自激励门限自回归模型下我国人口增长率的时间序列分析

应用自激励门限自回归模型对我国1949年以来人口增长率的动态路径进行了模拟分析.通过估计和检验发现我国人口增长率具有明显的非线性特征,模型拟合的效果优于线性自回归模型,可以为政府决策提供更精确的数量依据.     

农业生产中四组数据的Logistic模型的参数确定

本文介绍了求非线性回归模型参数的基本理论,选择Logistic回归模型作为模型函数.以牧草再生长的数据集1为例,用Mathematica软件绘制了数据集1的点图.最后给出四组数据的拟合曲线和置信域.     

自回归移动平均模型在医疗服务需求预测中的应用

目的 拟合医疗服务需求时间序列资料的预测模型。方法 采用自回归移动平均模型对出院人次进行模型拟合。结果 模型拟合得到的最优模型为一阶自回归移动平均模型,模型预测2020年某市三甲医院的出院总人次将为93.88万人次。结论 自回归移动平均模型适用于出院总人次时间序列模型拟合,预测结果显示,在没有外来干预因素影响的情况下,三甲医院出院总人次将会延续2009年以前的上升趋势继续上涨。     

TRIA处理西葫芦的聚类分析及对早期产量影响的回归分析

本文以TRIA的6个浓度梯度对西葫芦进行处理,通过聚类分析及对早期产量的回归分析．结果表明：TRIA的适宜处理浓度范围为0.10～1.O0ppm,其中以0.50ppm效果最好,拟合的模型为Y=0.17＋0.82X-0.57X~2,有显著相关的非线性回归．     

度量误差模型及其应用

本文介绍度量误差模型的基本概念和参数估计的基本结果以及与通常回归之间的关系．并讨论了这个模型在生物学中应用的可能性．     

珍稀濒危植物的野外回归研究进展

由于人类干扰及气候变化,很多珍稀濒危植物面临加速灭绝风险,进行植物回归是实现其有效保护的方式之一.本文从回归生物学建立并变成生物多样性保护的重要工具、回归中的遗传多样性问题、全球气候变化下的回归、回归过程中的定居限制及其克服、回归与生态恢复等5个方面综述了植物回归研究进展,并对植物回归发展趋势进行了展望.     

长白山低山区森林土壤有机碳及养分空间异质性

以吉林延边汪清林业局金仓林场境内森林土壤为对象,采用多元线性回归方法和地统计学回归克里格方法,研究了土壤有机碳及养分的垂直分布规律,预测了其空间分布,并对预测结果进行插值.结果表明: 0～60 cm深度土壤有机碳密度为(16.14±4.58) kg·m^-2.随土壤深度增加,土壤有机碳含量、有机碳密度以及土壤全N、全P、全K、有效P及速效K含量都呈减小趋势,其中不同土层间土壤有机碳含量、有机碳密度差异显著(P<0.01).0～60 cm土层土壤有机碳含量和碳密度的拟合方程中,地形因子中高程和坡向余弦值是最优的拟合因子,方程的决定系数分别为0.34和0.39(P<0.01).0～20和0～60 cm土层的半方差函数模型分别为高斯模型和指数模型,利用回归克里格插值方法得到土壤有机碳的空间分布图.与普通克里格法相比,回归克里格法的空间预测精度改进了18%～58%.利用回归克里格插值方法预测了土壤全N的空间分布特征.     

三种预测林木生长量方法的比较

本研究选择了三种方法灰色GM(1,1)模型法、回归法、灰色线性回归组合模型法,经过数据的加载,灰色GM(1,1)为Ⅱ级合格模型,发展系数|a|＜0.3可用于中长期预测;在回归法中选用5个模型进行拟合,以Richards方程的复相关系高,残差平方和最小,被选中;灰色线性回组合模型达到Ⅲ级勉强可用模型.用三个模型分别对32、34龄阶的生长量进行预测,其平均相对精度分别为94.64%、80.68%、92.41%.     

基于分位数回归的长白落叶松人工林最大密度线

基于东北地区378块固定样地和415块临时样地的调查数据和Reineke方程,利用线性分位数回归技术建立了不同分位点(τ=0.90、0.95、0.99)下的长白落叶松人工林最大林分密度与林木平均胸径的关系模型,选出拟合长白落叶松人工林最大密度线的最优模型. 利用人为选取最大的拟合数据,采用最小二乘(OLS)和最大似然(ML)回归同时建立最大密度线模型. 采用极值统计理论的广义Pareto模型推算现实林分特定径阶的极限最大株数,进一步建立极限密度线模型. 将线性分位数回归模型与其他方法进行对比.结果表明: 在全部径阶范围内选取5个最大数据点拟合的方法能够得到现实林分的最大密度线,选取的样点过多会使模拟结果偏离最大密度线,且ML法要优于OLS法. 分位点为0.99的线性分位数回归模型能够取得与ML接近的拟合结果,但分位数回归模型参数的估计结果更稳定. 人为选取拟合数据具有一定的人为性,最终选取分位点为0.99的分位数回归模型为拟合最大密度线的最优模型,参数估计结果为k=11.790、β=-1.586,极限密度线模型的参数估计结果为k=11.820、β=-1.594. 所确定的极限密度线位置略高于最大密度线,但二者差异不明显. 由固定样地数据的验证结果可知,所建立的最大林分密度线及极限密度线能够对现实林分的最大密度及极限密度进行预测,为长白落叶松人工林的合理经营提供依据.     

遗传密码与氨基酸含量的非线性关系

本文利用回归分析方法给出了遗传密码与氨基酸含量之间的相关关系,结果表明;氨基酸的相对含量与遗传密码子数呈四次多项式回归,回归方程的复相关指数高达0.96以上,模型的平均拟合误差在2～7％之间．     

When is Piece-Wise Regression Really Necessary?

Results are obtained showing that when a response surface can be modelled as a single function, then a single regressor is more efficient and less biased than a segmented regression. However, if the surface is segmented, a segmented regressor is less biased than a single regressor. Areas of application are indicated.     

Bayesian Methods for Regression Using Surrogate Variables

If a dependent variable in a regression analysis is exceptionally expensive or hard to obtain the overall sample size used to fit the model may be limited. To avoid this one may use a cheaper or more easily collected “surrogate” variable to supplement the expensive variable. The regression analysis will be enhanced to the degree the surrogate is associated with the costly dependent variable. We develop a Bayesian approach incorporating surrogate variables in regression based on a two‐stage experiment. Illustrative examples are given, along with comparisons to an existing frequentist method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametric modal regression with varying precision

In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.     

An Improved Goodness of Fit Statistic for Probability Prediction Models

We consider the general case of probability prediction models having two or more outcomes and propose an adjusted χ² statistic which can be used to assess the goodness of fit of these models. We present a simulation study to show that our proposed statistic has an approximate χ² distribution under the null hypothesis. Two applications are provided to illustrate the use of the new statistic. The first application examines the fit of a logistic regression model using both the proposed statistic and the popular Hosmer-Lemeshow statistic and we compare and contrast these two methods. The second application evaluates the goodness of fit of a polychotomous regression model.     

Segmented linear regression models applied to the analysis of data from a cross-sectional growth experiment

Several different methods of analysis are applied to data consisting of weight measurements, taken at specified post-treatment times, of harvested thyroids from rats given one of four treatments. Previous studies of this type of data indicated that the growth is initially rapid, and that a second phase of less rapid growth is followed by a final phase in which little additional growth occurs. The data are further characterized by increasing variance through time. The primary purpose of the analysis is to study the effect of the treatments at the end of the study period. One-way analysis of variance tests among groups are performed on each day, but the results are not particularly helpful. However, results from two-way analyses of variance (over subsets of days and groups) are consistent with the three phase model and accordingly indicate significant group differences during each. Finally, maximum likelihood methods are used to fit a three part segmented linear regression model.     

Land use improves spatial predictions of mountain plant abundance but not presence‐absence

Question: Does a land‐use variable improve spatial predictions of plant species presence‐absence and abundance models at the regional scale in a mountain landscape? Location: Western Swiss Alps. Methods: Presence‐absence generalized linear models (GLM) and abundance ordinal logistic regression models (LRM) were fitted to data on 78 mountain plant species, with topo‐climatic and/or land‐use variables available at a 25‐m resolution. The additional contribution of land use when added to topo‐climatic models was evaluated by: (1) assessing the changes in model fit and (2) predictive power, (3) partitioning the deviance respectively explained by the topo‐climatic variables and the land‐use variable through variation partitioning, and (5) comparing spatial projections. Results: Land use significantly improved the fit of presence‐absence models but not their predictive power. In contrast, land use significantly improved both the fit and predictive power of abundance models. Variation partitioning also showed that the individual contribution of land use to the deviance explained by presence‐absence models was, on average, weak for both GLM and LRM (3.7% and 4.5%, respectively), but changes in spatial projections could nevertheless be important for some species. Conclusions: In this mountain area and at our regional scale, land use is important for predicting abundance, but not presence‐absence. The importance of adding land‐use information depends on the species considered. Even without a marked effect on model fit and predictive performance, adding land use can affect spatial projections of both presence‐absence and abundance models.     

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.     

An effective method for accurate nymphal-stage delimitation of the cicada Hyalessa fuscata

Subterranean nymphal development in cicadas presents challenges to researchers in accurately estimating the number of their developmental stages, although such information is crucial to understanding and predicting their population dynamics. While most studies have relied on head width as an attribute for life-stage determination to date, such character in cicadas can be highly variable and thus differentiation solely based on such morphology is prone to subjectivity in practice. Here, we propose a reliable method for instar estimation that is applicable to Hyalessa fuscata nymphs. We first obtained morphometrics of nymphs in all stages. Second, we computed logarithm-transformation and principal component analysis to extract a transformed variable that captures most of the variance of morphological characteristics. Third, k-means were computed to divide the dataset into distinct clusters assuming four-, five- and six life-stage scenarios for the best interferences of life stages. Finally, simple linear regression analysis was conducted to compare and select the best fit model. Our result shows that five nymphal stages best fit for H. fuscata nymphs. This method is expected to provide an easy-to-handle ecological tool for the study of life history of cicadas as well as other insects that have long life cycles and multiple developmental stages.     

Discretizing a Normal Prior for Change Point Estimation in Switching Regressions

Bayes decision procedures are considered for change point estimation in the simple bilinear segmented model. A discretized normal prior density is employed as the prior distribution for the change point index. Posterior probability functions are developed for this index under a vague prior formulation on the regression parameters. The procedure is applied to an example involving mercury toxicity data.     

Embracing asymmetry in nature: How to account for skewness in ecological data

Asymmetric regression is an alternative to conventional linear regression that allows us to model the relationship between predictor variables and the response variable while accommodating skewness. Advantages of asymmetric regression include incorporating realistic ecological patterns observed in data, robustness to model misspecification and less sensitivity to outliers. Bayesian asymmetric regression relies on asymmetric distributions such as the asymmetric Laplace (ALD) or asymmetric normal (AND) in place of the normal distribution used in classic linear regression models. Asymmetric regression concepts can be used for process and parameter components of hierarchical Bayesian models and have a wide range of applications in data analyses. In particular, asymmetric regression allows us to fit more realistic statistical models to skewed data and pairs well with Bayesian inference. We first describe asymmetric regression using the ALD and AND. Second, we show how the ALD and AND can be used for Bayesian quantile and expectile regression for continuous response data. Third, we consider an extension to generalize Bayesian asymmetric regression to survey data consisting of counts of objects. Fourth, we describe a regression model using the ALD, and show that it can be applied to add needed flexibility, resulting in better predictive models compared to Poisson or negative binomial regression. We demonstrate concepts by analyzing a data set consisting of counts of Henslow’s sparrows following prescribed fire and provide annotated computer code to facilitate implementation. Our results suggest Bayesian asymmetric regression is an essential component of a scientist’s statistical toolbox.