Estimating detailed distributions from grouped sociodemographic data: ‘get me started in’ curve fitting using nonlinear models

In much demographic analysis, it is important to know how occurrence-exposure rates or transition probabilities vary continuously by age or by time. Often we have coarse or fluctuating data so there can be a need for estimation and smoothing. Since the distributions of rates or counts across age or another variable are often curved, a nonlinear model is likely to be appropriate. The main focus of this paper is on the estimation of detailed information from grouped data such as age and income bands; however, the methods we outline could also be applied to other settings such as smoothing rates where the original data are ragged. The ability to carry out curve fitting is a very useful skill for population geographers and demographers. Curve fitting is not well covered in statistics textbooks, and whilst there is a large literature in journals thoroughly discussing the detail of functions which define curves, these texts are likely to be inaccessible to researchers who are not specialists in mathematics. We aim here to make nonlinear modelling as accessible as possible. We demonstrate how to carry out nonlinear regression using SPSS, giving stepped-through hypothetical and research examples. We note other software in which nonlinear regression can be carried out, and outline alternative methods of curve fitting.     

GMM inference in spatial autoregressive models

In this study, we investigate the finite sample properties of the optimal generalized method of moments estimator (OGMME) for a spatial econometric model with a first-order spatial autoregressive process in the dependent variable and the disturbance term (for short SARAR(1, 1)). We show that the estimated asymptotic standard errors for spatial autoregressive parameters can be substantially smaller than their empirical counterparts. Hence, we extend the finite sample variance correction methodology of Windmeijer (2005 Windmeijer, F. (2005). A finite sample correction for the variance of linear efficient two-step GMM estimators. Journal of Econometrics 126(1):25–51.[Crossref], [Web of Science ®] , [Google Scholar]) to the OGMME for the SARAR(1, 1) model. Results from simulation studies indicate that the correction method improves the variance estimates in small samples and leads to more accurate inference for the spatial autoregressive parameters. For the same model, we compare the finite sample properties of various test statistics for linear restrictions on autoregressive parameters. These tests include the standard asymptotic Wald test based on various GMMEs, a bootstrapped version of the Wald test, two versions of the C(α) test, the standard Lagrange multiplier (LM) test, the minimum chi-square test (MC), and two versions of the generalized method of moments (GMM) criterion test. Finally, we study the finite sample properties of effects estimators that show how changes in explanatory variables impact the dependent variable.     

Comparing the Distribution of Education Across the Developing World, 1960–2005: What Does the Grade Enrollment Distribution Tell about Latin America?

The present paper introduces a new indicator of educational inequality, the grade distribution ratio (GDR), focusing on levels of grade repetition and drop out rates in primary and secondary education. The indicator is specifically suitable to evaluate the distributive implications of expanding educational systems in developing countries. A comparative analysis of grade enrollment distributions across 92 developing countries from 1960 to 2005 reveals that the decline in educational inequality has been substantial and wide spread since 1960, but that progress has slowed down in the last two decades. Latin American countries were characterized by very large initial levels of educational inequality, but contrary to other developing regions continued to equalize their grade enrollment distribution in the last two decades.

Relationship Between Sarcopenia and Fracture Risks in Obese Postmenopausal Women

ABSTRACT

It is known that obesity is inversely correlated with fracture risk. It remains unclear if a low muscle mass (sarcopenia) modulates the relationship between obesity and bone mass density. Twenty-seven obese women were matched for total fat mass (± 0.5 kg) and age (± 4 yrs) and divided in 3 equal groups: class II sarcopenic, class I sarcopenic, and nonsarcopenic. Body composition (DXA) and dietary intake were measured. Our results suggest that obesity may offer some protection against osteoporosis, even in sarcopenic postmenopausal women. However, further studies are needed to examine the actual implication of these results on a clinical standpoint.     

A Central Limit Theorem in Non‐parametric Regression with Truncated,Censored and Dependent Data

On the basis of the idea of the Nadaraya–Watson (NW) kernel smoother and the technique of the local linear (LL) smoother, we construct the NW and LL estimators of conditional mean functions and their derivatives for a left‐truncated and right‐censored model. The target function includes the regression function, the conditional moment and the conditional distribution function as special cases. It is assumed that the lifetime observations with covariates form a stationary α‐mixing sequence. Asymptotic normality of the estimators is established. Finite sample behaviour of the estimators is investigated via simulations. A real data illustration is included too.     

Be Careful Where You Smile: Culture Shapes Judgments of Intelligence and Honesty of Smiling Individuals

Smiling individuals are usually perceived more favorably than non-smiling ones—they are judged as happier, more attractive, competent, and friendly. These seemingly clear and obvious consequences of smiling are assumed to be culturally universal, however most of the psychological research is carried out in WEIRD societies (Western, Educated, Industrialized, Rich, and Democratic) and the influence of culture on social perception of nonverbal behavior is still understudied. Here we show that a smiling individual may be judged as less intelligent than the same non-smiling individual in cultures low on the GLOBE’s uncertainty avoidance dimension. Furthermore, we show that corruption at the societal level may undermine the prosocial perception of smiling—in societies with high corruption indicators, trust toward smiling individuals is reduced. This research fosters understanding of the cultural framework surrounding nonverbal communication processes and reveals that in some cultures smiling may lead to negative attributions.     

Why resilient workers perform better: The roles of job satisfaction and work engagement

Previous studies have confirmed correlations between resilience and job performance, but surprisingly little is known about the nature of this relationship. This study sheds light on the roles of two important positive dimensions of work-related well-being: job satisfaction and work engagement. Data were collected from 360 Czech workers in helping professions using an online survey. Levels of resilience and perceived job performance were indeed positively associated. Using structural equation modeling, the best-fitting model showed partial mediation by work engagement; conversely, job satisfaction was not found to be a mediator of this relationship. Additionally, the finding that job performance is related more strongly to work engagement than to job satisfaction contributes to the debate about the concurrent validity of job attitudes.     

Augmentation schemes for particle MCMC

Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how particle MCMC can be generalised beyond this. Our key idea is to introduce new latent variables. We then use the MCMC moves to update the latent variables, and the particle filter to propose new values for the parameters and stochastic process given the latent variables. A generic way of defining these latent variables is to model them as pseudo-observations of the parameters or of the stochastic process. By choosing the amount of information these latent variables have about the parameters and the stochastic process we can often improve the mixing of the particle MCMC algorithm by trading off the Monte Carlo error of the particle filter and the mixing of the MCMC moves. We show that using pseudo-observations within particle MCMC can improve its efficiency in certain scenarios: dealing with initialisation problems of the particle filter; speeding up the mixing of particle Gibbs when there is strong dependence between the parameters and the stochastic process; and enabling further MCMC steps to be used within the particle filter.     

The relationship between vitamin D level and erectile dysfunction in patients with type 2 diabetes mellitus

Recent studies have suggested that a relationship could exist between 25-hydroxyvitamin D [25(OH)D] deficiency and erectile dysfunction (ED). The present study evaluated the relationship between 25(OH)D levels and ED in male patients with type 2 diabetes mellitus (DM). The study included 98 patients with type 2?DM aged between 18–80 years. The International Index of Erectile Function (IIEF-5) Questionnaire was administered. The patients were divided into three groups according to IIEF-5 scoring: IIEF-5 score between 5–10, severe ED; IIEF-5 score between 11–20, moderate ED; IIEF-5 score between 21–25, no ED. Biochemical parameters, 25(OH)D and hormonal analysis tests were obtained in all patients. All parameters were compared between these three groups. Of 98 patients included in the study, 32 had severe ED, 45 had moderate ED and 21 had no ED. The mean age was 55.12?±?9.39 years and the mean 25(OH)D level was 13.69?±?8.15?ng/ml. When the three groups were compared, 25(OH)D levels were significantly lower in patients with the IIEF-5 score between 5–10 (p?=?0.020). There was a moderate positive relationship between IIEF-5 score and 25(OH)D level (r?=?0.21, p?=?0.038). The patients with severe ED have considerably lower 25(OH)D levels.