical organisation hypothesis. An analysis of published and unpublished data collected on a large number of subjects showed that orientational hierarchical effects are independent from the absolute size of the RFI. In experiments 4 to 7 we examined the perceptual conditions of the inner stimulus (enclosure, orientation, and presence of luminance borders) critical for obtaining a hierarchical organisation effect. Although an inner vertical square was effective in reducing the illusion (experiment 3), an inner circle enclosing the rod was ineffective (experiment 4). This indicates that definite orientation is necessary to modulate the illusion. However, orientational information provided by a vertical or horizontal rectangle presented near the rod, but not enclosing it, did not modulate the RFI (experiment 5). This suggests that the presence of a figure with oriented contours enclosing the rod is critical. In experiments 6 and 7 we studied whether the presence of luminance borders is important or whether the inner upright square might be effective also if made of subjective contours. When the subjective contour figure was salient and the observers perceived it clearly, its effectiveness in modulating the RFI was comparable to that observed with luminance borders.     

The hierarchy of task decision and response selection: A task-switching event related potentials study

According to “hierarchical” multi-step theories, response selection is preceded by a decision regarding which task rule should be executed. Other theories assume a “flat” single-step architecture in which task information and stimulus information are simultaneously considered. Using task switching, the authors independently manipulated two kinds of conflict: task conflict (with information that potentially triggers the relevant or the competing task rule/identity) and response conflict (with information that potentially triggers the relevant or the competing response code/motor response). Event related potentials indicated that the task conflict effect began before the response conflict effect and carried on in parallel with it. These results are more in line with the hierarchical view.     

Memory retrieval tasks determine the serial position curves of linear orders with categorical structures

I examined 2 different views on organization of linear order information in memory: the linear schema view and the hierarchical structure view. The linear schema view holds that there is a strong tendency in memory to organize an array of transitively related elements into a unidimensional order. The hierarchical structure view maintains that the transitively related elements are organized in memory in a hierarchy of items. I proposed an input structure and retrieval compatibility hypothesis as a coherent explanation for the contradictory views on the memory organization of serial elements. I argue that the organization of linear order information in memory is determined by the nature of the memory retrieval task used. For example, a comparative judgment task is more compatible with a unidimensional structure, whereas a sequential recall or serial position identification task is more compatible with a hierarchical organization. The input structure and retrieval compatibility concept can also explain why dichotomous categories imposed on a linear order play very little role in comparative judgments.