>Magister Scientiae - MSc / Most standard statistical techniques illustrated in text books assume that the data are collected from a simple random sample (SRS) and hence are independently and identically distributed (i.i.d.). In reality, data are often sourced through complex sampling (CS) designs, with a combination of stratification and clustering at different levels of the design. Consequently, the CS data are not i.i.d. and sampling weights that are developed over different stages, are calculated and included in the analysis of this data to account for the sampling design. Logistic regression is often employed in the modelling of survey data since the response under investigation typically has a dichotomous outcome. Furthermore, since the logistic regression model has no homogeneity or normality assumptions, it is appealing when modelling a dichotomous response from survey data. This research considers the comparison of the estimates of the logistic regression model parameters when the CS design is accounted for, i.e. weighting is present, to when the data are modelled using an SRS design, i.e. no weighting. In addition, the standard errors of the estimators will be obtained using three different variance techniques, viz. Taylor series linearization, the jackknife and the bootstrap. The different estimated standard errors will be used in the calculation of the standard (asymptotic) interval which will be compared to the bootstrap percentile interval in terms of the interval coverage probability. A further level of comparison is obtained when using only design weights to those obtained using calibrated and integrated sampling weights. This simulation study is based on the Income and Expenditure Survey (IES) of 2005/2006. The results showed that generally when weighting was used the estimators performed better as opposed to when the design was ignored, i.e. under the assumption of SRS, with the results for the Taylor series linearization being more stable.

Orientador: Luzia Aparecida Trinca / Resumo: A depressão é apontada como a doença crônica não transmissível que terá maior abrangência até 2030, atingindo direta ou indiretamente vários setores nos quais a população está inserida. No Brasil, a situação da depressão é alarmante, respondendo pela maior taxa do continente latino-americano. A Pesquisa Nacional de Saúde (PNS) é um inquérito de base domiciliar de abrangência nacional. Trata-se de uma iniciativa do Ministério da Saúde em parceria com o Instituto Brasileiro de Geografia e Estatística (IBGE) e tem como objetivo caracterizar a situação de saúde e os estilos de vida da população brasileira, e assim conhecer como acontece a atenção à saúde em diversos grupos da população. Neste trabalho a depressão será o objeto de estudo por ser caracterizada como uma doença complexa de difícil mensuração e observação devido a suas causas multifatoriais. O levantamento de dados da PNS utilizou um planejamento amostral complexo, o que demanda uma atenção especial em relação à análise das informações coletadas. Considerando a magnitude da pesquisa e levando em consideração as diversidades regionais, foram ajustados modelos com base na teoria de classes latentes. Essa abordagem identifica grupos baseados nos padrões de respostas observadas nas variáveis categóricas utilizando um modelo probabilístico. Assim é possível classificar cada indivíduo como pertencente a um grupo, estimar a prevalência e identificar características decisivas para o surgimento dos grupos. A partir de itens qu... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Depression is indicated as the non-transmissible chronic disease that will be more widespread until 2030, reaching directly or indirectly several sectors in which the population is inserted. In Brazil, the situation of depression is alarming, accounting for the highest rate in the Latin American continent. The National Health Survey (PNS) is a nationwide household survey. It is an initiative of the Ministry of Health in partnership with the Brazilian Institute of Geography and Statistics (IBGE) and aims to characterize the health situation and the lifestyles of the Brazilian population, and thus to know how health care happens in different groups of the population. In this study, depression will be the object of study because it is characterized as a complex disease of difficult measurement and observation due to its multifactorial causes. The PNS data collection used a complex sampling plan, which demands special attention in relation to the analysis of the information collected. Considering the magnitude of the research and taking into account the regional diversities, models were adjusted based on latent class theory. This approach identifies groups based on the patterns of responses observed in the categorical variables using a probabilistic model. Thus it is possible to classify each individual as belonging to a group, to estimate the prevalence and identify decisive characteristics for the emergence of groups. Based on items dealing with mental health, it was possible t... (Complete abstract click electronic access below) / Doutor

Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and pregnancy (Thompson and Pantoja-Galicia 2003), the interrelation between entry into marriage for individuals in a consensual union and first pregnancy (Blossfeld and Mills 2003), and the association between job loss and divorce (Charles and Stephens 2004, Huang 2003 and Yeung and Hofferth 1998). Establishing causation in observational studies is seldom possible. Nevertheless, if one of two events tends to precede the other closely in time, a causal interpretation of an association between these events can be more plausible. The role of longitudinal surveys is crucial, then, since they allow sequences of events for individuals to be observed. Thompson and Pantoja-Galicia (2003) discuss in this context several notions of temporal association and ordering, and propose an approach to investigate a possible relationship between two lifetime events. In longitudinal surveys individuals might be asked questions of particular interest about two specific lifetime events. Therefore the joint distribution might be advantageous for answering questions of particular importance. In follow-up studies, however, it is possible that interval censored data may arise due to several reasons. For example, actual dates of events might not have been recorded, or are missing, for a subset of (or all) the sampled population, and can be established only to within specified intervals. Along with the notions of temporal association and ordering, Thompson and Pantoja-Galicia (2003) also discuss the concept of one type of event "triggering" another. In addition they outline the construction of tests for these temporal relationships. The aim of this thesis is to implement some of these notions using interval censored data from longitudinal complex surveys. Therefore, we present some proposed tools that may be used for this purpose. This dissertation is divided in five chapters, the first chapter presents a notion of a temporal relationship along with a formal nonparametric test. The mechanisms of right censoring, interval censoring and left truncation are also overviewed. Issues on complex surveys designs are discussed at the end of this chapter. For the remaining chapters of the thesis, we note that the corresponding formal nonparametric test requires estimation of a joint density, therefore in the second chapter a nonparametric approach for bivariate density estimation with interval censored survey data is provided. The third chapter is devoted to model shorter term triggering using complex survey bivariate data. The semiparametric models in Chapter 3 consider both noncensoring and interval censoring situations. The fourth chapter presents some applications using data from the National Population Health Survey and the Survey of Labour and Income Dynamics from Statistics Canada. An overall discussion is included in the fifth chapter and topics for future research are also addressed in this last chapter.

Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and pregnancy (Thompson and Pantoja-Galicia 2003), the interrelation between entry into marriage for individuals in a consensual union and first pregnancy (Blossfeld and Mills 2003), and the association between job loss and divorce (Charles and Stephens 2004, Huang 2003 and Yeung and Hofferth 1998). Establishing causation in observational studies is seldom possible. Nevertheless, if one of two events tends to precede the other closely in time, a causal interpretation of an association between these events can be more plausible. The role of longitudinal surveys is crucial, then, since they allow sequences of events for individuals to be observed. Thompson and Pantoja-Galicia (2003) discuss in this context several notions of temporal association and ordering, and propose an approach to investigate a possible relationship between two lifetime events. In longitudinal surveys individuals might be asked questions of particular interest about two specific lifetime events. Therefore the joint distribution might be advantageous for answering questions of particular importance. In follow-up studies, however, it is possible that interval censored data may arise due to several reasons. For example, actual dates of events might not have been recorded, or are missing, for a subset of (or all) the sampled population, and can be established only to within specified intervals. Along with the notions of temporal association and ordering, Thompson and Pantoja-Galicia (2003) also discuss the concept of one type of event "triggering" another. In addition they outline the construction of tests for these temporal relationships. The aim of this thesis is to implement some of these notions using interval censored data from longitudinal complex surveys. Therefore, we present some proposed tools that may be used for this purpose. This dissertation is divided in five chapters, the first chapter presents a notion of a temporal relationship along with a formal nonparametric test. The mechanisms of right censoring, interval censoring and left truncation are also overviewed. Issues on complex surveys designs are discussed at the end of this chapter. For the remaining chapters of the thesis, we note that the corresponding formal nonparametric test requires estimation of a joint density, therefore in the second chapter a nonparametric approach for bivariate density estimation with interval censored survey data is provided. The third chapter is devoted to model shorter term triggering using complex survey bivariate data. The semiparametric models in Chapter 3 consider both noncensoring and interval censoring situations. The fourth chapter presents some applications using data from the National Population Health Survey and the Survey of Labour and Income Dynamics from Statistics Canada. An overall discussion is included in the fifth chapter and topics for future research are also addressed in this last chapter.

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Thesis (M.Sc. (Statistics)) -- University of Limpopo, 2019 / This research study has demonstrated the complexity involved in complex survey sample design (CSSD). Furthermore the study has proposed methods to account for each step taken in sampling and at the estimation stage using the theory of survey sampling, CSSD-based case studies and practical implementation based on census attributes. CSSD methods are designed to improve statistical efficiency, reduce costs and improve precision for sub-group analyses relative to simple random sample(SRS).They are commonly used by statistical agencies as well as development and aid organisations. CSSDs provide one of the most challenging fields for applying a statistical methodology. Researchers encounter a vast diversity of unique practical problems in the course of studying populations. These include, interalia: non-sampling errors,specific population structures,contaminated distributions of study variables,non-satisfactory sample sizes, incorporation of the auxiliary information available on many levels, simultaneous estimation of characteristics in various sub-populations, integration of data from many waves or phases of the survey and incompletely specified sampling procedures accompanying published data. While the study has not exhausted all the available real-life scenarios, it has outlined potential problems illustrated using examples and suggested appropriate approaches at each stage. Dealing with the attributes of CSSDs mentioned above brings about the need for formulating sophisticated statistical procedures dedicated to specific conditions of a sample survey. CSSD methodologies give birth to a wide variety of approaches, methodologies and procedures of borrowing the strength from virtually all branches of statistics. The application of various statistical methods from sample design to weighting and estimation ensures that the optimal estimates of a population and various domains are obtained from the sample data.CSSDs are probability sampling methodologies from which inferences are drawn about the population. The methods used in the process of producing estimates include adjustment for unequal probability of selection (resulting from stratification, clustering and probability proportional to size (PPS), non-response adjustments and benchmarking to auxiliary totals. When estimates of survey totals, means and proportions are computed using various methods, results do not differ. The latter applies when estimates are calculated for planned domains that are taken into account in sample design and benchmarking. In contrast, when the measures of precision such as standard errors and coefficient of variation are produced, they yield different results depending on the extent to which the design information is incorporated during estimation. The literature has revealed that most statistical computer packages assume SRS design in estimating variances. The replication method was used to calculate measures of precision which take into account all the sampling parameters and weighting adjustments computed in the CSSD process. The creation of replicate weights and estimation of variances were done using WesVar, astatistical computer package capable of producing statistical inference from data collected through CSSD methods. Keywords: Complex sampling, Survey design, Probability sampling, Probability proportional to size, Stratification, Area sampling, Cluster sampling.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-07-23T13:46:12Z No. of bitstreams: 1 anapaulakern.pdf: 1782580 bytes, checksum: 77a0ee41fafd9e9c8361ed2cf8d8dfc0 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-09-03T16:19:18Z (GMT) No. of bitstreams: 1 anapaulakern.pdf: 1782580 bytes, checksum: 77a0ee41fafd9e9c8361ed2cf8d8dfc0 (MD5) / Made available in DSpace on 2018-09-03T16:19:18Z (GMT). No. of bitstreams: 1 anapaulakern.pdf: 1782580 bytes, checksum: 77a0ee41fafd9e9c8361ed2cf8d8dfc0 (MD5) Previous issue date: 2018-06-26 / Esta tese tem por objetivo avaliar o impacto do Programa Bolsa Família sobre o desenvolvimento humano em saúde, educação e mercado de trabalho, respectivamente. É importante dizer que os trabalhos voltados para avaliar o impacto do Programa Bolsa Família estão basicamente apoiados nas análises dos dados da PNAD e do Censo Demográfico, que podem possuir um possível viés de representatividade. Portanto, para essa tese foi construído um painel longitudinal, no nível de indivíduo, a partir dos dados da AIBF I e AIBF II. Esse painel constitui um marco para os estudos de avaliação de impacto do Programa Bolsa Família, uma vez que é o primeiro painel que acompanha o mesmo indivíduo ao longo do tempo, e assim pode gerar resultados mais robustos. O modelo utilizado foi de diferenças em diferenças com balanceamento por entropia. Além disso, esta tese representa mais um avanço na literatura a respeito de programas de transferência de renda, por fazer todas as análises de impacto levando em consideração o plano amostral, que é outra característica importante normalmente ignorada. Em pesquisas por amostragem, ignorar características do plano amostral pode enviesar a estimação do impacto e produzir estimativas incorretas. O primeiro ensaio investiga o impacto do Bolsa Família nas condições de saúde das mulheres e das crianças de até 7 anos de idade, sendo considerada principalmente a saúde das gestantes e vacinação das crianças. No segundo ensaio avalia-se o impacto do Programa Bolsa Família sobre a educação das crianças de 6 a 17 anos, com enfoque sobre a participação, progressão, repetência e abandono escolar. O terceiro ensaio avalia o impacto do programa sobre o mercado de trabalho, mais especificamente na oferta de trabalho dos indivíduos. No primeiro ensaio, os principais resultados mostram que o Bolsa Família aumenta o status de imunização das crianças de 2005 para 2009, mas não o suficiente para manter o calendário vacinal em dia. Para o segundo ensaio, os resultados obtidos indicam que o PBF não afetou a matricula escolar das crianças de 2005 para 2009, quando separadas por gênero. No entanto, o Bolsa Família aumentou a probabilidade das crianças se matricularem, especialmente para crianças mais velhas, residentes na área urbana na região Nordeste. Para progressão, repetência e evasão, o Bolsa Família não apresentou impacto. Para o terceiro ensaio, os resultados indicam que não há efeito do PBF sobre a probabilidade de trabalhar dos homens ou das mulheres, e que o impacto de redução nas horas de trabalho, se concentra nas mulheres residentes em áreas rurais. Com isso, não é pertinente a crítica de que o PBF seria responsável por gerar dependência dos benefícios do programa. / This thesis is made up of three essays that aim to evaluate the impact of the Bolsa Família Program on human development in health, education and the labor market, respectively. It is important to say that the work aimed at evaluating the impact of the Bolsa Família Program is basically supported by the analysis of PNAD and Demographic Census data, which may have a representative bias. Therefore, for this thesis a longitudinal panel, at the individual level, was constructed from the data of AIBF I and AIBF II. This panel constitutes a milestone for impact assessment studies of the Bolsa Família Program, since it is the first panel that accompanies the same individual over time, and thus can generate more robust results. The model used was of differences in differences. In addition, this thesis represents a further advance in the literature regarding income transfer programs, for making all impact analyzes taking into consideration the sampling design, which is another important characteristic usually ignored. In sampling design, ignoring characteristics of the sampling plan may bias the impact estimation and produce incorrect estimates. The first essay evaluates the impact of the Bolsa Família Program on the education of children aged 6 to 17 years, with a focus on participation, progression, repetition and drop-out. The second essay investigates the impact of Bolsa Família on the health conditions of women and children up to 7 years of age, mainly considering the health of pregnant women, vaccination of children and health expenses. The third essay assesses the impact of the program on the labor market, more specifically on the labor supply of individuals. For the first trial, the preliminary results obtained indicate that the PBF has a positive and significant impact only for school dropout for female children residing in rural areas, from 6 to 14 years of age. For urban children, the PBF had no impact. In the second trial, it is examined whether the PBF generates an increase in the likelihood of children aged 0 to 7 years having a vaccination card and a decrease in monthly health care expenses for all individuals. For the third test, a positive relation between hours worked is expected.

Les performances en mathématiques sont associées à de nombreux enjeux dans notre société, des enjeux de nature individuelle et des enjeux de nature sociétale. Malgré le fait que les élèves québécois réussissent très bien sur la scène internationale en mathématiques, dans le cadre des évaluations à grande échelle en éducation, les analyses selon le genre, elles, font état d’écarts préoccupants. En effet, à plusieurs des cycles de ces grandes enquêtes, les filles ont obtenu des résultats statistiquement inférieurs à ceux des garçons. L’anxiété mathématique, pourrait expliquer, à tout le moins en partie, les écarts de performances observés entre les filles et les garçons (Stoet et al., 2016). En effet, les recherches menées sur le sujet depuis les années 70 révèlent que, de manière générale, chez les adolescents et les adultes, les filles ont tendance à se dire davantage anxieuses à l’égard des mathématiques que les garçons (p.ex. Else-Quest et al., 2010; Hyde et al., 1990; Stoet et al. 2016). Également, dans ces mêmes groupes d’âge, une corrélation linéaire négative est observée entre le niveau d’anxiété mathématique des individus et leurs performances en mathématiques (p.ex. Barroso et al.,2021; Hembree, 1990; Ma, 1999; Zhang et al., 2019). En 2003 et en 2012, le PISA s’est intéressé à l’anxiété mathématique. En effet, comme les mathématiques ont constitué le domaine majeur d’évaluation lors de ces deux enquêtes, l’anxiété mathématique a été documentée, à ces occasions, au même titre que bon nombre d’autres facteurs non-cognitifs liés aux performances dans le domaine. Le portrait canadien, issu du PISA de 2003 et de 2012, supporte et renforce l’idée selon laquelle l’anxiété mathématique pourrait contribuer aux écarts de performance observés entre les garçons et les filles, en mathématiques, au Québec. Devant l’absence de portrait québécois en regard du phénomène, et souhaitant, à terme, fournir des leviers en vue de réduire les écarts de performances observés entre les filles et les garçons québécois, nous énonçons l’objectif général de recherche comme suit : quantifier les écarts d’anxiété mathématique entre les filles et les garçons, étudier le lien anxiété mathématique/performances en mathématiques et ensuite, identifier des facteurs ayant le potentiel de réduire les écarts d’anxiété mathématique observés, chez les élèves québécois francophones de 15 ans, à partir d’une analyse secondaire des données du PISA de 2003 et de 2012. Afin de répondre à cet objectif général de recherche, nous définissons trois objectifs spécifiques de recherche. Chacun d’eux est traité dans un des trois articles de cette thèse par articles. Le premier objectif spécifique de notre recherche vise à identifier les considérations méthodologiques inhérentes aux données issues du PISA et à proposer des techniques d’analyse qui permettent de les traiter, adéquatement. Cet objectif spécifique est traité dans le premier article, un article de nature méthodologique. Les deuxième objectif spécifique de notre recherche vise à quantifier les écarts d’anxiété mathématique entre les garçons et les filles francophones de 15 ans du Québec, à partir d’une analyse secondaire des données du PISA de 2003 et de 2012, et à étudier le lien négatif anxiété mathématique/performances en mathématiques, chez ces mêmes élèves. Cet objectif spécifique est traité dans le second article de la thèse, un article de nature empirique, qui prend appui sur les fondements méthodologiques proposés dans l’article 1. Le troisième objectif spécifique de notre recherche vise à identifier des facteurs qui permettent d’expliquer les écarts d’anxiété mathématique observés entre les garçons et les filles francophones du Québec et qui ont le potentiel de guider, à terme, la mise en œuvre d’interventions visant à réduire les écarts observés. Répondre à cet objectif spécifique fait l’objet du troisième article de la thèse. Cet article prend également appui sur les fondements méthodologiques exposés dans l’article 1. Des résultats issus de l’article 2, il ressort que : 1) en moyenne, les filles francophones de 15 ans du Québec font état d’un niveau d’anxiété mathématique statistiquement plus élevé que les garçons et 2) le lien entre l’anxiété mathématique et les performances en mathématiques est un lien négatif et équivalent entre les garçons et les filles francophones du Québec. Des résultats issus de l’article 3, il ressort que les écarts d’anxiété mathématique observés entre les filles et les garçons québécois francophones ayant participé au PISA de 203 et de 2012 pourraient s’expliquer par : 1) un concept de soi en mathématiques plus faible chez les filles et 2) un lien direct genre/anxiété mathématique. Des implications scientifiques et pratiques de ces résultats découlent des recommandations en vue de réduire les écarts d’anxiété mathématique observés entre les filles et les garçons francophones du Québec, de même que des avenues de recherche à explorer dans le futur. Ces recommandations et avenues de recherches sont présentées au terme de la thèse. / Performance in mathematics is linked to a number of issues in our society, both individual and societal. Even though Quebec students are doing very well internationally in mathematics, in large-scale educational assessments, gender-based analyses reveal disturbing gaps. Over the course of several cycles of these large-scale surveys, girls achieved statistically lower results than boys. Mathematics anxiety could at least partially explain the performance gaps observed between girls and boys (Stoet et al., 2016). Indeed, research conducted since the 1970s has shown that, in general, in adolescents and adults, girls tend to report greater anxiety about mathematics than boys (e.g.Else-Quest et al., 2010; Hyde et al., 1990; Stoet et al. 2016). Furthermore, in these same age groups, there is a negative linear correlation between individuals' level of anxiety in mathematics and their performance in mathematics (e.g.Hembree, 1990; Ma, 1999; Zhang et al., 2019). In 2003 and 2012, PISA turned its attention to mathematics anxiety. Indeed, since mathematics was the main domain of assessment in both surveys, mathematical anxiety was documented on these occasions, along with many other non-cognitive factors related to performance in the domain. The Canadian portrait, from both the 2003 and 2012 PISA surveys, supports and reinforces the idea that mathematics anxiety could explain, at least in part, the observed performance gaps between boys and girls in mathematics in Quebec. Given the absence of a Quebec portrait of the phenomenon, and wishing, in the long run, to provide levers for reducing the observed performance gaps between Quebec girls and boys, we state the general research objectives as follows: 1) quantify the gaps between girls and boys with respect to mathematics anxiety, 2) study the link between mathematics anxiety and mathematical performance, and finally 3) identify factors that may reduce the gaps observed in mathematical anxiety among 15-year-old French-speaking students in Québec, based on a secondary analysis of the 2003 and 2012 PISA data. 7 In order to meet this overall research objective, three specific research objectives are identified. Each of these is discussed in one of the three articles of the present thesis per article. The first specific objective of our research is to identify the methodological considerations inherent to the PISA data and to propose analytical techniques that will allow us to adequately address them. This specific objective is discussed in the first article, a methodology article. The second specific objective of our research is to quantify the differences in mathematical anxiety between 15-year-old French-speaking boys and girls in Quebec, based on a secondary analysis of the 2003 and 2012 PISA data, and to investigate the negative relation between mathematical anxiety and mathematical performance in these same students. This specific objective is discussed in the second article of the thesis, an empirical article, which is based on the methodological bases proposed in Article 1. The third specific objective of our research is to identify factors that contribute to explaining the differences observed in mathematical anxiety between French-speaking boys and girls in Quebec and have the potential to guide, over the long run, the implementation of interventions aimed at reducing the observed gaps. The third paper in the thesis focuses on this specific objective. This article is also based on the methodological bases set out in Article 1. The results of Article 2 show that: 1) on average, French-speaking 15-year-old girls in Quebec report a statistically higher level of mathematical anxiety than boys and 2) the relationship between mathematical anxiety and mathematical performance is negative and equivalent between French-speaking boys and girls in Quebec. From the results of Article 3, it appears that the differences in mathematical anxiety observed between Quebec French-speaking girls and boys who participated in PISA 2003 and 2012 can be explained by: 1) a lower perception of mathematical competence among girls and 2) a direct gender/mathematical anxiety link. The scientific and practical implications of these results lead to recommendations to reduce the differences observed in mathematical anxiety among French-speaking girls and boys in Quebec, as well as lines of future research. These recommendations and lines of research are presented at the end of the thesis.