Probability distributions of number of children and maternal age at various order births using age-specific fertility rates by birth order

In this study, a simple analytical framework to find the probability distributions of number of children and maternal age at various order births by making use of data on age-specific fertility rates by birth order was proposed. The proposed framework is applicable to both the period and cohort fertility schedules. The most appealing point of the proposed framework is that it does not require stringent assumptions. The proposed framework has been applied to the cohort birth order-specific fertility schedules of India and its different regions and period birth order-specific fertility schedules, including the United States of America, Russia, and the Netherlands, to demonstrate its usefulness.

Decadence in the Forest: Smyth's Der Wald in its Critical Context

Ethel Smyth’s opera, Der Wald, met with mixed reactions at its premiere in Berlin in 1902. Many factors contributed to this, not least, as Smyth herself observed, anti-British sentiment in Germany following the second Boer War. One might have expected that the reception of the opera at its British premiere on 18 July at Covent Garden might have been more positive, but even here critical opinion was divided. Even positive reviews were not free from gender discrimination, and other reviews condemned the opera for being too German or Wagnerian. What was meant by ‘Wagnerian’? This article answers the question in three ways. Firstly, I argue that ‘Wagnerian’ meant not a leitmotif-filled, through-composed work (as distinct from a number opera), but simply a lyrical drama; for British audiences the model for this was Tannhäuser or Lohengrin, not the Ring or Tristan. Secondly, taking this definition on board, I analyse the musical language of the opera, in particular the key structure. The central duet sung by the doomed lovers, Heinrich and Röschen, is in F major, almost the furthest possible distance from the home key of the opera (E major), which characterizes the forest and ‘nature’ in general; by contrast, the next scene, where the Kundry-like Iolanthe attempts to seduce Heinrich (a crucial reversal of the more conventional power relations of the love duet), sees a return to the home key. Thirdly, I set the hermeneutical implications of this reversal in the context of the decadent movement, with which late nineteenth-century Wagnerism was associated, and which, following the conviction of Oscar Wilde in 1895, was discredited. Der Wald thus failed because of its ‘guilt by association’ with an aesthetic that had fallen into disrepute.

Statistical Inference for Computable General Equilibrium Models with Application to a Model of the Moroccan Economy

We study the problem of measuring the uncertainty of CGE (or RBC)-type model simulations associated with parameter uncertainty. We describe two approaches for building confidence sets on model endogenous variables. The first one uses a standard Wald-type statistic. The second approach assumes that a confidence set (sampling or Bayesian) is available for the free parameters, from which confidence sets are derived by a projection technique. The latter has two advantages: first, confidence set validity is not affected by model nonlinearities; second, we can easily build simultaneous confidence intervals for an unlimited number of variables. We study conditions under which these confidence sets take the form of intervals and show they can be implemented using standard methods for solving CGE models. We present an application to a CGE model of the Moroccan economy to study the effects of policy-induced increases of transfers from Moroccan expatriates.

Use of a predictive model for food insecurity estimates in Brazil

In 2004 the National Household Survey (Pesquisa Nacional par Amostras de Domicilios - PNAD) estimated the prevalence of food and nutrition insecurity in Brazil. However, PNAD data cannot be disaggregated at the municipal level. The objective of this study was to build a statistical model to predict severe food insecurity for Brazilian municipalities based on the PNAD dataset. Exclusion criteria were: incomplete food security data (19.30%); informants younger than 18 years old (0.07%); collective households (0.05%); households headed by indigenous persons (0.19%). The modeling was carried out in three stages, beginning with the selection of variables related to food insecurity using univariate logistic regression. The variables chosen to construct the municipal estimates were selected from those included in PNAD as well as the 2000 Census. Multivariate logistic regression was then initiated, removing the non-significant variables with odds ratios adjusted by multiple logistic regression. The Wald Test was applied to check the significance of the coefficients in the logistic equation. The final model included the variables: per capita income; years of schooling; race and gender of the household head; urban or rural residence; access to public water supply; presence of children; total number of household inhabitants and state of residence. The adequacy of the model was tested using the Hosmer-Lemeshow test (p=0.561) and ROC curve (area=0.823). Tests indicated that the model has strong predictive power and can be used to determine household food insecurity in Brazilian municipalities, suggesting that similar predictive models may be useful tools in other Latin American countries.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

Characterization of the variable cow's age at last calving as a measurement of longevity by using the Kaplan-Meier estimator and the Cox model

In most studies on beef cattle longevity, only the cows reaching a given number of calvings by a specific age are considered in the analyses. With the aim of evaluating all cows with productive life in herds, taking into consideration the different forms of management on each farm, it was proposed to measure cow longevity from age at last calving (ALC), that is, the most recent calving registered in the files. The objective was to characterize this trait in order to study the longevity of Nellore cattle, using the Kaplan-Meier estimators and the Cox model. The covariables and class effects considered in the models were age at first calving (AFC), year and season of birth of the cow and farm. The variable studied (ALC) was classified as presenting complete information (uncensored = 1) or incomplete information (censored = 0), using the criterion of the difference between the date of each cow's last calving and the date of the latest calving at each farm. If this difference was >36 months, the cow was considered to have failed. If not, this cow was censored, thus indicating that future calving remained possible for this cow. The records of 11 791 animals from 22 farms within the Nellore Breed Genetic Improvement Program ('Nellore Brazil') were used. In the estimation process using the Kaplan-Meier model, the variable of AFC was classified into three age groups. In individual analyses, the log-rank test and the Wilcoxon test in the Kaplan-Meier model showed that all covariables and class effects had significant effects (P < 0.05) on ALC. In the analysis considering all covariables and class effects, using the Wald test in the Cox model, only the season of birth of the cow was not significant for ALC (P > 0.05). This analysis indicated that each month added to AFC diminished the risk of the cow's failure in the herd by 2%. Nonetheless, this does not imply that animals with younger AFC had less profitability. Cows with greater numbers of calvings were more precocious than those with fewer calvings. Copyright © The Animal Consortium 2012.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.

NLCHECK: Stata module to check linearity assumption after model estimation

nlcheck is a simple diagnostic tool that can be used after fitting a model to quickly check the linearity assumption for a given predictor. nlcheck categorizes the predictor into bins, refits the model including dummy variables for the bins, and then performs a joint Wald test for the added parameters. Alternative, nlcheck uses linear splines for the adaptive model. Support for discrete variables is also provided. Optionally, nlcheck also displays a graph of the adjusted linear predictions from the original model and the adaptive model

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.