Multilevel Dynamic Generalized Structured Component Analysis for Brain Connectivity Analysis in Functional Neuroimaging Data

We extend dynamic generalized structured component analysis (GSCA) to enhance its data-analytic capability in structural equation modeling of multi-subject time series data. Time series data of multiple subjects are typically hierarchically structured, where time points are nested within subjects who are in turn nested within a group. The proposed approach, named multilevel dynamic GSCA, accommodates the nested structure in time series data. Explicitly taking the nested structure into account, the proposed method allows investigating subject-wise variability of the loadings and path coefficients by looking at the variance estimates of the corresponding random effects, as well as fixed loadings between observed and latent variables and fixed path coefficients between latent variables. We demonstrate the effectiveness of the proposed approach by applying the method to the multi-subject functional neuroimaging data for brain connectivity analysis, where time series data-level measurements are nested within subjects.     

A practical guide to understanding reliability in studies of within-person variability

This article concerns how to estimate reliability (defined as the internal consistency of responses to a scale) in designs that are commonly used in studies of within-person variability. I present relevant issues, describe common errors, make recommendations for best practice, and discuss unresolved issues and future directions. I describe how to estimate the reliability of scales administered in studies in which observations are nested within persons, such as daily diary and “beeper” studies and studies of social interaction. Multilevel modeling analyses that include a measurement level can estimate the occasionlevel (e.g., days or beeps or interactions) reliability of scales. In such models, items on a scale are nested within occasions of measurement and occasions of measurement are nested within persons.     

ANALYZING UTTERANCES AS THE OBSERVATIONAL UNIT

If utterances are the observational unit of analysis and there are no sequential patterns to the interaction, two alternative statistical models may be applied. A hierarchical design in which utterances are nested within subjects and subjects are nested within treatment condition is considered. One method of analysis pools utterances within treatment condition; the other method collapses across utterances to obtain subject means. Inappropriate application of the pooling model instead of the subject means model can lead to Type I errors, decreased generalizability, and inflated variance estimates that attenuate univariate and multivariate correlations. The effect of utterance reliability on the apparent unidimensionality and parallelism of multiple indicators is also discussed.     

Computing Power of Tests of the Variance of Treatment Effects in Designs With Two Levels of Nesting

Experiments that involve nested structures may assign treatment conditions either to entire groups (such as classrooms or schools) or individuals within groups (such as students). Although typically the interest in field experiments is in determining the significance of the overall treatment effect, it is equally important to examine the inconsistency of the treatment effect in different groups. This study provides methods for computing power of tests for the variability of treatment effects across level-2 and level-3 units in three-level designs, where, for example, students are nested within classrooms and classrooms are nested within schools and random assignment takes place at the first or the second level. The power computations take into account nesting effects at the second (e.g., classroom) and at the third (e.g., school) level as well as sample size effects (e.g., number of level-1 and level-2 units). The methods can also be applied to quasi-experimental studies that examine the significance of the variation of group differences in an outcome or associations between predictors and outcomes across level-2 and level-3 units.     

In the shadow of the boss's boss: effects of supervisors' upward exchange relationships on employees

Dyadic relationships in an organizational hierarchy are often nested within one another. For instance, the relationship between a supervisor and an employee is nested within the relationship between that supervisor and his or her boss. In that context, the authors propose that the supervisor's relationship with his or her boss (leader-leader exchange) moderates the effects of the supervisor's relationship with the employee (leader-member exchange). Specifically, the authors argue that leader-member exchange has a stronger positive effect on employees' attitudes toward the organization and its customers when leader-leader exchange is higher. Cross-level analysis of data from 581 frontline nurses and 29 supervisors in a midwestern hospital supports this contention. Implications for research and practice are discussed.     

Nested prospectivity in perception: perceived maximum reaching height reflects anticipated changes in reaching ability

Perception of possibilities for behavior is a necessarily prospective (i.e., forward-looking) act. Such prospectivity is highlighted by the fact that, in general, behaviors are nested within behaviors over a number of spatial and temporal scales. Participants reported their maximum vertical reaching height when they expected to walk across the room and (1) reach for an object while standing on the floor, (2) step up on a step stool and then reach for the object, and (3) pick up a plastic rod and use it to reach for the object. The results show that perception of maximum reaching height was action scaled both when participants expected to perform a nested behavior that would change their action capabilities and when they expected to perform a nested behavior that would not do so. Moreover, the results suggest that nested behaviors that change reaching ability in functionally equivalent ways may bring about functionally equivalent changes in perception of maximum reaching height.     

Nested ideation and the problem of reality: dreams and works of art in works of art

This paper continues a line of investigation begun in a previous paper on nested dreams and works of art in dreams (Balter 2005). Part I of the present paper seeks to establish that works of art with nested dreams and works of art within them display certain phenomena also observed in comparable dreams: (i) they unsuccessfully deny a painful reality represented in the nested element; (2) they present an antithetical view of that reality (both denying and affirming); and (3) they are consistently associated with the problem of reality (the problem of deciding what is real or true). Part II of this paper seeks to establish the heuristic value of this line of investigation in dreams and art to elucidate the origin of reality testing.     

Recall of grammatical relations within clause-containing sentences

Two major findings were obtained in a study of college students' recall of meaningful grammatical relations within sentences: (1) verb-object relations in object focus relative clauses were recalled less accurately than verb-object relations in subject focus relative clauses, thus supporting the hypothesis that permuted word order in certain relative clauses interferes with adequate encoding of underlying grammatical relations, and (2) subject-verb relations in nested sentences in which a relative clause intervened between subject and verb (nested sentences) were retained in memory as accurately as uninterrupted subject-verb relations (not nested sentences).     

Nested ideation and the problem of reality: dreams and works of art in dreams

This study uses seven well-analyzed dreams to establish three empirical generalizations about dreams and works of art nested in dreams: (1) Those dreams attempt to deny a painful reality in some way depicted in the nested element; (2) they present an antithetical view of that reality (both denying and affirming); and (3) they are consistently associated with the problem of reality (the problem of deciding what is real or true). The explanation of these empirical generalizations is based on a hypothesis derived from Freud's 1911 formulation of the dream within a dream.     

Fictions within fictions

This paper examines the logic of fictions within fictions. I argue that consistently nested consistent fictions must have certain formal characteristics. The most important is that they form a tree structure. Depending on one’s theory of fictional objects, additional constraints may apply regarding the appearance of a fictional object in two or more fictional universes. The background motivation for the paper is to use iterated fiction operators as a tool for making sense of iterated modal operators; I conclude by noting briefly where the results about nested fictions can, and where they cannot, be extended to nested possible worlds.     

TEMPEST in a gallimaufry: applying multilevel systems theory to person-in-context research

Terminological ambiguity and inattention to personal and contextual multilevel systems undermine personality, self, and identity theories. Hierarchical and heterarchical systems theories are used to describe contents and processes existing within and across three interrelated multilevel systems: levels of organization, representation, and integration. Materially nested levels of organization are used to distinguish persons from contexts and personal from social identity. Functionally nested levels of representation are used to distinguish personal identity from the sense of identity and symbolic (belief) from iconic (schema) systems. Levels of integration are hypothesized to unfold separately but interdependently across levels of representation. Multilevel system configurations clarify alternative conceptualizations of traits and contextualized identity. Methodological implications for measurement and analysis (e.g., integrating variable- and pattern-centered methods) are briefly described.     

Mapping the intimate relationship mind: comparisons between three models of attachment representations

This study compared three models of how attachment working models might be cognitively represented. Model 1 posits that attachment representations consist of a single global working model summarizing attachment across specific relationships and domains. Model 2 proposes three independent working models for the relationship domains of family, platonic friendships, and romantic partners. Model 3 postulates that specific relationship models are nested under relationship domain representations that are, in turn, nested under an overarching global working model. Participants completed standard attachment scales for the relationship domains of family, platonic friendships, and romantic partners and also provided attachment ratings for three specific relationships within each domain. As expected, confirmatory factor analyses showed that Model 3 attained the best fit, regardless of analysis strategy, measurement strategy, gender, and relationship status. Implications are discussed.     

Estimation of maximal reliability for multiple‐component instruments in multilevel designs

A procedure for point and interval estimation of maximal reliability of multiple‐component measuring instruments in multi‐level settings is outlined. The approach is applicable to hierarchical designs in which individuals are nested within higher‐order units and exhibit possibly related performance on components of a given homogeneous scale. The method is developed within the framework of multi‐level factor analysis. The proposed procedure is illustrated with an empirical example.     

The Tesseract,the Cube and Truthless Knowledge

Philosophia - Virtually all epistemologists agree that truth is a necessary condition for knowledge. Assuming that our three-dimensional world is nested within a higher-dimensional space, I use...     

On the use of multilevel modeling as an alternative to items analysis in psycholinguistic research

The use of multilevel modeling is presented as an alternative to separate item and subject ANOVAs (F1 x F2) in psycholinguistic research. Multilevel modeling is commonly utilized to model variability arising from the nesting of lower level observations within higher level units (e.g., students within schools, repeated measures within individuals). However, multilevel models can also be used when two random factors are crossed at the same level, rather than nested. The current work illustrates the use of the multilevel model for crossed random effects within the context of a psycholinguistic experimental study, in which both subjects and items are modeled as random effects within the same analysis, thus avoiding some of the problems plaguing current approaches.     

Multilevel factorial experiments for developing behavioral interventions: power, sample size, and resource considerations

Factorial experimental designs have many potential advantages for behavioral scientists. For example, such designs may be useful in building more potent interventions by helping investigators to screen several candidate intervention components simultaneously and to decide which are likely to offer greater benefit before evaluating the intervention as a whole. However, sample size and power considerations may challenge investigators attempting to apply such designs, especially when the population of interest is multilevel (e.g., when students are nested within schools, or when employees are nested within organizations). In this article, we examine the feasibility of factorial experimental designs with multiple factors in a multilevel, clustered setting (i.e., of multilevel, multifactor experiments). We conduct Monte Carlo simulations to demonstrate how design elements-such as the number of clusters, the number of lower-level units, and the intraclass correlation-affect power. Our results suggest that multilevel, multifactor experiments are feasible for factor-screening purposes because of the economical properties of complete and fractional factorial experimental designs. We also discuss resources for sample size planning and power estimation for multilevel factorial experiments. These results are discussed from a resource management perspective, in which the goal is to choose a design that maximizes the scientific benefit using the resources available for an investigation.     

Fractal Characteristics of Response Time Variability

The relations between English spellings and pronunciations have been described as a fractal pattern. Manipulations of word properties are constructed to coincide with the fractal pattern of ambiguity in these relations (sampled as random variables). New word naming and lexical decision experiments replicate previously established effects of relations between word spellings and pronunciations. The structure of these relations establishes a measurement scale, which is nested in a manner that is loosely analogous to the way that centimeters are nested within meters, and so on. The experiments revealed that broader, increasingly stretched-more variable-distributions of pronunciation and response time accompany the introduction of higher resolution measurement scales to the naming and lexical decision measurement process. Moreover, the distribution of lexical decision response times is shown to obey an inverse power-law scaling relation, which implies lexical decision does not conform to a characteristic measurement scale.     

Visual nesting of stimuli affects rhesus monkeys’ (Macaca mulatta) quantity judgments in a bisection task

Nonhuman animals are highly proficient at judging relative quantities presented in a variety of formats, including visual, auditory, and even cross-modal formats. Performance typically is constrained by the ratio between sets, as would be expected under Weber’s law and as is described in the approximate number system (ANS) hypothesis. In most cases, tests are designed to avoid any perceptual confusion for animals regarding the stimulus sets, but despite this, animals show some of the perceptual biases that humans show based on organization of stimuli. Here, we demonstrate an additional perceptual bias that emerges from the illusion of nested sets. When arrays of circles were presented on a computer screen and were to be classified as larger than or smaller than an established central value, rhesus monkeys (Macaca mulatta) underestimated quantities when circles were nested within each other. This matched a previous report with adult humans (Chesney & Gelman, Attention, Perception, & Psychophysics 24:1104–1113, 2012), indicating that macaques, like humans, show the pattern of biased perception predicted by ANS estimation. Although some macaques overcame this perceptual bias, demonstrating that they could come to view nested stimuli as individual elements to be included in the estimates of quantity used for classifying arrays, the majority of the monkeys showed the bias of underestimating nested arrays throughout the experiment.     

The role of team and sport social contexts: Are three-level models needed in studies of sport conduct?

In this work, I examined how variation in sport conduct is allocated across the three different levels (i.e., athlete, team, and sport) in order to consider how the team and sport environment might contribute to athletes' sport conduct. Specifically, three-level models were utilized for sportspersonship, technical and mental gamesmanship, and instrumental aggression to examine whether there is unique variance due to sport and team clustering with athletes (N = 1412) nested within teams (J = 92) that are in turn nested within sports (K = 17). Results showed that clustering due to sport accounted for unique variance above and beyond team clustering. However, sex and invasion team sport explained most of the sport-level variance. The implication is that it is important to account for the sport clustering. However, when accounting for the sport-level clustering is not feasible, controlling for sex is necessary at the very least.     

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two‐factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander–Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed‐effect two‐stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.