Hierarchical Datasets Research Articles

Generalized sample size determination formulas for experimental research with hierarchical data

Hierarchical data sets arise when the data for lower units (e.g., individuals such as students, clients, and citizens) are nested within higher units (e.g., groups such as classes, hospitals, and regions). In data collection for experimental research, estimating the required sample size beforehand is a fundamental question for obtaining sufficient statistical power and precision of the focused parameters. The present research extends previous research from Heo and Leon (2008) and Usami (2011b), by deriving closed-form formulas for determining the required sample size to test effects in experimental research with hierarchical data, and by focusing on both multisite-randomized trials (MRTs) and cluster-randomized trials (CRTs). These formulas consider both statistical power and the width of the confidence interval of a standardized effect size, on the basis of estimates from a random-intercept model for three-level data that considers both balanced and unbalanced designs. These formulas also address some important results, such as the lower bounds of the needed units at the highest levels.

An Extensive Evaluation of Decision Tree–Based Hierarchical Multilabel Classification Methods and Performance Measures

Hierarchical multilabel classification is a complex classification problem where an instance can be assigned to more than one class simultaneously, and these classes are hierarchically organized with superclasses and subclasses, that is, an instance can be classified as belonging to more than one path in the hierarchical structure. This article experimentally analyses the behavior of different decision tree–based hierarchical multilabel classification methods based on the local and global classification approaches. The approaches are compared using distinct hierarchy‐based and distance‐based evaluation measures, when they are applied to a variation of real multilabel and hierarchical datasets' characteristics. Also, the different evaluation measures investigated are compared according to their degrees of consistency, discriminancy, and indifferency. As a result of the experimental analysis, we recommend the use of the global classification approach and suggest the use of the Hierarchical Precision and Hierarchical Recall evaluation measures.

Graph hierarchies for phylogeography

Bayesian phylogeographic methods simultaneously integrate geographical and evolutionary modelling, and have demonstrated value in assessing spatial spread patterns of measurably evolving organisms. We improve on existing phylogeographic methods by combining information from multiple phylogeographic datasets in a hierarchical setting. Consider N exchangeable datasets or strata consisting of viral sequences and locations, each evolving along its own phylogenetic tree and according to a conditionally independent geographical process. At the hierarchical level, a random graph summarizes the overall dispersion process by informing which migration rates between sampling locations are likely to be relevant in the strata. This approach provides an efficient and improved framework for analysing inherently hierarchical datasets. We first examine the evolutionary history of multiple serotypes of dengue virus in the Americas to showcase our method. Additionally, we explore an application to intrahost HIV evolution across multiple patients.

TreeVersity

Transportation data sets of all kinds are hierarchical in nature and therefore are easily represented in tree structures. Visually comparing the changes in these hierarchical data sets over time can be extremely difficult, even when the trees are relatively small. TreeVersity is a novel inter active visualization that allows users to detect and analyze changes in the structure and value of various components of the tree. TreeVersity uses dual comparison techniques (side by side and explicit differences) coupled with a tabular representation to help users understand and explore changes to the tree over time. TreeVersity uses carefully selected color palettes to show positive or negative absolute and relative value changes and glyphs that show these changes preattentively. A study illustrated the value of this visualization technique through various short case studies based on federal transportation budget data, airline maintenance budget data, and transportation publication data. Hypotheses for TreeVersity's future relevance for congestion trend analysis are provided.

Growing self-organizing trees for autonomous hierarchical clustering

This paper presents a new unsupervised learning method based on growing processes and autonomous self-assembly rules. This method, called Growing Self-organizing Trees (GSoT), can grow both network size and tree topology to represent the topological and hierarchical dataset organization, allowing a rapid and interactive visualization. Tree construction rules draw inspiration from elusive properties of biological organization to build hierarchical structures. Experiments conducted on real datasets demonstrate good GSoT performance and provide visual results that are generated during the training process.

Application of multilevel analysis in animal sciences

Abstract Multilevel modeling is considerably useful way to analyze hierarchical data sets. The main purpose of this paper is to apply multilevel analysis in animal science and also show that this modeling technique is appropriate to analyze this kind of data. Thus multilevel modeling technique is used to analyze the milk yield data which has hierarchical structures, sires nested within cows. As a result of the analysis done in this paper, it is obvious that multilevel modeling is needed to use for analyzing this data. This illustrates that it is a convenient way to use multilevel analysis for the data which obtained from animals when the data have hierarchies.

Statistical Power of Experimental Research with Hierarchical Data

Hierarchical data sets arise when data for units (e.g., students) are nested within various clusters (e.g., classes and schools), and often appear in behavioral research. Estimating statistical power and sample size requirements is one of the fundamental questions in data collection, especially in experimental research where obtaining large samples is sometimes unrealistic. In the present research, we discuss a general procedure for evaluating statistical power to test intervention effects in experimental research with hierarchical data, focusing mainly on a two-way between-subjects design. This approach enables the statistical power of various types of contrasts to be evaluated with respect to main effects and interaction effects by using multiparameter tests based on Wald statistics. Additionally, several numerical examples are presented to show how the statistical power for various contrasts changes with various values of sample size, sizes of intervention effects, intraclass correlation and some data assumptions. Extensions of the proposed method and issues for practical applications are noted in discussion.

Multi‐level models of stress and well‐being

tional stress researchers may investigate individual factors related to stress and well-being (e.g. personality, work-life balance, emotions, coping skills, etc.); job and organizational factors (e.g., work hours and schedules, role overload/underload/ambiguity, emotional labour, job insecurity, organizational climate); and even societal and national factors (e.g. cultural values; social, economic and environmental indicators). Yet, all too often, these variables are all measured at a single level, usually at the individual level. Thus, while we acknowledge that individual, group, organizational and even cultural variables are theoretically necessary to understand and predict stress outcomes, we rarely measure these variables at their appropriate level. The purpose of this editorial is to encourage researchers to take a multilevel approach to considering the relationships between occupational stress and wellbeing. This entails intentionally refl ecting on the individual, job, organizational and macroeconomic antecedents of employee stress. Such a multilevel framework can be fruitful not only for understanding the stress-strain process, but also crucial in developing and conceptualizing stress interventions. Thus, a multilevel approach can enhance both our theoretical and empirical understanding of occupational stress as well as the practical implications stemming from our research. Using a multi-level modelling (MLM) approach means explicitly taking into account the often hierarchical nature of our data structure (e.g. individuals working in groups, students in classrooms, children in families). Such a hierarchical dataset has traditionally posed three problems within an ordinary least squares (OLS) regression approach: (1) the units of analysis problem; (2) the violation of independent observations assumption problem; and (3) the heterogeneity of slopes problem. Let us consider each in turn. Most behavioural science models of stress acknowledge that a complete understanding of the structure and process of stress invariably requires a consideration of individual, group and environmental/situational characteristics (Sulsky & Smith, 2005). Such models originally arose from an awareness that purely biological models of stress fail to reliably predict which potential stressors will be perceived as stressful and how this process is infl uenced by personal and contextual factors. For example, the cognitive-transactional model of stress (Lazarus & Launier, 1978) posits that there are few, if any, universal stressors. Rather, the perception of and reactions to a potential stressor will vary within and across individuals and may differ over occasions and time. Whether the potential stressor is perceived to be stressful, therefore, intimately depends on characteristics of the individual (e.g. needs, abilities, personality) and the situation (e.g. demands, resources). As a result, most contemporary models of stress include some variation of a person-environment (P-E) fi t perspective [e.g. Karasek’s (1979) demands-control model; Hobfall’s (1989) Conservation of Resources theory; French and colleagues’ P-E fi t model, (French, Caplan, & Van Harrison, 1982, Van Harrison, 1978)]. Despite the fact that our models of stress explicitly consider individual and contextual factors, researchers often do not appropriately model these environmental and individual factors either in their research design, data collection or subsequent analyses. Thus, organiza-

HIDS

In the research of high-speed data streams, large amounts of synthetic data are needed. These days, more and more researchers focus on hierarchical multi-dimensional data streams or data sets, which is beyond the ability of traditional synthetic data generators. In this paper we propose a two-phased method to generate hierarchical multi-dimensional data streams, in which a tree-like structure is built first, and then an unlimited number of items chosen among the tree leaves according to a distribution are inserted into the stream. Our generator, HIDS, integrates all of the functions of existing data generators, and can customize the tree structure according to usersý requirements, producing tree structures such as equal-depth trees, equal-fan-out trees, balanced trees and different-fan-out trees. An experimental study using real data streams shows that HIDS can generate data streams tailored to specific applications.

A linear mixed model with temporal covariance structures in modelling catch per unit effort of Baltic herring

Abstract Mikkonen, S., Rahikainen, M., Virtanen, J., Lehtonen, R., Kuikka, S., and Ahvonen, A. 2008. A linear mixed model with temporal covariance structures in modelling catch per unit effort of Baltic herring. – ICES Journal of Marine Science, 65: 1645–1654. Changes in the structure and attributes of a fleet over time will break down the proportionality of catch per unit effort (cpue) and stock biomass. Moreover, logbook data from commercial fisheries are hierarchical and autocorrelated. Such features not only complicate the analysis of cpue data but also seriously limit the application of a generalized linear model approach, which nevertheless is applied commonly. We demonstrate a linear mixed model application for a large hierarchical dataset containing autocorrelated observations. In the analysis, the key idea is to explore the properties of the error term of the model. We modified the residual covariance matrix, allowing the introduction of assumed fisher behaviour, influencing the catch rate. Fisher behaviour consists of accumulated knowledge and learning processes from their earlier area- and time-specific catch rates. Also, we investigated the effects of vessel-specific parameters by introducing random intercepts and slopes in the model. A model with the autoregressive moving average residual covariance matrix structure was superior over the block-diagonal and autoregressive (AR1) structure for the data, having a time-dependent correlation among trawl hauls. The results address the benefits of statistically advanced methods in obtaining precise and unbiased estimates from cpue data, to be used further in stock assessment. Fisheries agencies are encouraged to monitor the relevant vessel and gear attributes, including engine power and gear size, and the deployment practices of the gear.

Sorting hierarchical data in external memory for archiving

Sorting hierarchical data in external memory is necessary for a wide variety of applications including archiving scientific data and dealing with large XML datasets. The topic of sorting hierarchical data, however, has received little attention from the research community so far. In this paper we focus on sorting arbitrary hierarchical data that far exceed the size of physical memory. We propose HErMeS, an algorithm that generalizes the most widely-used techniques for sorting flat data in external memory. HErMeS efficiently exploits the hierarchical structure to minimize the number of disk accesses and optimize the use of available memory. We extract the theoretical bounds of the algorithm with respect to the structure of the hierarchical dataset. We then show how the algorithm can be used to support efficient archiving. We have conducted an experimental study using several workloads and comparing HErMeS to the state-of-the-art approaches. Our results show that our algorithm ( a ) meets its theoretical expectations, ( b ) allows for scalable database archiving, and ( c ) outperforms the competition by a significant factor. These results, we believe, prove our technique to be a viable and scalable solution to the problem of sorting hierarchical data in external memory.

Latent class and finite mixture models for multilevel data sets

An extension of latent class (LC) and finite mixture models is described for the analysis of hierarchical data sets. As is typical in multilevel analysis, the dependence between lower-level units within higher-level units is dealt with by assuming that certain model parameters differ randomly across higher-level observations. One of the special cases is an LC model in which group-level differences in the logit of belonging to a particular LC are captured with continuous random effects. Other variants are obtained by including random effects in the model for the response variables rather than for the LCs. The variant that receives most attention in this article is an LC model with discrete random effects: higher-level units are clustered based on the likelihood of their members belonging to the various LCs. This yields a model with mixture distributions at two levels, namely at the group and the subject level. This model is illustrated with three rather different empirical examples. The appendix describes an adapted version of the expectation-maximization algorithm that can be used for maximum likelihood estimation, as well as providing setups for estimating the multilevel LC model with generally available software.

Browsing Zoomable Treemaps: Structure-Aware Multi-Scale Navigation Techniques

Treemaps provide an interesting solution for representing hierarchical data. However, most studies have mainly focused on layout algorithms and paid limited attention to the interaction with treemaps. This makes it difficult to explore large data sets and to get access to details, especially to those related to the leaves of the trees. We propose the notion of zoomable treemaps (ZTMs), an hybridization between treemaps and zoomable user interfaces that facilitates the navigation in large hierarchical data sets. By providing a consistent set of interaction techniques, ZTMs make it possible for users to browse through very large data sets (e.g., 700,000 nodes dispatched amongst 13 levels). These techniques use the structure of the displayed data to guide the interaction and provide a way to improve interactive navigation in treemaps.

Sampling for Bayesian Computation with Large Datasets

Multilevel models are extremely useful in handling large hierarchical datasets. However, computation can be a challenge, both in storage and CPU time per iteration of Gibbs sampler or other Markov chain Monte Carlo algorithms. We propose a computational strategy based on sampling the data, computing separate posterior distributions based on each sample, and then combining these to get a consensus posterior inference. With hierarchical data structures, we perform cluster sampling into subsets with the same structures as the original data. This reduces the number of parameters as well as sample size for each separate model fit. We illustrate with examples from climate modeling and newspaper marketing.

RadMonitor: Radiology Operations Data Mining in Real Time

This paper describes the web-based visualization interface of RadMonitor, a platform-independent web application designed to help manage the complexity of information flow within a health care enterprise. The system eavesdrops on Health Layer 7 traffic and parses statistical operational information into a database. The information is then presented to the user as a treemap--a graphical visualization scheme that simplifies the display of hierarchical information. While RadMonitor has been implemented for the purpose of analyzing radiology operations, its XML backend allows it to be reused for virtually any other hierarchical data set.

V1R promoters are well conserved and exhibit common putative regulatory motifs

BackgroundThe mouse vomeronasal organ (VNO) processes chemosensory information, including pheromone signals that influence reproductive behaviors. The sensory neurons of the VNO express two types of chemosensory receptors, V1R and V2R. There are ~165 V1R genes in the mouse genome that have been classified into ~12 divergent subfamilies. Each sensory neuron of the apical compartment of the VNO transcribes only one of the repertoire of V1R genes. A model for mutually exclusive V1R transcription in these cells has been proposed in which each V1R gene might compete stochastically for a single transcriptional complex. This model predicts that the large repertoire of divergent V1R genes in the mouse genome contains common regulatory elements. In this study, we have characterized V1R promoter regions by comparative genomics and by mapping transcription start sites.ResultsWe find that transcription is initiated from ~1 kb promoter regions that are well conserved within V1R subfamilies. While cross-subfamily homology is not evident by traditional methods, we developed a heuristic motif-searching tool, LogoAlign, and applied this tool to identify motifs shared within the promoters of all V1R genes. Our motif-searching tool exhibits rapid convergence to a relatively small number of non-redundant solutions (97% convergence). We also find that the best motifs contain significantly more information than those identified in controls, and that these motifs are more likely to be found in the immediate vicinity of transcription start sites than elsewhere in gene blocks. The best motifs occur near transcription start sites of ~90% of all V1R genes and across all of the divergent subfamilies. Therefore, these motifs are candidate binding sites for transcription factors involved in V1R co-regulation.ConclusionOur analyses show that V1R subfamilies have broad and well conserved promoter regions from which transcription is initiated. Results from a new motif-finding algorithm, LogoAlign, designed for this context and more generally for searching large, hierarchical datasets, suggest the existence of common information-rich regulatory motifs that are shared across otherwise divergent V1R subfamilies.

The utility of site‐based datasets and regional ecosystem mapping for biodiversity conservation in the Southeast Queensland Bioregion: Past, present, future

The utility of site-based datasets and regional ecosystem mapping for biodiversity conservation in the Southeast Queensland Bioregion: Past, present, future. Ben E. Lawson. School of Natural and Rural Systems Management (NRSM) & School of Geography, Planning and Architecture (GPA), The University of Queensland, Brisbane 4072, Australia. Email: b.lawson@uq.edu.au. Key words: conservation, ecosystem mapping, regional ecosystems, site-based data. Ecosystem mapping and site-based datasets are core components of conservation planning and management schemes. In Queensland, regional ecosystem mapping is used for landscape-level planning, underpinned by site-based data. This doctoral research assesses their utility as surrogates for biodiversity patterns with a view to future needs. The research is supervised by Dr Grant Wardell-Johnson, Associate Professor Bob Beeton (NRSM) and Dr David Pullar (GPA) from the University of Queensland. The ecologically diverse Southeast Queensland (SEQ) Bioregion is the focus of this research. Issues and limitations in the two datasets, which underpin this research, were the first component examined. Regional ecosystem mapping showed a decrease in the number of heterogeneous polygons (i.e. a polygon with multiple ecosystems assigned) across successive versions. Polygon heterogeneity levels were positively correlated with endangered ecosystems and lower polygon accuracy, and strongly related to particular regional ecosystem and geomorphology types (see Lawson 2006). Retrospective analysis of the Queensland Herbarium's site-based floristic dataset, ‘CORVEG’, showed improved data quality and completeness in the past decade as a consequence of more explicit sampling protocols, although missing information continues to limit data utility (see Lawson in press). Case studies were used to explore the application of regional ecosystem mapping in varied circumstances. The first case study examined SEQ sand islands where high levels of map unit homogeneity relative to adjacent mainland areas were observed. Analysis showed that mapping effectively portrayed ecological patterns and that homogeneity existed across various map scales and map authors across the islands, suggesting that high polygon homogeneity were ecological, not cartographic, phenomena (see Lawson & Wardell-Johnson in press). The second case study came from Toohey Forest in southern SEQ, an area mapped as a single regional ecosystem type at 1:100 000 scale despite its recognized biotic and abiotic diversity. Fine-scale mapping approaches were explored to assess the representation of floristic patterns, indicating that ongoing reduction in regional ecosystem mapping scale and incorporation of fine-scale geomorphic mapping were vital to improve the representation of floristic diversity. Core components of the research which are yet to be completed will elucidate species richness and dissimilarity patterns within and between map units and reveal the ecosystem types that are (and aren't) well portrayed by the mapped patterns, the reasons for this, and measures to improve representation. Queensland's regional ecosystem mapping program shows continued improvement in the representation of biodiversity patterns, with some areas more effectively portrayed than others. The use of heterogeneous polygons to identify ecosystems otherwise unrecognizable at particular map scales is simultaneously a major advantage and disadvantage to representing biodiversity patterns. Opportunities are available to focus limited resources on particular geomorphological and regional ecosystem types, and for alternate methods of representing geographically restricted ecosystems. Greater consideration of current and future uses of site-based floristic data is necessary. For example, hierarchical datasets serving multiple biodiversity objectives should be considered. These issues are directly relevant to the mapping of biodiversity condition.

Decomposition of Prediction Error in Multilevel Models

ABSTRACT We present a decomposition of prediction error for the multilevel model in the context of predicting a future observable y *j in the jth group of a hierarchical dataset. The multilevel prediction rule is used for prediction and the components of prediction error are estimated via a simulation study that spans the various combinations of level-1 (individual) and level-2 (group) sample sizes and different intraclass correlation values. Additionally, analytical results present the increase in predicted mean square error (PMSE) with respect to prediction error bias. The components of prediction error provide information with respect to the cost of parameter estimation versus data imputation for predicting future values in a hierarchical data set. Specifically, the cost of parameter estimation is very small compared to data imputation.

Prediction in Multilevel Models

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. This article addresses the problem of predicting a future observable y*j in thej th group of a hierarchical data set. Three prediction rules are considered and several analytical results on the relative performance of these prediction rules are demonstrated. In addition, the prediction rules are assessed by means of a Monte Carlo study that extensively covers both the sample size and parameter space. Specifically, the sample size space concerns the various combinations of Level 1 (individual) and Level 2 (group) sample sizes, while the parameter space concerns different intraclass correlation values. The three prediction rules employ OLS, prior, and multilevel estimators for the Level 1 coefficientsβj The multilevel prediction rule performs the best across all design conditions, and the prior prediction rule degrades as the number of groups, J, increases. Finally, this article investigates the robustness of the multilevel prediction rule to misspecifications of the Level 2 model.

Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects

Abstract Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables. The models can include several nested random effects (intercepts and coefficients) representing unobserved heterogeneity at different levels of a hierarchical dataset. The required multivariate integrals are evaluated efficiently using spherical quadrature rules. Simulations show that adaptive quadrature performs well in a wide range of situations.