Modeling household fertility decisions with generalized Poisson regression

Migration, Partner Selection, and Fertility in Germany: How Many Children are Born in Mixed Unions?

For the German context, we investigate whether the number of children ever born differs between mixed unions (exogamous unions between natives and migrants or migrant descendants) and endogamous unions (unions among co-ethnics). Our theoretical considerations are derived from assimilation theories, which view exogamous unions as indicators of assimilation processes, and the framework on migrant fertility. The migrant (or descendant) partner in an exogamous union may adapt to the majority group, both partners may adapt to each other, or both partners may constitute a selected group in their fertility preferences. However, due to the higher likelihood of conflicts within the partnership and of separation, exogamy may disrupt family formation processes and depress couples' fertility. Drawing on data from the GSOEP (1984-2020), we estimate generalized Poisson regressions. The results reveal that the number of children ever born is higher in exogamous unions than in endogamous native couples. This general pattern largely persists across migrant generations and regions of origin, but we identify gender differences. While fertility in exogamous unions of native women/migrant (descendant) men is not statistically different from fertility in native/native couples, unions of migrant (descendant) women/native men have more children, especially when controlling for socio-demographic confounders. Our results demonstrate that in the German context, exogamy does not lead to fertility disruptions, and is not straightforwardly associated with assimilation to the fertility of the majority group. Instead, differences in gendered partner choice patterns and life-course transitions may influence the number of children exogamous couples have.

Testing latent classes in gut microbiome data using generalized Poisson regression models

Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over-dispersion and zero-inflation. To address dispersion-related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over-dispersion, equi-dispersion, and under-dispersion. Furthermore, the realm of zero-inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over-dispersion and zero-inflation. The phenomenon of zero-inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed-form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study.

Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model

We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables.

Generalized Poisson Hurdle Model for Count Data and Its Application in Ear Disease

For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

Modelling adoption intensity of improved soybean production technologies in Ghana - a Generalized Poisson approach

Soybean is an important cash crop especially for farmers in the north of Ghana. However, cultivation of the commodity is dominated by smallholders equipped with traditional tools, coupled with low or no adoption of improved soybean production technologies. Using primary data collected from 300 soybean farmers across northern Ghana, the study employed count data modelling to estimate the determinants of adoption intensity of sustainable soybean production technologies. The study accounted for potential estimation errors due to under-dispersion and over-dispersion, by using a model based on the generalized Poisson distribution. On the average, a farmer adopted 50% of the identified sustainable soybean production technologies. Age, education, extension visits, mass media through radio, and the perception of adoption of soybean production technologies being risky are significant with positive influence on the adoption intensity of sustainable soybean production technologies. The study therefore recommends among others, that various extension programmes should intensify education on the benefits of adopting sustainable soybean production practices. There is the need to set up many technology demonstration farms to give farmers hands-on training during field days.

Ethnic fertility behavior and internal migration in Nigeria: revisiting the migrant fertility hypotheses

Fertility patterns in Nigeria are high and widely skewed away from the targets of the country’s population policy. As population growth is fueled by natural increase and migration, and with spatial disparities in fertility preferences among the different ethnic groups in Nigeria, this study investigates the fertility behavior of ethnic migrants in their destinations, the place-effects on such behavior, and the convergence or otherwise of the behavior with fertility behaviors in the migrants’ places of origin and destination. Explanations for the behavioral pattern are provided in the hypotheses of migrant fertility and in the sociodemographic confounders of the behavior. Study data was extracted for the three major ethnic groups in Nigeria from the Nigerian Demographic and Health Survey. Median numbers of children ever born (CEB) were 7, 6, and 4 for the Hausa-Fulani, Igbo, and Yoruba ethnic groups respectively. Relative to the destination fertility patterns, Hausa-Fulani and Yoruba migrants had lower CEB in Igboland while Igbo and Yoruba migrants recorded lower CEB in the North-West home of the Hausa-Fulani ethnic group. Whereas the Igbo migrants maintained an equal CEB with their Yoruba hosts, the Hausa-Fulani group replicated their home fertility behavior in Yorubaland. Overall, the adaptation, socialization, and selectivity hypotheses were found valid for some of the disparities in migrant fertility behavior and the influence of the sociodemographic predictors of fertility behavior varied among the different ethnic groups.

Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data

The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

Socioeconomic determinants of rural women's desired fertility: A survey in rural Shaanxi, China

There has been evidence demonstrating that China has had a persistently low and below-replacement level fertility since early 1990s, causing concerns of a rapidly aging population and sustainability of the Chinese economy. To avoid adverse effects of excessively low fertility, the Chinese government has recently changed its family planning policy from "one-child policy" to "two-child policy." Nonetheless, the effectiveness of the newly initiated two-child policy is questionable if women's average desired number of children or desired fertility for their lifetime is below the threshold fertility allowed by the two-child policy. Therefore, this study argues that it would be interesting and pertinent to know women's fertility desires under the circumstances of no policy restrictions and understand major factors that may affect their desired fertility. Based on a multi-stage stratified cluster sampling survey with 2,516 women respondents in rural Shaanxi, this study tries to estimate desired fertility of rural women and evaluate the impact of important socioeconomic factors on their desired fertility. The results of this study reveal that the average lifetime desired fertility for rural women of childbearing age in Shaanxi is about 1.71, below the total fertility rate at the replacement level. The findings of this study suggest that women's marriage age, the pecuniary costs of having children, women's income forgone for having children, and social security benefits available for rural residents at retirement age, are significantly and negatively related to desired fertility. However, rural women's cultural views towards fertility are significantly but positively related to their desired fertility. This study further confirms that China has entered an era of low fertility, and thus, any policy restrictions on fertility may no longer be necessary. Instead, government programs which support childbearing and childrearing are needed to prevent excessive low fertility and rapid aging of the population.

Assessment of length of stay in a general surgical unit using a zero-inflated generalized Poisson regression

Background: The effective use of limited health care resources is of prime importance. Assessing the length of stay (LOS) is especially important in organizing hospital services and health system. This study was conducted to identify predictors of LOS among patients who were admitted to a general surgical unit.

Methods: In this cross-sectional study, the sample included all patients who were admitted to the general surgical unit of Shariati hospital in 2013 (n= 334). To determine the factors affecting LOS, Zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), and zero-inflated generalized Poisson (ZIGP) regression models were fitted using R software, and then the best model was selected.

Results: Among all 334 patients, the mean (±SD) age of the patients was 45.2 (±16.47) years and 220 (65.9%) of them were male. The results revealed that based on ZIGP model, type of surgery (appendicitis, abdomen and its contents, hemorrhoids, lung, and skin), type of insurance, comorbid diseases (hypertension, heart disease, and hyperlipidemia), place of residence (local and non-local), age, and number of tests had significant effects on the LOS of GS patients.

Conclusion: According to the Akaike information criterion (AIC) in each fitted model, it was found that ZIGP regression model is more appropriate than ZIP and ZINB regression models in assessing LOS in GS patients, especially due to the presence of excess zeros and overdispersion in count data.

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data

In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

The sociodemographic, behavioral, reproductive, and health factors associated with fertility in Brazil

High fertility rates among disadvantaged subgroups are a public health problem because fertility levels significantly affect socioeconomic conditions and a population’s welfare. This paper aims to analyze the sociodemographic, behavioral, and reproductive factors associated with fertility rates among Brazilian women aged between 15–49 years. A Poisson regression was used to analyze data from the 2006 PNDS (Pesquisa Nacional de Demografia e Saúde da Criança e da Mulher), which evaluates socioeconomic, demographic, geographic, reproductive, behavioral, and chronic disease variables. The results show that the following characteristics are positively associated with an increase in the number of children born: being aged 20–24, residing in the North, being nonwhite, not being in paid employment, having lower education levels, having lower socioeconomic status, being in a stable union, having the first sexual intercourse before the age of 16 and having the first child before the age of 20. Thus, it is important to implement efficient family planning policies targeting these subgroups in order to improve life conditions, reduce inequalities and avoid the adverse outcomes of high fertility.

Orthogonality of the Mean and Error Distribution in Generalized Linear Models

We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the error distribution is known completely, known up to a finite vector of parameters, or left completely unspecified, in which case the likelihood is taken to be an appropriate semiparametric likelihood. Moreover, the maximum likelihood estimator of the mean-model parameter will be asymptotically independent of the maximum likelihood estimator of the error distribution. This generalizes some well-known results for the special cases of normal, gamma and multinomial regression models, and, perhaps more interestingly, suggests that asymptotically efficient estimation and inferences can always be obtained if the error distribution is nonparametrically estimated along with the mean. In contrast, estimation and inferences using misspecified error distributions or variance functions are generally not efficient.

Sample size and informetric model goodness-of-fit outcomes: a search engine log case study

The influence of sample size on informetric characteristics is examined to determine whether theoretical mathematical models can adequately fit large data sets. Two large data sets of queries submitted to the Excite search service were sampled for search characteristics (term frequencies, terms used per query, pages viewed per query, queries submitted per session) producing data sets of various sizes that were fitted to theoretical models to determine how the sample may influence a model’s goodness-of-fit. Although theoretical models could adequately fit smaller data sets of up to 5000 observations in some cases, larger data sets could not be satisfactorily fitted using several goodness-of-fit techniques. Investigators must take into account that sample size does influence goodness-of-fit outcomes. The nature of the data and not the limitations of given goodness-of-fit tests results in significant outcomes. Such goodness-of-fit tests should be used for comparative purposes, rather than significance testing.

Predictors of the number of under-five malnourished children in Bangladesh: application of the generalized poisson regression model

Background

Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable.

Methods

The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model.

Results

The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance < mean) property. Our study also identify several significant predictors of the outcome variable namely mother’s education, father’s education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman.

Conclusions

Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh.

Women's employment and fertility: a welfare regime paradox

In this article we methodologically assess the paradox posited by other researchers of fertility: namely, why fertility is so much lower in the familialistic countries of Southern and Eastern Europe. We examine the relationship between individual attributes, aggregate female labor force participation, child care enrollment, family leave, and individual fertility in 20 developed countries using a hierarchical Bayesian model. Our results indicate that women's full-time employment and country-level employment rates decrease expected fertility in contrast to recent research which shows a reversal in the negative association between total fertility rates and female labor force participation during the 1980s. However, the positive association between child care enrollment and fertility indicates that child care services might mitigate some of the decline in fertility, possibly by reducing labor force exit among women with young children.

Testing approaches for overdispersion in poisson regression versus the generalized poisson model

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.

Generalized Poisson Distribution: the Property of Mixture of Poisson and Comparison with Negative Binomial Distribution

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.