Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses.

The importance of plant life form on spatial associations along a subtropical coastal dune gradient

Questions Does the spatial association between isolated adult trees and understorey plants change along a gradient of sand dunes? Does this association depend on the life form of the understorey plant? Location Coastal sand dunes, southeast Brazil. Methods We recorded the occurrence of understorey plant species in 100 paired 0.25 m2 plots under adult trees and in adjacent treeless sites along an environmental gradient from beach to inland. Occurrence probabilities were modelled as a function of the fixed variables of the presence of a neighbour, distance from the seashore and life form, and a random variable, the block (i.e. the pair of plots). Generalized linear mixed models (GLMM) were fitted in a backward step-wise procedure using Akaike's information criterion (AIC) for model selection. Results The occurrence of understorey plants was affected by the presence of an adult tree neighbour, but the effect varied with the life form of the understorey species. Positive spatial association was found between isolated adult neighbour and young trees, whereas a negative association was found for shrubs. Moreover, a neutral association was found for lianas, whereas for herbs the effect of the presence of an adult neighbour ranged from neutral to negative, depended on the subgroup considered. The strength of the negative association with forbs increased with distance from the seashore. However, for the other life forms, the associational pattern with adult trees did not change along the gradient. Conclusions For most of the understorey life forms there is no evidence that the spatial association between isolated adult trees and understorey plants changes with the distance from the seashore, as predicted by the stress gradient hypothesis, a common hypothesis in the literature about facilitation in plant communities. Furthermore, the positive spatial association between isolated adult trees and young trees identified along the entire gradient studied indicates a positive feedback that explains the transition from open vegetation to forest in subtropical coastal dune environments.

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.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

On the relationship between squid and the environment: artisanal jigging for Loligo plei at Sao Sebastiao Island (24 degrees S), southeastern Brazil

The squid Loligo plei concentrates in the southeastern Brazil Bight, where it has traditionally supported small-scale fisheries around Sao Sebastiao Island (SSI). Sea surface temperature (SST), chlorophyll-a (Chl a), windspeed, wave height, rainfall, and lunar phase are related to fishing records and to the results of a survey of local fishers to investigate how they believe environmental variables might affect catches of L. plei. Daily fishery-dependent data over the years 2005-2009 were obtained from a fishing cooperative and were matched with satellite and meteorological forecast data. Generalized linear models were used to explore the significance of environmental variables in relation to variability in catch and catch per unit effort (cpue). Squid are fished with jigs in water shallower than 20 m, generally where SST is warmer and Chl a and windspeed are lower. Cpue and monthly catches decreased from 2005 to 2008, followed by a slight increase in 2009. The correlations between fishery and environmental data relate well to fishers` oceanological knowledge, underscoring the potential of incorporating such knowledge into evaluations of the fishery.

A mixed model QTL analysis for sugarcane multiple-harvest-location trial data

Sugarcane-breeding programs take at least 12 years to develop new commercial cultivars. Molecular markers offer a possibility to study the genetic architecture of quantitative traits in sugarcane, and they may be used in marker-assisted selection to speed up artificial selection. Although the performance of sugarcane progenies in breeding programs are commonly evaluated across a range of locations and harvest years, many of the QTL detection methods ignore two- and three-way interactions between QTL, harvest, and location. In this work, a strategy for QTL detection in multi-harvest-location trial data, based on interval mapping and mixed models, is proposed and applied to map QTL effects on a segregating progeny from a biparental cross of pre-commercial Brazilian cultivars, evaluated at two locations and three consecutive harvest years for cane yield (tonnes per hectare), sugar yield (tonnes per hectare), fiber percent, and sucrose content. In the mixed model, we have included appropriate (co)variance structures for modeling heterogeneity and correlation of genetic effects and non-genetic residual effects. Forty-six QTLs were found: 13 QTLs for cane yield, 14 for sugar yield, 11 for fiber percent, and 8 for sucrose content. In addition, QTL by harvest, QTL by location, and QTL by harvest by location interaction effects were significant for all evaluated traits (30 QTLs showed some interaction, and 16 none). Our results contribute to a better understanding of the genetic architecture of complex traits related to biomass production and sucrose content in sugarcane.

Atmospheric pollution: influence on hospital admissions in paediatric rheumatic diseases

Objective: To investigate the lag structure effects from exposure to atmospheric pollution in acute outbursts in hospital admissions of paediatric rheumatic diseases (PRDs). Methods: Morbidity data were obtained from the Brazilian Hospital Information System in seven consecutive years, including admissions due to seven PRDs (juvenile idiopathic arthritis, systemic lupus erythematosus, dermatomyositis, Henoch-Schonlein purpura, polyarteritis nodosa, systemic sclerosis and ankylosing spondylitis). Cases with secondary diagnosis of respiratory diseases were excluded. Daily concentrations of inhaled particulate matter (PM10), sulphur dioxide (SO2) nitrogen dioxide (NO2), ozone (O-3) and carbon monoxide (CO) were evaluated. Generalized linear Poisson regression models controlling for short-term trend, seasonality, holidays, temperature and humidity were used. Lag structures and magnitude of air pollutants' effects were adopted to estimate restricted polynomial distributed lag models. Results: The total number of admissions due to acute outbursts PRD was 1,821. The SO2 interquartile range (7.79 mu g/m(3)) was associated with an increase of 1.98% (confidence interval 0.25-3.69) in the number of hospital admissions due to outcome studied after 14 days of exposure. This effect was maintained until day 17. Of note, the other pollutants, with the exception of O-3, showed an increase in the number of hospital admissions from the second week. Conclusion: This study is the first to demonstrate a delayed association between SO2 and PRD outburst, suggesting that oxidative stress reaction could trigger the inflammation of these diseases. Lupus (2012) 21, 526-533.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the Sao Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p < 0.05) and lower physical activity levels (p < 0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p < 0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

Clinical correlates of social adjustment in patients with obsessive-compulsive disorder

Background: Patients with obsessive-compulsive disorder (OCD) frequently show poor social adjustment, which has been associated with OCD severity. Little is known about the effects that age at symptom onset, specific OCD symptoms, and psychiatric comorbidities have on social adjustment. The objective of this study was to investigate the clinical correlates of social functioning in OCD patients. Methods: Cross-sectional study involving 815 adults with a primary DSM-IV diagnosis of OCD participating in the Brazilian Research Consortium on Obsessive-Compulsive Spectrum Disorders. Patients were assessed with the Social Adjustment Scale, the Medical Outcomes Study 36-item Short-Form Health Survey, the Yale-Brown Obsessive-Compulsive Scale, the Dimensional Yale-Brown Obsessive-Compulsive Scale, and the Structured Clinical Interview for DSM-IV Axis I Disorders. Clinical correlates of social adjustment were assessed with generalized linear models with gamma distribution. Results: Poor overall social functioning was associated with greater OCD severity (p = 0.02); hoarding symptoms (p = 0.004); sexual/religious obsessions (p = 0.005); current major depressive disorder (p = 0.004); current post-traumatic stress disorder (p = 0.002); and current eating disorders (p = 0.02). Poor social adjustment was also associated with impaired quality of life. Conclusions: Patients with OCD have poor social functioning in domains related to personal relationships and professional performance. Hoarding symptoms and sexual/religious obsessions seem to have the strongest negative effects on social functioning. Early age at OCD symptom onset seems to be associated with professional and academic underachievement and impairment within the family unit, whereas current psychiatric comorbidity worsen overall social functioning. In comparison with quality of life, social adjustment measures seem to provide a more comprehensive overview of the OCD-related burden. (C) 2012 Elsevier Ltd. All rights reserved.