Background: Understanding the relationship of education to fertility requires the disentangling of the potentially confounding effect of social status, which is highly correlated with education. Objective: We contribute to this aim by examining educational fertility differentials within occupational groups and industries across a broad swath of Central and Eastern Europe, specifically Austria, Greece, Hungary, Romania, Slovenia, and Switzerland. Methods: Cross-sectional individual-level census samples from the Integrated Public Use Microdata Series (IPUMS) are sufficiently large to contain sizeable numbers of unusual combinations, e.g., university graduates in low-status jobs or primary school dropouts in professional categories. Completed cohort fertility, as well as the share childless and with high parity, are regressed on effects for educational attainment, occupation, industry, and all their interactions within a Bayesian framework, and the contributions to the outcome variation are analysed. Results: Education has a strong, consistent association with fertility outcomes when industry and occupation are held constant. Furthermore, fertility by industry and occupation yields fairly disparate patterns. We also find that differences in completed fertility across countries can be attributed to country-specific compositional differences in education, industry, and occupation, and to interaction effects. However, differences by country in the baseline rate of childlessness and high parity cannot be attributed to such compositional effects. Conclusions: The educational fertility gradient in the settings studied cannot be attributed to an occupational composition effect. (authors' abstract)

In 2018, Raul Matsushita, Donald Pianto, Bernardo B. De Andrade, Andre Can§ado & Sergio Da Silva published a paper titled âTouchard distributionâ, which presented a model that is a two-parameter extension of the Poisson distribution. This model has its normalizing constant related to the Touchard polynomials, hence the name of this model. This diploma thesis is concerned with the properties of the Touchard distribution for which delta is known. Two asymptotic tests based on two different statistics were carried out for comparison in a Touchard model with two independent samples, supported by simulations in R.

In many agricultural and biological contexts, the response variable is a nonnegative integer value which we wish to explain or analyze in terms of a set of covariates. Unlike the Gaussian linear model, the response variable is discrete with a distribution that places probability mass at natural numbers only. The Poisson regression is the standard model for count data. However, assumptions of this model forces the equality between mean and variance, which may be implausible in many applications. Motivated by experimental data sets, this work intended to develop more realistic methods for the analysis of count data. We proposed a novel parametrization of the COM-Poisson distribution and explored the regression models based on it. We extended the model to allow the dispersion, as well as the mean, depending on covariates. A set of count statistical models, namely COM-Poisson, Gamma-count, discrete Weibull, generalized Poisson, double Poisson and Poisson-Tweedie, was reviewed and compared, considering the dispersion, zero-inflation, and heavy tail indexes, together with the results of data analyzes. The computational routines developed in this dissertation were organized in two R packages available on GitHub. / Em diversos estudos agrícolas e biológicos, a variável resposta é um número inteiro não negativo que desejamos explicar ou analisar em termos de um conjunto de covariáveis. Diferentemente do modelo linear Gaussiano, a variável resposta é discreta com distribuição de probabilidade definida apenas em valores do conjunto dos naturais. O modelo Poisson é o modelo padrão para dados em forma de contagens. No entanto, as suposições desse modelo forçam que a média seja igual a variância, o que pode ser implausível em muitas aplicações. Motivado por conjuntos de dados experimentais, este trabalho teve como objetivo desenvolver métodos mais realistas para a análise de contagens. Foi proposta uma nova reparametrização da distribuição COM-Poisson e explorados modelos de regressão baseados nessa distribuição. Uma extensão desse modelo para permitir que a dispersão, assim como a média, dependa de covariáveis, foi proposta. Um conjunto de modelos para contagens, nomeadamente COM-Poisson, Gamma-count, Weibull discreto, Poisson generalizado, duplo Poisson e Poisson-Tweedie, foi revisado e comparado, considerando os índices de dispersão, inflação de zero e cauda pesada, juntamente com os resultados de análises de dados. As rotinas computacionais desenvolvidas nesta dissertação foram organizadas em dois pacotes R disponíveis no GitHub.

Competition between species is believed to lead to patterns of either competitive exclusion or limiting similarity within ecological communities; however, to date the amount of support for either as an outcome has been relatively weak. The two classes of null model commonly used to assess co-occurrence and limiting similarity have both been well studied for statistical performance; however, the methods used to evaluate their performance, particularly in terms of type II statistical errors, may have resulted in the underreporting of both patterns in the communities tested. The overall purpose of this study was to evaluate the efficacy of the negative co-occurrence and limiting similarity null models to detect patterns believed to result from competition between species and to develop an improved method for detecting said patterns. The null models were tested using synthetic but biologically realistic presence-absence matrices for both type I and type II error rate estimations. The effectiveness of the null models was evaluated with respect to community dimension (number of species × number of plots), and amount of pattern within the community. A novel method of subsetting species was developed to assess communities for patterns of co-occurrence and limiting similarity and four methods were assessed for their ability to isolate the species contributing signal to the pattern. Both classes of null model provided acceptable type I and type II error rates when matrices of more than 5 species and more than 5 plots were tested. When patterns of negative co-occurrence or limiting similarity were add to all species both null models were able to detect significant pattern (β > 0.95); however, when pattern was added to only a proportion of species the ability of the null models to detect pattern deteriorated rapidly with proportions of 80% or less. The use of species subsetting was able to detect significant pattern of both co-occurrence and limiting similarity when fewer than 80% of species were contributing signal but was dependent on the metric used for the limiting similarity null model. The ability of frequent pattern mining to isolate the species contributing signal shows promise; however, a more thorough evaluation is required in order to confirm or deny its utility.

[pt] Esta dissertação descreve a aplicação de Modelos Lineares Generalizados (MLGs) à análise de um experimento visando identificar a combinação dos níveis das variáveis independentes: concentração de hidróxido de sódio (A), volume de hipoclorito de sódio (B) e sua interação (AB), que minimiza a variável resposta: proporção de itens com defeitos, em um processo de beneficiamento numa indústria têxtil de pequeno porte. A variável resposta encontra-se na forma de proporção, violando os pressupostos básicos do Modelo Linear Clássico e com isso as estimativas dos coeficientes pelo método de Mínimos Quadrados Ordinários (MQO) é menos confiável. O planejamento utilizado foi o fatorial completo 22 com ponto central e replicado. Após o planejamento, a modelagem pelo MLG é aplicada, só então é possível identificar uma subdispersão dos dados, verificar que o modelo empregado está correto e que o volume de hipoclorito de sódio (B) é o único fator significativo, no processo de alvejamento industrial da empresa. Portanto, como a finalidade é minimizar a resposta, utiliza-se o nível inferior (-1) desta variável. Consequentemente, como o intuito é reduzir os custos com insumos químicos pode-se utilizar o nível mínimo da concentração de hidróxido de sódio (A) e o nível máximo da interação entre os fatores (AB), já que eles não são significativos ao modelo. / [en] This dissertation describes the application of Generalized Linear Models (GLMs) to the analysis of an experiment with the purpose identify the levels combination of independent variables: concentration of sodium hydroxide (A) volume of sodium hypochlorite (B) and their interaction (AB), that minimizes the response variable: proportion of defective items, in a process in a small plant of the textile industry. The response variable takes the form of a proportion, that violates the basic assumptions of the Classic Linear Model and, as a result, the estimates of the coefficients by Ordinary Least Squares method is less reliable. The design employed was a replicated complete 22 factorial design with central point. After doing the planning, the modeling by MLG is applied, and then it is possible to identify a underdispersion data; to verify that the model used is correct and that the volume of sodium hypochlorite (B) is the only significant factor in the industrial process of bleaching the company. Therefore, as the purpose is to minimize the response, it is used the lower level (-1) of this variable. Consequently, as the aim is to reduce costs of chemical inputs can use the minimum level of concentration of hydroxide sodium (A) and the maximum level of interaction between factors (AB), since they are not significant to the model.

進行調查時，最後的抽樣單位常是從不同的群集取得的，而同一群集內的樣本對象，因背景類似而對於某些問題常會傾向相同或類似的反應，研究者若忽略這種群內相關性，仍以獨立性樣本進行分析時，因其共變異數矩陣通常會與多項模式的共變異數矩陣相差懸殊，而造成所謂的額外變異或不足變異的現象。本文在不同的情況下，提出了Dirichlet-Multinomial模式(簡稱DM模式)、擴展的DM模式、以及兩種平均數-共變異數矩陣模式，以適當的彙整所有的群集資料。並討論DM與EDM模式中相關之參數及格機率之最大概似估計法，且分別對此兩種平均數-共變異數矩陣模式，提出求導廣義最小平方估計的程序。此外，也針對幾種特殊的二維表及三維表結構，探討對應的參數及格機率之估計方法。並提出計算簡易的Score統計檢定量以判斷群內相關(intra-cluster correlation)之存在性，及判斷資料集具有額外或不足變異，而對於不同母體的群內相關同質性檢定亦提出討論。 / This paper presents a modelling method of analyzing categorical data with overdispersion or underdispersion.　In many studies, data are collected from differ clusters, and members within the same cluster behave similary.　Thus, the responses of members within the same cluster are not independent and the multinomial distribution is not the correct distribution for the observed counts.　Therefore, the covariance matrix of the sample proportion vector tends to be much different from that of the multinomial model.　We discuss four different models to fit counts data with overdispersion or underdispersion feature, witch include Dirichlet-Multinomial model (DM model), extended DM model (EDM model), and two mean-covariance models.　Method of maximum-likelihood estimation is discussed for DM and EDM models.　Procedures to derive generalized least squares estimates are proposed for the two mean-covariance models respectively. As to the cell probabilities, we also discuss how to estimate them under several special structures of　two-way and three-way tables.　More easily evaluated Score test statistics are derived for the DM and EDM models to test the existence of　the intra-cluster correlation.　And the test of homogeneity of intra-cluster correlation among several populations is also derived.