An Application of the Logistic Distribution to the Analysis of a Measles Epidemic

The relationship between the development of measles and age at immunization and time since immunization is examined using a trichotomous logistic distribution with maximum likelihood estimation of the parameters. The first and second partial derivatives used in the estimation scheme are presented.     

A generalized two-sex logistic model

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.     

比较逻辑斯蒂与地理加权逻辑斯蒂回归模型在福建林火发生的适用性

林火预测预报是科学有效进行林火管理的前提,是林业管理部门和科研工作者的广泛关注的领域。逻辑斯蒂回归(Logistic Regression,LR)是目前国内外广泛应用于森林火灾预测的模型方法,然而近年来有学者发现该方法没有充分考虑林火影响因子的空间相关性和异质性,从而导致模型拟合结果偏差。地理加权逻辑斯蒂回归(Geographically weighted logistic regression,GWR)模型考虑到了模型变量之间的空间相关性,有效提高的模型的拟合能力。为探讨GWLR模型在福建林火预测上的适用性,本研究应用LR和GWLR两种方法分别建立福建省森林火灾与气象因子的预测模型,通过模型拟合能力对比,判断在GWLR的适用性。研究以2000—2005年福建地区森林火灾卫星火点数据和每日气象因子为基础,将全样本分为60%的建模数据和40%的校验数据,并重复5次,建立5个样本组。选择在5个样本组中3个及以上表现显著的变量进入最终模型。研究结果表明GWLR在模型拟合度、模型残差、空间自相关性以及预测准确率等方面均优于LR模型,说明充分考虑模型变量的空间异质性有助于提高模型的预测精度,同时也验证了GWLR在福建地区林火预测上的适应性。此外,模型参数结果显示,"日最高地表气温"、"日最低地表气温"、"日平均风速"、"24小时降水量"、"日最高本站气压"、"日照时数"、"日最高气温"和"日最小相对湿度"8个因子对福建省林火发生有显著影响,研究结论为福建地区林火预测预报提供了新的方法。     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

Predicting observed and latent responses to BLUP selection involving logistic variates

Multivariate BLUPs can be derived when data are a mixture of continuous traits and observed discrete traits controlled by logistic latent traits. Algorithms were developed for predicting discrete responses to BLUP selection, and latent responses when the selection process included additional culling on scores. These algorithms were Taylor expansions using well-known expressions such as the probabilities and the two first moments of the truncated multinormal distribution, after appropriate re-parametrizations. They were compared to very accurate quadrature integrations. The test examples were suggested by a situation found in chickens where selection can involve body weight and leg deformity described by two logistic latent variates. Quadratic Taylor expansions generally provided a good accuracy. Therefore, they could be recommended when quadrature methods are too demanding, e.g., for complex breeding schemes.     

Pattern of growth in weight of alate and apterous nymphs of the English grain aphid, Sitobion avenae

Daily increase in fresh weight was recorded for apterous and alate nymphs of S. avenae at 20°C. Comparison with a control group indicated that daily disturbance and weighing of nymphs did not affect significantly their growth, developmental time or survival. The increase in fresh weight of apterous and alate virginoparae at 20°C was best described by logistic equations. Alate virginoparae were significantly heavier than apterous virginoparae at birth and throughout most of their nymphal life, but they experienced a weight loss at the final ecdysis. The relative growth rate did not remain constant, but declined during development. The decline is associated with a decline in honeydew production per unit body weight. The implications of an inconstant relative growth rate and the marked loss in weight at the adult moult in alates are discussed.

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Résumé L'enregistrement de l'augmentation quotidienne du poids frais à 20°C des larves ailées et aptères de S. avenae a montré que des perturbations quotidiennes n'affectent pas significativement la croissance, la durée du développement et la survie. Les équations logistiques décrivent plus exactement l'augmentation de poids frais des aptères et des ailés virginipares à 20°C. Les virginipares ailés étaient significativement plus lourds que les virginipares aptères à la naissance et pendant la plus grande partie de la vie larvaire, mais présentaient une perte de poids à la mue finale. Le taux de croissance relative ne restait pas constant, mais diminuait au cours du développement. La diminution était associée à une diminution de la production de miellat par unité de poids du corps. La discussion porte sur les conséquences de la variation de l'augmentation du poids relatif et de la perte marquée de poids à la mue imaginale.

     

Habitat suitability for tsessebe Damaliscus lunatus lunatus

The distribution and numbers of tsessebe (Damaliscus lunatus lunatus) have declined considerably in South Africa, partly due to deteriorating habitat conditions. Identifying important habitat variables will assist in managing the species. The objective of this study was to identify habitat variables important for tsessebe and to develop a predictive model of habitat selection for this species in a savanna biome. The study was conducted in the Nylsvley Nature Reserve over a 2‐year period. A total of eighteen habitat variables were measured in ten plant communities at 200 sites. Logistic regression analyses were used to identify predictor variables and to construct a habitat model. Tsessebe were found <2 km from the nearest source of water, in flat areas with slopes of <3° and with <10% rockiness. Their distribution was not influenced by the woody component. Sites where tsessebe were present had significantly lower grass heights and tuft heights, with a higher grass density compared with areas not utilized by tsessebe. Nitrogen and sodium levels were also higher at present sites. Habitat type and grass height were the most significant predictors of tsessebe presence. The selected model had an overall percentage prediction of 85.0%. The model was subdivided into five vegetation‐specific models and each model was tested with independent data.     

Modification of the Minimum Logit Chi-Squared Estimator in Simple Linear Logistic Regression

A new modification of Berkson's minimum logit chi-squared estimator in simple linear logistic regression is suggested in order to achieve reduction of first order bias of the estimator as well as in the model. Furthermore, unlike estimators currently available, our procedure is quite simple to apply in practice and is valid even in the presence of zero frequencies in the table.     

Identifying Populations at High Risk for Occupational Back Injury with Neutral Networks

For this study a simulation is conducted to investigate the accuracy of neural networks and logistic regression in identifying populations at high risk for occupational back injury. In contrast to most standard regression techniques, neural networks do not rely on linearity or explicitly specifying the nature of the association. Because the underlying relationships between work exposures, personal risk factors, and injury are often not well defined, neural networks may prove useful for injury risk assessment. Accuracy was assessed by comparing the injury status to the predicted level of risk in each worker. In simulations of a non-linear association, workers (used in the training data) were correctly classified 85% of the time with neural networks, 74% of the time with the main effects logistic model, and 79% of the time with the fully-specified logistic model. Using the test data, however, workers were correctly classified 67% of the time with neural networks, and 71% and 69% of the time with the main effects and fully specified logistic models, respectively. Simulations of a null association indicated that neural networks may be more likely to overfit random associations. These findings provide a valuable guide concerning statistical methodology for identifying high-risk worker populations.     

Brief communication: discrimination between European-American and African-American children based on deciduous dental metrics and morphology

This study employs metric and morphological features of the deciduous dentition for discriminating between European-American and African-American children and providing allocation rules (regression equations). Five logistic regression equations are presented, with the percentage of correct allocation to group of between 90.1-92.6%. All five equations employ three metric traits (the mesiodistal diameters of the mandibular deciduous canines and anterior and posterior deciduous premolars) and one morphological feature (cusp number of the maxillary deciduous anterior premolar). In addition to these four variables, only two or three additional morphological features are added in carious combinations in the final equations. Correct allocation to group is 4-12% greater when combining metric and morphological features compared to using the features separately.     

方程N′(t)=r(t)N(t)(1-bN(t-τ)-cN~2(t-τ))正平衡点的全局吸引性

本文给出保证平方Ｌｏｇｉｓｔｉｃ方程Ｎ′（ｔ）＝ｒ（ｔ）Ｎ（ｔ）（ｌ-ｂＮ（ｔ-τ）－ｃＮ２（ｔ-τ））的每一正解Ｎ（ｔ）趋于正平衡点Ｎ*的一组充分条件．改进了 Ｇａｐａｌｓａｍｙ,Ｌａｄａｓ和罗交晚等人的结果．     

Nesting habitat preference of the African White-backed Vulture Gyps africanus and the effects of anthropogenic disturbance

The African White-backed Vulture Gyps africanus is widely distributed across sub-Saharan Africa but populations are in decline. Loss of suitable habitat for foraging and breeding are among the most important causes, and future conservation will require identification of suitable remaining habitat and the threats to it and to the vultures in it. Like many large raptors, African White-backed Vultures have a long breeding cycle and thus spend much of each year near their nest site, but ecological correlates of nest sites have not been quantified for any African vulture species. We use nest-site data for African White-backed Vultures collected during aerial and ground surveys and habitat data derived from a GIS to develop statistical models that estimate the probability of nest presence in relation to habitat characteristics, and test these models against an independent dataset. The models predicted that both direct and indirect disturbance by humans limit the potential distribution. Suitable habitat needs to be identified and receive adequate protection from poaching. Poaching of vultures is thought to be mainly for use in traditional medicine and does not target any particular species, so all vulture species can be considered equally at risk. We predict the likelihood of individuals nesting in currently unprotected areas should they become protected. These predictions show that readily available GIS data combined with relatively simple statistical modelling can provide meaningful large-scale predictions of habitat availability.     

Seasonal incidence of hospital admissions for Stanford type A aortic dissection

The objective of this study was to test the hypothesis that there is seasonal variation in the incidence of Stanford type A aortic dissection (SA-AoD) among patients admitted to our cardiovascular surgical service. A sinusoidal logistic regression model was used to analyze event data for 6081 calendar days. A cyclic peak risk for SA-AoD was observed for calendar day 304 (p?=?0.019). The odds ratios for the 3- and 6-month window surrounding this peak were 1.6 (p?=?0.054) and 1.7 (p?=?0.0040), respectively. Our results suggest than a seasonal variation exists in the incidence of SA-AoD.     

An assessment of non-randomized medical treatment of long-term schizophrenia relapse using bivariate binary-response transition models

The analyses of observational longitudinal studies involving concurrent changes in treatment and medical conditions present difficulties because of the multitude of directions of potential relationships: past medication influences current symptoms; past symptoms influence current medication; and current medication is associated with current symptoms. In the context of a long-term study of non-randomized pharmacological treatment of schizophrenic relapse, we present an analysis of bivariate discrete-time transitional data with binary responses in an attempt to understand the transitional and concurrent relationships between schizophrenia relapse and medication use. A naive analysis does not show any association between previous medication and current relapse. However, we provide evidence suggesting that current treatment may impact current relapse for those who have previously taken medication, but not for those who haven't taken medication in the past. When univariate models are specified to assess these associations, the bivariate nature of the problem requires a choice of which response, relapse or medication, should be the dependent variable. In this case, the choice of relapse or medication as a dependent variable does matter. Hence, our results derive from models where both relapse and medication are treated as dependent variables. Specifically, we specify a bivariate log odds ratio for current relapse and current medication use and a separate univariate logit component for each of these outcomes. Each of these components contains transitional associations with previous relapse and medication. Such models represent extensions of univariate transitional association models (e.g. Diggle et al. (1994)) and correspond to bivariate transitional models (e.g. Zeger and Liang (1991)). We incorporate changes in transitional associations into the full-data parametric model for final inference, and investigate if these temporal changes are due to learning effects or the impact of drop-out. We also perform residual analyses and sensitivity analyses in the context of missing data patterns.     

A note on ‘A generalized two-sex logistic model’

We re-visit the recently published paper on a generalization of the two-sex logistic model by Maxin and Sega [A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302–318]. We show that the logistic assumption of a non-increasing birth rate can be replaced by a more general assumption of a non-increasing ratio between the female/male birth and mortality rate. In this note we indicate the changes necessary in the proofs of the theorems in [D. Maxin and L. Sega, A generalized two-sex logistic model, J. Biol. Dyn. 7(1) (2013), pp. 302–318] and discuss several situations where this new assumption is useful.     

补料分批培养过程模拟

引用广义对数方程描述了两次恒流补料分批培养的全过程。结果表明：过程模拟的好坏很大程度上取决于模拟精度的选择;微生物比生长速度μ及限制底物比消耗速度qs,与微生物细胞中棱糖核酸的含量存在某种定量关系。     

基于逻辑斯蒂回归模型的鹭科水鸟栖息地适宜性评价

近年来湿地生态系统遭到不同程度破坏,湿地水鸟及其生存空间日益受到威胁。以香港米埔-后海湾湿地为例,收集2003年1月份与鹭科水鸟密切相关的15个自变量和鹭科水鸟实测数据作为因变量构建逻辑斯蒂回归模型,通过筛选获取9个变量因子,分别为土地利用,NDVI,坡度,降雨,TM4纹理,TM3纹理,道路密度,道路距离,人居密度。经Nagelkerke R2检验模型精度达到0.743,拟合度较高。利用模型结果快速聚类,对栖息地进行适宜性分级,分级结果与同期鹭科水鸟实测数据做拟合,精度达到77.4%。最后采集2009年1月份各变量因子数据对回归方程进行时间尺度检验,与同期实测鹭科水鸟数据拟合精度同样达到75.8%,模型具有较好的通用性。