Generalized additive models for location, scale and shape

Summary.  A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y , as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton–Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.     

Factor analysis for ranked data with application to a job selection attitude survey

Summary.  Factor analysis is a powerful tool to identify the common characteristics among a set of variables that are measured on a continuous scale. In the context of factor analysis for non-continuous-type data, most applications are restricted to item response data only. We extend the factor model to accommodate ranked data. The Monte Carlo expectation–maximization algorithm is used for parameter estimation at which the E-step is implemented via the Gibbs sampler. An analysis based on both complete and incomplete ranked data (e.g. rank the top q out of k items) is considered. Estimation of the factor scores is also discussed. The method proposed is applied to analyse a set of incomplete ranked data that were obtained from a survey that was carried out in GuangZhou, a major city in mainland China, to investigate the factors affecting people's attitude towards choosing jobs.     

Proportional reversed hazard rate model and its applications

The purpose of this paper is to study the structure and properties of the proportional reversed hazard rate model (PRHRM) in contrast to the celebrated proportional hazard model (PHM). The monotonicity of the hazard rate and the reversed hazard rate of the model is investigated. Some criteria of aging are presented and the inheritance of the aging notions (of the base distribution) by the PRHRM is studied. Characterizations of the model involving Fisher information are presented and the statistical inference of the parameters is discussed. Finally, it is shown that several members of the proportional reversed hazard rate class have been found to be useful and flexible in real data analysis.     

Parenting Behaviors Among Mainland Puerto Rican Adolescent Mothers: The Role of Grandmother and Partner Involvement

Relations between grandmother and partner involvement (coresidence, social support, child care) and Puerto Rican adolescent mothers' parenting behaviors were examined. Few associations between grandmother involvement and behavior emerged, and these were moderated by coresidence. In contrast, partner involvement showed a number of significant (positive) direct and moderated relations with behavior. For both providers, the direction of the relations between social support and behavior during teaching was the opposite depending on coresidence: Greater social support was related to the display of more positive behavior among coresiding mothers but to less competent behavior among non‐coresiding mothers. The relations between child care support and behavior differed across providers. For grandmothers, greater child care was related to less positive behavior during teaching among coresiding mothers but to more competent behavior among non‐coresiding mothers. For partners, greater child care was more strongly related to positive behavior during play among non‐coresiding than coresiding mothers. Results are discussed in light of Latino cultural values, developmental issues, and implications for intervention.     

Silphids in urban forests: Diversity and function

Many ecologists have examined the process of how urbanization reduces biological diversity but rarely have its ecological consequences been assessed. We studied forest-dwelling burying beetles (Coleoptera: Silphidae)—a guild of insects that requires carrion to complete their life cycles—along an urban-rural gradient of land use in Maryland. Our objective was to determine how forest fragmentation associated with urbanization affects (1) beetle community diversity and structure and (2) the ecological function provided by these insects, that is, decomposition of vertebrate carcasses. Forest fragmentation strongly reduced burying beetle diversity and abundance, and did so far more pervasively than urbanization of the surrounding landscape. The likelihood that beetles interred experimental baits was a direct, positive function of burying beetle diversity. We conclude that loss of burying beetle diversity resulting from forest fragmentation could have important ecological consequences in urban forests.     

HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIES

To capture mean and variance asymmetries and time‐varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy‐tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time‐delay parameter. Self‐exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value‐at‐risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models.     

Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

Summary. The paper develops methods for the design of experiments for mechanistic models when the response must be transformed to achieve symmetry and constant variance. The power transformation that is used is partially justified by a rule in analytical chemistry. Because of the nature of the relationship between the response and the mechanistic model, it is necessary to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples are given of optimum designs, not only for single-response models, but also for experiments in which multivariate responses are measured and for experiments in which the model is defined by a set of differential equations which cannot be solved analytically. The extension to designs for checking models is discussed.