Regardless of age, background, or socioeconomic status, children must learn to read in order to be successful in school and in their future careers. Reading is an essential skill necessary to be successful in all other academic content areas. Despite the importance of this skill, American Indian children consistently score below the national average on tests of reading ability and reading comprehension. During recent years, many schools in the Bureau of Indian Education (BIE) system requested funding through the Reading First initiative. Schools used the funding and support provided by the BIE Reading First grant to attempt system-wide change at the school level in order to refocus efforts on increasing reading achievement. The current study investigated the impact of the Reading First Initiative on American Indian students in kindergarten through third grade. Results suggest that the models and methods employed using funding from the Reading First grant had a positive impact on certain aspects of reading achievement in students. Instructional Leadership Changes had a negative impact on student achievement while certain reading programs were found to have a more positive impact on some students than others. Furthermore, regardless of beginning of year reading level, all students showed increased gain in end-of-year outcome scores over time. Same grade cohort groups of students in kindergarten, second, and third grades demonstrated increased average scores over time as schools continued to implement Reading First models. Finally, while the gap between students with intensive needs and their peers was not erased, it also did not widen. Based on research indicating gain for these students is often below that of their peers, this is an important finding. Thus, it appears that the impact of Reading First in relation to teaching younger students the basic building blocks needed to read with fluency in the later grades was positive in the current sample.

Cette thèse de doctorat est consacrée à la modélisation statistique de l'impact des environnements académiques sur les croyances et la réussite des élèves au Chili. Nous contribuons au domaine de l'efficacité éducative avec une discussion statistique et deux études empiriques. La discussion statique questionne la façon de combiner les modèles multiniveaux avec des méthodes pour le biais de sélection et pour les données manquantes. Cette discussion statistique sera utilisée pour prendre des décisions méthodologiques dans les études empiriques. La première étude empirique consiste en une évaluation d'intervention de l'impact des cours de sciences sur les croyances des étudiants. La deuxième étude empirique concerne l'effet des écoles sur les trajectoires des scores de mathématiques et de lecture des élèves. Dans la partie statistique, nous avons décrit et analysé les méthodes d'ajustement linéaire et d'appariement des scores de propension pour modéliser le biais de sélection. En ce qui concerne les problèmes de données manquantes, nous avons analysé la méthode d'imputation multiple. Chacune de ces méthodes est compatible avec les modèles multi-niveaux. En revanche, l'utilisation combinée de ces méthodes pour des données hiérarchiques n'est pas résolu. Nous présentons alors une discussion statistique qui analyse et classe des stratégies pour combiner ces méthodes.La première étude empirique concerne l'influence des disciplines scientifiques qui s'intéressent à des objets vivants et non-vivants sur les croyances épistémiques et le sentiment d'auto-efficacité des étudiants de secondaire. Nous avons comparé, pour ces croyances, les étudiants qui ont suivi des cours de sciences à un groupe contrôle sur deux temps de mesure, à la fin des cours et 4 mois après. Nous avons constaté un effet positif du travail en laboratoire et des disciplines qui s'intéressent à des objets vivants (en contrôlant les variables confondues). Cette étude met en lumière des différences entre les disciplines qui s'intéressent à des objets vivant et des objets non-vivant qui devront être explorées.La deuxième étude empirique concerne l'effet des écoles sur les trajectoires des scores en mathématiques et en lecture des élèves. Le premier objectif est de décrire les caractéristiques des trajectoires et la variance expliquée par les écoles primaires et secondaires. Le deuxième objectif est de mesurer l'effet du type d'école, publique ou voucher (privée avec un financement de l'état), sur les trajectoires. Nous avons utilisé une base de données nationale longitudinale qui comprenait des mesures pour les mêmes élèves en 4ème, 8ème et 10ème années. Des modèles de croissance multiniveaux ont été utilisés pour modéliser les trajectoires. Nos résultats montrent que les écoles secondaires et primaires ont un effet sur les interceptes et les pentes des trajectoires. Par ailleurs, nous avons constaté un effet négatif de l'école publique, qui est devenu non significatif lorsque nous avons contrôlé la composition socio-économique de l'école et ses pratiques de sélection. Ces résultats illustrent la stratification entre le système public et le système voucher ainsi que la nécessité de questionner l'efficacité des écoles pour chaque système. / This PhD thesis is dedicated to the statistical modeling of the impact of academic environments on student’s beliefs and achievement in Chile. We contribute to the field of educational effectiveness with a statistical discussion regarding how to combine multilevel models with methods for selection bias and missing data and two empirical studies. The statistical discussion was used to take methodological decisions in the empirical studies. The first empirical study evaluates the impact of science courses on students’ beliefs. The second empirical study is about school effects on students’ trajectories in mathematics and reading scores. In the statistical part, we analyze linear adjustment and propensity score matching to address selection bias. Regarding the missing data problem, we considered multiple imputation techniques. Each of these methods is compatible with multilevel models. However, the problem of addressing selection bias and missing data simultaneously with hierarchical data is not resolved. We present a statistical discussion that classifies and analyzes strategies to combine the methods. The first empirical study regards the influence of Life and Non-life science courses in secondary students’ epistemic and self-efficacy beliefs related to sciences. We compared students that took summer science courses with a control group in a post and follow-up beliefs questionnaire. We found positive effects of Life courses and courses with laboratory work, controlling for confounding variables. The results show differences between Life and Non-life scientific disciplines that should be explored. The second empirical study concerns school effects on trajectories of Chilean students. It has two aims. The first aim is to describe the characteristics of the trajectories in mathematics and reading scores and the variation explained by primary and secondary schools. The second aim is to measure the effect of public schools in comparison with voucher schools on students’ trajectories in mathematics and reading scores. We used a longitudinal national database which included measures for the same students at 4th, 8th and 10th grade. Multilevel growth models were used to model the trajectories. We found effects of secondary and primary schools on intercepts and slopes. In addition, we found negative effects from public education, which became not significant after controlling for school’ socioeconomic composition and selection practices. The results illustrate the stratification between the public system and voucher system and the need to study inside each system which schools are more efficient.

abstract: Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values. In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2015

abstract: Accurate data analysis and interpretation of results may be influenced by many potential factors. The factors of interest in the current work are the chosen analysis model(s), the presence of missing data, and the type(s) of data collected. If analysis models are used which a) do not accurately capture the structure of relationships in the data such as clustered/hierarchical data, b) do not allow or control for missing values present in the data, or c) do not accurately compensate for different data types such as categorical data, then the assumptions associated with the model have not been met and the results of the analysis may be inaccurate. In the presence of clustered/nested data, hierarchical linear modeling or multilevel modeling (MLM; Raudenbush & Bryk, 2002) has the ability to predict outcomes for each level of analysis and across multiple levels (accounting for relationships between levels) providing a significant advantage over single-level analyses. When multilevel data contain missingness, multilevel multiple imputation (MLMI) techniques may be used to model both the missingness and the clustered nature of the data. With categorical multilevel data with missingness, categorical MLMI must be used. Two such routines for MLMI with continuous and categorical data were explored with missing at random (MAR) data: a formal Bayesian imputation and analysis routine in JAGS (R/JAGS) and a common MLM procedure of imputation via Bayesian estimation in BLImP with frequentist analysis of the multilevel model in Mplus (BLImP/Mplus). Manipulated variables included interclass correlations, number of clusters, and the rate of missingness. Results showed that with continuous data, R/JAGS returned more accurate parameter estimates than BLImP/Mplus for almost all parameters of interest across levels of the manipulated variables. Both R/JAGS and BLImP/Mplus encountered convergence issues and returned inaccurate parameter estimates when imputing and analyzing dichotomous data. Follow-up studies showed that JAGS and BLImP returned similar imputed datasets but the choice of analysis software for MLM impacted the recovery of accurate parameter estimates. Implications of these findings and recommendations for further research will be discussed. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2016

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-12-27T11:08:29Z No. of bitstreams: 2 Dissertação - Beatriz Proto Martins - 2016.pdf: 1655009 bytes, checksum: 46f4cf12ff9472395d82fc24f0e0ffbd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-12-27T11:09:09Z (GMT) No. of bitstreams: 2 Dissertação - Beatriz Proto Martins - 2016.pdf: 1655009 bytes, checksum: 46f4cf12ff9472395d82fc24f0e0ffbd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-12-27T11:09:09Z (GMT). No. of bitstreams: 2 Dissertação - Beatriz Proto Martins - 2016.pdf: 1655009 bytes, checksum: 46f4cf12ff9472395d82fc24f0e0ffbd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-12-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Motivation: Electronic Health Records contain clinical data and are found in Health Information Systems. In this scenario, openEHR specification defines the record structure to allow systems to be interoperable, that is, to have a common understanding over exchanged data. A record comprises data modeled according to health domain concepts, called archetypes (knowledge level). An archetype, in turn, is composed by a subset of fixed entities from the Reference Model (information level). Due to the required detailing, the defined structure can be highly granular. Thus, the persistence of records, with the same format used during data exchange, can be hampered in terms of performance, especially in devices with a considerable resource limitation. Method: This work presents a strategy that serves as reference for the storage and retrieval of clinical data based on openEHR. Considering resources limitation, health services can persist their records in an optimized format, different from the format used for exchange. In this way, each service must implement a strategy for packing and unpacking that makes the conversions between both formats. Results: The persistence strategy presented in this work employs mapping rules between the objects graph of the Reference Model and a serialized data array. The rules range from primitive data types, such as an integer, to complex types, such as a hashmap consisting of objects with variable types and sizes. Conclusions: The strategy was designed considering the reduction of memory space occupied, but without turning the processing time unfeasible. Studies should be carried out for the strategy implementation and its experimentation. / Motivação: Registros Eletrônicos em Saúde contém dados clínicos e estão presentes em Sistemas de Informação em Saúde. Neste cenário, a especificação do openEHR define a estrutura dos registros para permitir que os sistemas sejam interoperáveis, isto é, tenham um entendimento comum sobre os dados trocados. Os registros compreendem dados modelados conforme conceitos de domínio em saúde, chamados arquétipos (nível de conhecimento). Um arquétipo, por sua vez, é composto por um subconjunto de entidades fixas do Modelo de Referência (nível de informação). Devido ao detalhamento necessário, a estrutura definida pode ser altamente granular. Deste modo, a persistência dos registros com o mesmo formato empregado durante a troca, pode ser prejudicada em termos de desempenho, principalmente em dispositivos com considerável limitação de recursos. Método: Este trabalho apresenta uma estratégia que serve de referência para o armazenamento e recuperação de dados clínicos baseados no openEHR. Tendo em vista a limitação de recursos, serviços em saúde podem persistir seus registros em um formato otimizado em relação ao formato empregado para troca. Para isso, cada serviço deve aplicar uma estratégia de empacotamento e desempacotamento de dados que efetue a conversão entre ambos os formatos. Resultados: A estratégia de persistência apresentada emprega regras de mapeamento entre o grafo de objetos do Modelo de Referência e um vetor de dados serializados. As regras englobam desde tipos de dados primitivos, como um inteiro, até tipos complexos, como um hashmap composto por objetos de tipos e tamanhos variáveis. Conclusões: A estratégia foi projetada considerando a redução de espaço ocupado em memória, mas sem inviabilizar o tempo de processamento. Estudos devem ser realizados com a implementação e experimentação da estratégia.

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No. of bitstreams: 1 Dissertação_vfinal_3.pdf: 707611 bytes, checksum: ea22499a01aaeb82cd198735a62a6f94 (MD5) Previous issue date: 2012-06-15 / This study aims to evaluate the effect of regional concentrations in organizational performance of companies especially in the service sector. In order to achieve this goal we compared organizational performance of firms located in areas of geographical concentration to the performance of those outside these areas. We also compare the effects of regional concentration on the performance of companies in the service industry with companies in the industrial sector. The literature review revealed that there are advantages for companies located in concentration areas, leading to the main hypothesis of this study that such advantages would lead to a better performance of these firms. Thus, we sought to ascertain the existence of a relationship between organizational performance and geographic location of service industry companies. In order to identify regional concentrations we adapted the methodological criterion used in the industry sector. The indicators used were based on the number of establishments and employees obtained from the database of Annual Social Information Report (RAIS). The organizational performance was measured by two indicators of profitability (profit / net sales) and sales growth (growth rate). The source of performance data used was based on the following research database from the Brazilian Institute of Geography and Statistics (IBGE): Annual Industrial Survey (PIA) and Annual Survey of Services (PAS). The sample included 78,789 observations providers and 22,460 observations from the industrial sector between 2001 and 2005. The results were produced by using Hierarchical Linear Models or Multilevel Models. The results revealed a positive effect on the growth of businesses located in regional areas of concentration (for the industry and service sector), suggesting that firms located in such places grow faster than those which were located outside of these areas. However, there was no evidence of higher profitability. The findings of this study can inform management´s decision making process as it relates to locating firms in or outside regional concentrations. Furthermore, there are some implications for public policy, which include that a positive effect on the firm growth can orient incentive policies, in order to stimulate the regional development of concentration areas. / O presente trabalho tem por objetivo avaliar o impacto das concentrações regionais no desempenho organizacional das empresas brasileiras com ênfase no setor serviços. Com o intuito de atingir este objetivo realizou-se uma comparação entre o desempenho organizacional das firmas localizadas em áreas de concentração geográficas e aquelas situadas fora destas áreas. Além disso, procurou-se contrastar o efeito da concentração regional sobre o desempenho das empresas de serviços com as empresas do setor industrial. A revisão literária evidenciou a existência de vantagens para empresas concentradas regionalmente, o que levou à principal hipótese deste trabalho, de que tais vantagens ocasionariam melhor desempenho das firmas. Desta forma, buscou-se averiguar a existência de uma relação entre o desempenho organizacional e a localização geográfica das empresas de serviços regionalmente concentradas. O trabalho de identificação das concentrações regionais foi realizado adaptando-se os critérios utilizados no setor industrial para o setor serviços, a partir dos dados de número de estabelecimentos e de funcionários, obtidos através da base dados da Relação Anual de Informações Sociais (RAIS). O desempenho organizacional foi mensurado por dois indicadores: lucratividade e o crescimento de vendas. A fonte de dados de desempenho utilizada foi a base de microdados das seguintes pesquisas do Instituto Brasileiro de Geografia e Estatística (IBGE): Pesquisa Industrial Anual (PIA) e Pesquisa Anual de Serviços (PAS). A amostra utilizada incluiu 78.789 observações de prestadoras de serviços e 22.460 observações de empresas do setor industrial, entre 2001 e 2005. Os resultados foram produzidos por meio da aplicação dos modelos hierárquicos ou modelos multiníveis. Os resultados revelaram um efeito positivo sobre o crescimento das empresas situadas em áreas de concentração regional (tanto do setor serviços quanto da indústria), porém não foram encontradas evidências de maior lucratividade das mesmas. As conclusões deste trabalho contribuem para a tomada de decisão dos gestores, ao avaliar se deverão ou não situar seu empreendimento em uma área de concentração regional. Além de apresentar implicações para as políticas públicas, pois a constatação de um efeito positivo sobre o crescimento das firmas em determinadas concentrações pode direcionar políticas de incentivo, com o objetivo de estimular a formação de tais concentrações em determinadas localidades para desenvolvimento regional.

This thesis contains three essays covering different topics in the field of statistics<p>and econometrics of survey data. Chapters one and two analyse two aspects<p>of the Survey of Professional Forecasters (SPF hereafter) dataset. This survey<p>provides a large information on macroeconomic expectations done by the professional<p>forecasters and offers an opportunity to exploit a rich information set.<p>But it poses a challenge on how to extract the relevant information in a proper<p>way. The last chapter addresses the issue of analyzing the opinions on the euro<p>reported in the Flash Eurobaromenter dataset.<p>The first chapter Measuring Uncertainty and Disagreement in the European<p>Survey of Professional Forecasters proposes a density forecast methodology based<p>on the piecewise linear approximation of the individual’s forecasting histograms,<p>to measure uncertainty and disagreement of the professional forecasters. Since<p>1960 with the introduction of the SPF in the US, it has been clear that they were a<p>useful source of information to address the issue on how to measure disagreement<p>and uncertainty, without relying on macroeconomic or time series models. Direct<p>measures of uncertainty are seldom available, whereas many surveys report point<p>forecasts from a number of individual respondents. There has been a long tradition<p>of using measures of the dispersion of individual respondents’ point forecasts<p>(disagreement or consensus) as proxies for uncertainty. Unlike other surveys, the<p>SPF represents an exception. It directly asks for the point forecast, and for the<p>probability distribution, in the form of histogram, associated with the macro variables<p>of interest. An important issue that should be considered concerns how to<p>approximate individual probability densities and get accurate individual results<p>for disagreement and uncertainty before computing the aggregate measures. In<p>contrast to Zarnowitz and Lambros (1987), and Giordani and Soderlind (2003) we<p>overcome the problem associated with distributional assumptions of probability<p>density forecasts by using a non parametric approach that, instead of assuming<p>a functional form for the individual probability law, approximates the histogram<p>by a piecewise linear function. In addition, and unlike earlier works that focus on<p>US data, we employ European data, considering gross domestic product (GDP),<p>inflation and unemployment.<p>The second chapter Optimal Combination of Survey Forecasts is based on<p>a joint work with Christine De Mol and Domenico Giannone. It proposes an<p>approach to optimally combine survey forecasts, exploiting the whole covariance<p>structure among forecasters. There is a vast literature on forecast combination<p>methods, advocating their usefulness both from the theoretical and empirical<p>points of view (see e.g. the recent review by Timmermann (2006)). Surprisingly,<p>it appears that simple methods tend to outperform more sophisticated ones, as<p>shown for example by Genre et al. (2010) on the combination of the forecasts in<p>the SPF conducted by the European Central Bank (ECB). The main conclusion of<p>several studies is that the simple equal-weighted average constitutes a benchmark<p>that is hard to improve upon. In contrast to a great part of the literature which<p>does not exploit the correlation among forecasters, we take into account the full<p>covariance structure and we determine the optimal weights for the combination<p>of point forecasts as the minimizers of the mean squared forecast error (MSFE),<p>under the constraint that these weights are nonnegative and sum to one. We<p>compare our combination scheme with other methodologies in terms of forecasting<p>performance. Results show that the proposed optimal combination scheme is an<p>appropriate methodology to combine survey forecasts.<p>The literature on point forecast combination has been widely developed, however<p>there are fewer studies analyzing the issue for combination density forecast.<p>We extend our work considering the density forecasts combination. Moving from<p>the main results presented in Hall and Mitchell (2007), we propose an iterative<p>algorithm for computing the density weights which maximize the average logarithmic<p>score over the sample period. The empirical application is made for the<p>European GDP and inflation forecasts. Results suggest that optimal weights,<p>obtained via an iterative algorithm outperform the equal-weighted used by the<p>ECB density combinations.<p>The third chapter entitled Opinion surveys on the euro: a multilevel multinomial<p>logistic analysis outlines the multilevel aspects related to public attitudes<p>toward the euro. This work was motivated by the on-going debate whether the<p>perception of the euro among European citizenships after ten years from its introduction<p>was positive or negative. The aim of this work is, therefore, to disentangle<p>the issue of public attitudes considering either individual socio-demographic characteristics<p>and macroeconomic features of each country, counting each of them<p>as two separate levels in a single analysis. Considering a hierarchical structure<p>represents an advantage as it models within-country as well as between-country<p>relations using a single analysis. The multilevel analysis allows the consideration<p>of the existence of dependence between individuals within countries induced by<p>unobserved heterogeneity between countries, i.e. we include in the estimation<p>specific country characteristics not directly observable. In this chapter we empirically<p>investigate which individual characteristics and country specificities are<p>most important and affect the perception of the euro. The attitudes toward the<p>euro vary across individuals and countries, and are driven by personal considerations<p>based on the benefits and costs of using the single currency. Individual<p>features, such as a high level of education or living in a metropolitan area, have<p>a positive impact on the perception of the euro. Moreover, the country-specific<p>economic condition can influence individuals attitudes. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Cette thèse de doctorat a été réalisée en cotutelle entre les Universités de Rennes 1 en France et de Florence en Italie. L’objectif de ce travail est tout d’abord de rationaliser les propriétés inter- et intramoléculaires de molécules-aimants (Single Molecule Magnet – SMM) à base d’ions lanthanides (“partie moléculaire”) et puis leur évolution une fois absorbé sur surface (''partie sur surface''). Ces deux aspects ont été examinés dans un cadre théorique et computationnel, en utilisant différentes techniques multi-niveaux, de periodic Density Functional Theory (pDFT) en utilisant une approche post-Hartree-Fock, en fonction de la variable expérimentale d’intérêt. Les molécules-aimants sont d'un intérêt particulier pour le design de nouveaux matériaux magnétiques dans la science des surfaces (comme la spintronique), mais elles permettent également une connaissance des propriétés électroniques et magnétiques approfondie est également nécessaire. / The Ph.D. project was a joint agreement between two universities: Université de Rennes 1 in France and Università di Firenze in Italy. The project aimed to shed light on the rationalization of the inter- and intramolecular properties of novel lanthanide-based Single Molecule Magnets, SMMs, (“molecular part”) and their evolution once adsorbed on surface (“surface part”). Both aspects are examined within a theoretical and computational framework, with different multi-level techniques ranging from periodic Density Functional Theory (pDFT) to post-Hartree-Focks approaches, depending on the experimental observable of interest. SMMs are, indeed, at the cutting-edge in the design of novel magnetic materials in surface science (as spintronics or memory storage devices), but for their exploitation a deep understanding of their electronic and magnetic properties is needed.

This study compared 3 approaches for handling a fourth level of nesting structure when analyzing data from a cluster-randomized trial (CRT). CRTs can include 3 levels of nesting: repeated measures, individual, and cluster levels. However, above the cluster level, there may sometimes be an additional potentially important fourth level of nesting (e.g., schools, districts, etc., depending on the design) that is typically ignored in CRT data analysis. The current study examined the impact of ignoring this fourth level, accounting for it using a model-based approach, and accounting it using a design-based approach on parameter and standard error (SE) estimates. Several fixed effect and random effect variance parameters and SEs were biased across all 3 models. In the 4-level model, most SE biases decreased as the number of level 3 clusters increased and as the number of level 4 clusters decreased. Also, random effect variance biases decreased as the number of level 3 clusters increased. In the 3-level and complex models, SEs became more biased as the weight level 4 carried increased (i.e., larger intraclass correlation, more clusters at that level). The current results suggest that if a meaningful fourth level of nesting exists, future researchers should account for it using design-based approach; the model-based approach is not recommended. If the fourth level is not practically important, researchers may ignore it altogether.

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