A Weighted Least Squares Approach to Levene's Test of Homogeneity of Variance

In 1960 Levene suggested a potentially robust test of homogeneity of variance based on an ordinary least squares analysis of variance of the absolute values of mean-based residuals. Levene's test has since been shown to have inflated levels of significance when based on the F-distribution, and tests a hypothesis other than homogeneity of variance when treatments are unequally replicated, but the incorrect formulation is now standard output in several statistical packages. This paper develops a weighted least squares analysis of variance of the absolute values of both mean-based and median-based residuals. It shows how to adjust the residuals so that tests using the F -statistic focus on homogeneity of variance for both balanced and unbalanced designs. It shows how to modify the F -statistics currently produced by statistical packages so that the distribution of the resultant test statistic is closer to an F-distribution than is currently the case. The weighted least squares approach also produces component mean squares that are unbiased irrespective of which variable is used in Levene's test. To complete this aspect of the investigation the paper derives exact second-order moments of the component sums of squares used in the calculation of the mean-based test statistic. It shows that, for large samples, both ordinary and weighted least squares test statistics are equivalent; however they are over-dispersed compared to an F variable.     

Confidence intervals for secondary parameters following a sequential test

In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warrant a more detailed analysis, involving the estimation of parameters corresponding to effects that were not used to determine when to stop, and yet correlated with those that were. This paper describes methods for setting confidence intervals for secondary parameters in a way which provides the correct coverage probability in repeated frequentist realizations of the sequential design used. The method assumes that information accumulates on the primary and secondary parameters at proportional rates. This requirement will be valid in many potential applications, but only in limited situations in survival analysis.     

The exponentiated power exponential regression model with different regression structures: application in nursing data

We define the exponentiated power exponential distribution and propose a regression model with different systematic structures based on the new distribution. We show that the new regression model can be applied to dispersion data since it represents a parametric family of models that includes as sub-models some widely-known regression models. It then can be used more effectively in the analysis of real data. We use maximum likelihood estimation and derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. Some global-influence measurements are also investigated and simulation studies are performed to evaluate the accuracy of the estimates. We provide an application of the regression model with four systematic structures to nursing activities score data in the Unit of the Medical Clinic of University of São Paulo (USP) Hospital.     

Estimation of the intensity function of an inhomogeneous Poisson process with a change‐point

Recent work on point processes includes studying posterior convergence rates of estimating a continuous intensity function. In this article, convergence rates for estimating the intensity function and change‐point are derived for the more general case of a piecewise continuous intensity function. We study the problem of estimating the intensity function of an inhomogeneous Poisson process with a change‐point using non‐parametric Bayesian methods. An Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain estimates of the intensity function and the change‐point which is illustrated using simulation studies and applications. The Canadian Journal of Statistics 47: 604–618; 2019 © 2019 Statistical Society of Canada     

Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Infant Behavior and Competence Following Prenatal Exposure to a Natural Disaster: The QF2011 Queensland Flood Study

This study utilized a natural disaster to investigate the effects of prenatal maternal stress (PNMS) arising from exposure to a severe flood on maternally reported infant social–emotional and behavioral outcomes at 16 months, along with potential moderation by infant sex and gestational timing of flood exposure. Women pregnant during the Queensland floods in January 2011 completed measures of flood‐related objective hardship and posttraumatic stress (PTS). At 16 months postpartum, mothers completed measures describing depressive symptoms and infant social–emotional and behavioral problems (n = 123) and competence (n = 125). Greater maternal PTS symptoms were associated with reduced infant competence. A sex difference in infant behavioral problems emerged at higher levels of maternal objective hardship and PTS; boys had significantly more behavioral problems than girls. Additionally, greater PTS was associated with more behavioral problems in boys; however, this effect was attenuated by adjustment for maternal depressive symptoms. No main effects or interactions with gestational timing were found. Findings highlight specificity in the relationships between PNMS components and infant outcomes and demonstrate that the effects of PNMS exposure on behavior may be evident as early as infancy. Implications for the support of families exposed to a natural disaster during pregnancy are discussed.     

What are you thinking? Acculturation as an activating event for negative evaluative beliefs among Latinos/as

Negative evaluative beliefs and other cognitive structures have been tied to psychological distress across various populations but have not been sufficiently incorporated into acculturation models. The current study examines the relationships between acculturation and various activating events and mediating sources of support related to negative evaluative beliefs among people of Mexican descent (N = 319). Overall, model variables explained 26% of the variance in negative evaluative beliefs. Acculturation, marital commitment, and social capital associated with friends were negatively related to negative evaluative beliefs. Conversely, single relationship status, marital reward value, psychosocial stressors, and bridging social capital were positively related, and likely serve as activating events for negative evaluative beliefs. Identifying mechanisms related to psychological distress as well as supportive structures may help in constructing interventions that will address the specific needs of different groups. Future research should continue to explore appraisal and associated beliefs in acculturation models to understand why acculturative experiences may become stressful.     

Intergenerational cooperation within the household: a Public Good game with three generations

We analyze cooperation of individuals in a family context, using a Public Good game. In a lab experiment, 165 individuals from 55 three-generation families (youth, parent, and grandparent) play a repeated Public Good game in three different treatments: one in which three members of the same family play each other (family), a second with the youth and two non-family members, while preserving the previous generational structure (inter-generational), and a third in which three randomly-selected players play each other (random). We find that all the age groups cooperate more when playing with relatives, indicating that family ties may have a positive relationship to contributions to the Public Good. We also find that this trend is more evident for the youths and the parents than for the grandparents. Furthermore, young individuals tend to cooperate less than older generations, especially in non-family treatments. Our results serve as evidence of the relationship between family ties and inter-generational cooperative behaviors.

     

Is Sexual Abuse a Unique Predictor of Sexual Risk Behaviors,Pregnancy, and Motherhood in Adolescence?

This study tested sexual abuse as a unique predictor of subsequent adolescent sexual behaviors, pregnancy, and motherhood when in company with other types of maltreatment (physical abuse, neglect) and alternative behavioral, family, and contextual risk factors in a prospective, longitudinal study of maltreated (n = 275) and comparison (n = 239) nulliparous females aged 14–19 years old assessed annually through 19 years old. Hierarchical regression was used to disentangle risk factors that account for the associations of maltreatment type on risky sexual behaviors at 19 years old, adolescent pregnancy, and adolescent motherhood. Findings indicate that sexual and physical abuse remain significant predictors of risky sexual behaviors, and that sexual abuse remains a significant predictor of adolescent motherhood when alternative explanatory variables are controlled.