A Gauss-Newton-Based Broyden’s Class Algorithm for Parameters of Regression Analysis

In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical results show that the proposed method is interesting.

The Shortest Width Confidence Interval for Odds Ratio in Logistic Regression

The shortest width confidence interval (CI) for odds ratio (OR) in logistic regression is developed based on a theorem proved by Dahiya and Guttman (1982). When the variance of the logistic regression coefficient estimate is small, the shortest width CI is close to the regular Wald CI obtained by exponentiating the CI for the regression coefficient estimate. However, when the variance increases, the optimal CI may be up to 25% narrower. It is demonstrated that the shortest width CI is favorable because it has a smaller probability of covering the wrong OR value compared with the standard CI. The closed-form iterations based on the Newton's algorithm are provided, and the R function is supplied. A simulation study confirms the superior properties of the new CI for OR in small sample. Our method is illustrated with eight studies on parity as a preventive factor against bladder cancer in women.

Stepwise Regression： An Application in Earthquakes Localization

In this paper, an overview of an important feature in statistics field has shown： the stepwise multiple linear regression. Likewise, a link between stepwise multiple linear regression and earthquakes localization has been descripted. Precisely, the aim of this research is showing how stepwise multiple linear regression contributes to solution of earthquakes localization, describing its conditions of use in HYPO71PC, a software devoted to computation of seismic sources’ collocation. This aim is reached treating a concrete case, that is computation of earthquakes localization happening on Mount Vesuvius, Italy.

Identifying the dependency pattern of daily rainfall of Dhaka station in Bangladesh using Markov chain and logistic regression model

Bangladesh is a subtropical monsoon climate characterized by wide seasonal variations in rainfall, moderately warm temperatures, and high humidity. Rainfall is the main source of irrigation water everywhere in the Bangladesh where the inhabitants derive their income primarily from farming. Stochastic rainfall models were concerned with the occurrence of wet day and depth of rainfall for different regions to model the daily occurrence of rainfall and achieved satisfactory results around the world. In connection to the Markov chain of different order, logistic regression is conducted to visualize the dependence of current rainfall upon the rainfall of previous two-time period. It had been shown that wet day of the previous two time period compared to the dry day of previous two time period influences positively the wet day of current time period, that is the dependency of dry-wet spell for the occurrence of rain in the rainy season from April to September in the study area. Daily data are collected from meteorological department of about 26 years on rainfall of Dhaka station during the period January 1985-August 2011 to conduct the study. The test result shows that the occurrence of rainfall follows a second order Markov chain and logistic regression also tells that dry followed by dry and wet followed by wet is more likely for the rainfall of Dhaka station and also the model could perform adequately for many applications of rainfall data satisfactorily.

Customer Retention: Behaviour Perspective Model of Ghanaian Telecommunication Industry Using Multinomial Regression Analysis

To stay competitive, the mobile telecommunication companies spend millions of Ghana cedi each year on building long-term relationships with their customers. Marketing managers are constantly challenged with the problem of where to channel the limited resources in order to retain existing customers. This study approaches the customer retention problem in the mobile phone sector from a behavioural perspective, applying the Behavioural Perspective Model as the main analytical framework and further exploits some other factors that influence customer retention. The model includes a set of pre-behaviour and post-behaviour factors to study consumer choice, and explains its relevant drivers in a viable and comprehensive way, grounded in radical behaviourism. Data for the analysis were collected from tertiary students from Accra and Takoradi. Data collected were analysed using the multinomial regression technique. Analysis of the data revealed that the Behaviour setting factor is the only significant element in Behaviour Perspective Model. Further exploitation of behaviour situation revealed that the number of networks a customer uses, previous experience of a customer and customer’s intention are significant factors in determining customer retention in Ghana’s mobile telecommunication industry.

Regression of Barrett＇s Esophagus： Is There a Difference between Clinical and Surgical Treatment？

Objective： To evaluate the response to clinical and surgical treatment of Walter Cantidio University Hospital patients who were diagnosed with Barrett＇s esophagus between 2012 and 2016. Methodology： From the database analysis of Walter Cantidio University Hospital＇s pathology service, we identified all patients with a diagnosis of Barrett＇s esophagus between 2012 and 2016. We analyzed the patients＇ medical records and collected epidemiological and clinical data. Results： 22 patients were included in the study, 13 of whom were surgically treated and 9 were clinically treated. The regression was 33.3% in the clinical group and 30.7% in the surgical group, with no statistical difference between these two groups. Conclusions： The results show synchrony with data from the medical literature regarding the response of Barrett＇s esophagus to clinical and surgical treatment.

The Prediction of Engel's Coefficient and Education Expenditure Based on the Linear Regression Model for Heilongjiang and Ontario

It is meaningful to study trends in food and education expenditure as proportions of total household expenditure.In this study,based on year 2006 to 2017 data from Heilongjiang province in China and Ontario province in Canada,a linear regression model is used to forecast the Engel’s coefficients(proportion spent on food)and the education proportion from year 2018 to 2027 for those two regions.The results suggest that in both regions the Engel’s coefficients show a decreasing trend,while the education expenditure proportions show an increasing trend.The ratios of education expenditure to food expenditure in both places show an increasing trend.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

App Store Analysis: Using Regression Model for App Downloads Prediction

App store provides rich information for software vendors and customers to understand the market of mobile applications. However, app store analysis don’t consider some vital factors such as version number, app description and app name currently. In this paper we propose an approach that App Store Analysis can be used to predict app downloads. We use data mining to extract app name and description and app rank information etc. from the Wandoujia App Store and AppCha App Store. We use questionnaire and sentimentanalysis to quantify some app nonnumeric information. We revealed strong correlations app name score, app rank, app rating with app downloads by Spearman’s rank correlation analysis respectively. Finally, we establish a multiple nonlinear regression model which app downloads defined as dependent variable and three relevant attributes defined as independent variable. On average, 59.28 % of apps in Wandoujia App Store and 66.68 % of apps in AppCha App Store can be predicted accurately within threshold which error rate is 25 %. One can observe the more detailed classification of app store, the more accurate for regression modeling to predict app downloads. Our approach can help app developers to notice and optimize the vital factors which influence app downloads.

ASD与非ASD语言发育迟缓儿童的语言行为能力差异分析

目的通过比较孤独症谱系障碍(autism spectrum disorder,ASD)与非ASD语言发育迟缓儿童的各项语言行为能力,分析两者的特征差异。方法回顾收集2020年1月至2022年12月就诊的确诊为ASD(98例)和非ASD(122例)语言发育迟缓儿童的年龄、性别、ABC量表和S-S量表得分资料,对两组儿童的结果先进行单因素分析,对单因素分析有统计学差异的项目进行多因素二元logistic回归分析。结果经单因素分析,两组儿童年龄无统计学差异,其他项目包括性别,S-S交流态度能力、S-S操作性课题能力、S-S语言理解能力、S-S语言表达能力和ABC总分均有统计学差异(均P<0.05)。采用输入法把两组有差异的性别、S-S交流态度能力、S-S操作性课题能力、S-S语言理解能力、S-S语言表达能力和ABC总分共6个项目进行多因素二元logistic回归分析,结果表明S-S交流态度能力和ABC总分两个项目是区分两组儿童的独立影响因素(均P<0.05),S-S交流态度不良和ABC总分高均是危险因素。结论S-S交流态度能力和ABC总分是区分ASD和非ASD语言发育迟缓儿童的独立影响因素,临床上对于S-S交流态度不良及ABC总分高的语言发育迟缓儿童要高度警惕是否ASD儿童。

基于ADS-B与Mode-SEHS联合观测的民航空域风场重建方法

准确实时的风场数据对保障民航飞行安全有着重要作用,针对风场的精确重构问题,提出了一种基于飞行器监测数据的风场重建方法。旨在利用广播式自动相关监视和S模式增强型监视联合观测数据计算空域内的风观测值,并结合机器学习中的高斯过程回归模型,利用时间和空间上离散的风观测值进行模型训练,完整重建目标空域风场。实验结果表明,重建的风场风速的平均绝对误差为2.72m/s,相对误差为8.21%,风向的平均绝对误差为3.66°,证明了方法能够快速地完成准确实时的风场重建。

广义S形曲线及其非线性回归分析

在给出S形曲线特征关系式的基础上,推导出满足该关系式的广义S形曲线的解析式: y_i=a[1+bd exp(-cx)]^(-1/d)+ε_i,i=1,2,…,n.从而使得非线性回归分析中较为困难的期望函数和参数初估值的选取问题得以较好解决。以SAS软件编程处理的实例分析结果,肯定了广义S形曲线作为备择期望函数所具有的普适性和灵活性。

基于SPSS回归分析的锂渣混凝土抗压强度预测模型

利用SPSS软件的逐步回归分析法、多元非线性回归法建立锂渣混凝土的强度预测模型,分析各模型的残差图、预测值与试验值的对比,并结合均方根误差、平均绝对误差、平均绝对百分比误差和模型可决系数值对各模型的精确度等进行综合评价,最终确定出较优的锂渣混凝土强度预测模型。结果表明:水胶比、锂渣掺量和减水剂掺量对锂渣混凝土强度的影响十分显著;经残差分析和95%预测值区间检验,5个建议模型都有较好的精确度;经综合评价建议最佳的锂渣混凝土强度预测模型是以水泥强度、胶水比、锂渣掺量和减水剂掺量为自变量的非线性回归方程,其相应的可决系数R2=0.920,均方根误差为3.684,平均绝对误差为3.15,平均绝对百分比误差为5.44。

基于Sen+Mann-Kendall的北京植被变化趋势分析

基于1998年到2011年长时序SPOTVEGETATION归一化植被指数数据,采用一元线性回归斜率变化法和Sen+Mann-Kendall法对北京地区的植被变化趋势做了时空分析。实验结果表明:在1998年到2011年期间,北京市城区、延庆县、怀柔区和平谷区的植被变化趋势显著上升;而植被恶化区则集中在北京市城区北部、东部和南部,并以马蹄形包围北京市区。两种方法实验结果在植被上升(下降)区域具有一致性。同时,Sen+Mann-Kendall法以其良好的抗噪性和对数据分布无要求性可广泛应用到其他区域的植被变化趋势分析中。

基于GWR和改进CLUE-S模型的区域土地利用格局模拟研究——以浙江省桐庐县为例

本文以浙江省桐庐县为研究区,在CLUE-S模型空间分析模块的回归建模中,考虑驱动因子对土地利用格局影响的空间不稳定性,用GWR Logistic模型取代全局最小二乘法(OLS)Logistic回归模型来建立土地利用格局与其驱动因子之间的回归模型,实现了对CLUE-S模型的改进,并进行土地利用格局模拟的实证研究与模型比较。研究结果表明,运用GWR Logistic对CLUE-S模型进行改进,不但可以获得更高的模拟准确率,而且可以获得各驱动因子对土地利用格局影响的空间分异特征。同时,运用改进的模型定量地分析影响区域土地利用变化的内在机制,进行土地利用格局的动态模拟,预测土地利用未来变化的趋势,可以为桐庐县及其类似地区的土地利用规划决策提供科学依据。

基于CLUE-S模型的煤矿城市土地利用变化模拟

以淮南市为研究区,选择1985、1995、2005、2016年土地利用数据,在分析土地利用动态变化特征的基础上,利用CLUE-S模型模拟预测了未来土地利用格局。结果表明:1985-2016年,研究区耕地面积减少11.62%;建设用地和水体面积百分比分别增加7.98个百分点和4.29个百分点。2005-2016年是各地类变化最强烈的阶段,其综合土地利用动态度最大,为13.46%。建设用地变化速率最快,其土地利用动态度为5.19%。土地转移主要发生在耕地、水体和建设用地之间,以耕地向建设用地和水体的转换为主。耕地转为建设用地的面积达207.61 km^(2),新增水体集中分布在潘谢矿区。加入空间自相关性和土壤质量因子后,耕地和建设用地的Logistics回归效果显著改善,ROC分别增加0.201和0.133。年均降水量是影响耕地变化的主要驱动因子,与耕地分布概率呈负相关;而建设用地变化主要驱动因子为GDP。土地利用模拟的Kappa系数为0.74,CLUE-S模型在研究区域具有较好的模拟能力。运用CLUE-S模型预测了研究区2028、2034、2040年土地利用空间分布,未来土地利用空间分布格局总体上没有明显变化,各用地类型面积变化相对稳定。

基于粗糙集理论与D-S证据理论改进的多元回归负荷预测方法研究

当前,中长期负荷预测大多采用多元回归算法,但在建模时对影响因子及历史年的选择缺乏良好的依据,很难在考虑更多影响因子及历史年数据与降低回归模型误差之间做出平衡。这使多元回归算法在实际负荷预测中的精准度很不稳定。将粗糙集理论与D-S证据理论引入多元回归算法,利用粗糙集理论对影响因子进行重要性排序。分别以历史年和影响因子为对象进行聚类,以此建立多个多元回归模型。利用D-S证据理论对多个组合预测的权重分配方案进行权重融合,得出最终基于多元回归分析法的组合预测模型。经算例验证,该模型能较好地平衡影响因子和历史年的选取,能有效提高多元回归算法在中长期负荷预测中的准确性,适用性强。

基于CLUE-S模型的别拉洪河流域土地利用变化模拟

以别拉洪河流域为研究区,根据3期(1986年、2000年和2005年)土地利用数据,结合道路、河流、居民点、湖泊、沟渠、海拔、坡度、坡向、人口等驱动因子,运用Logistic逐步回归分析,筛选出具有决定作用的驱动因子,然后构建了模拟别拉洪河流域土地利用变化的CLUE-S模型,动态模拟了该流域土地利用变化的时空模式。结果表明,人口密度、坡度和海拔是影响土地利用空间分布的重要因素。经检验,CLUE-S模型模拟取得了较为理想的结果,在基本单元(300 m×300 m栅格)的水平上,模型对研究区2000年和2005年土地利用分布格局模拟的总体精度分别达到78.45%、90.93%,Kappa指数分别为0.74、0.89。这说明模型具有成功模拟区域土地利用时空动态变化的能力。

Logistic回归模型评价常规超声及实时剪切波弹性成像技术对甲状腺结节良恶性鉴别诊断的价值

目的应用Logistic回归模型评价常规超声特征及实时剪切波弹性成像技术对甲状腺良恶性结节鉴别诊断的价值。方法对80例甲状腺结节患者(108个结节)行常规超声及实时剪切波弹性成像检查,测得结节的杨氏模量值,以病理结果为金标准,应用ROC曲线得出良恶性结节的诊断临界值。总结结节术前二维灰阶、彩色多普勒及剪切波弹性成像的声像图特征,筛选出对甲状腺结节良恶性鉴别诊断最有价值的指标,并建立二分类Logistic回归模型。结果病理诊断108个甲状腺结节,良性组36个,恶性组72个。甲状腺良、恶性结节的最大杨氏模量值分别为(46.43±20.84)k Pa和(81.79±32.06)k Pa;平均杨氏模量值分别为(36.59±19.29)k Pa和(62.96±29.13)k Pa。良、恶性结节杨氏模量最大值和平均值差异均有统计学意义(P<0.05)。最大值与平均值ROC曲线下面积分别为0.828和0.783,分别以最大值52.00 k Pa和平均值37.35 k Pa作为诊断截点值,其诊断敏感度、特异度为91.7%、61.1%和86.1%、55.6%。Logistic回归分析显示进入回归方程的3个特征变量为纵横比、钙化及杨氏模量值,该Logistic回归模型对甲状腺结节良恶性预报的正确率为89.7%(35/39),ROC曲线下面积为0.949。结论实时剪切波弹性成像技术有助于鉴别甲状腺结节的良恶性,二分类Logistic回归模型筛选出对甲状腺结节良恶性鉴别诊断有意义的诊断指标,具有较高的临床应用价值。

一种地震P波和S波初至时间自动拾取的新方法

地震P波、S波初至时间的拾取是地震波分析的一项基础性工作.本文提出了一种新的地震波初至时间自动拾取的方法:首先,把地震波的三分量时程曲线变换为一组空间向的能量变化率时程曲线;然后对能量变化率时程曲线进行STA/LTA(Short Time Average/Long Time Average,短时间的均值/长时间的均值)处理,拾取地震P波和S波的大致初至时间;最后提出采用一种二次方自回归模型对初至附近的能量变化率曲线进行二次方自回归处理,精确拾取出P波和S波的初至时间.本文采用了10组芦山地震的记录数据和150组汶川地震的记录数据对此方法的可靠性进行了检验.以人工拾取结果为参考,此方法具有很高的准确率和稳定性,同时,相比于常用的STA/LTA方法和AIC(Akaike Information Criterion,Akaike信息准则)方法,此方法在计算时间效率方面稍微逊色,但是对S波初至时间的拾取精度和可靠性更高.此方法丰富了地震P波、S波初至时间的自动拾取方法.