适应性回归分析(Ⅳ)——与非适应性回归分析的比较

本文目的是分析一个已知真实情况的资料,比较适应性回归分析与非适应性回归分析建模的效果。结论如下:当资料中存在与因变量确有关系的自变量时,ADAPTIVEREG过程具有较好的甄别能力;REG过程具有较好的甄别能力,但需要满足一定条件,即采用"前进法"或"逐步法"筛选自变量,同时还需要"假定模型包含截距项"。当资料中不存在与因变量确有关系的自变量时,ADAPTIVEREG过程几乎完全失去了甄别能力;REG过程具有较好的甄别能力,但需要满足一定条件,即采用"前进法"筛选自变量,同时还需要"假定模型包含截距项"。若研究者基于"基本常识"和"专业知识"确定的自变量都与因变量有关系,对因变量进行Logistic变换,并且,假定回归模型中不含截距项时,会在回归模型中保留非常多的自变量。     

提高回归模型拟合优度的策略(Ⅰ)——哑变量变换与其他变量变换

本文目的是介绍第一种提高回归模型拟合优度的策略,即哑变量变换与其他变量变换。具体方法包括以下几个方面:①对多值名义自变量采取"哑变量变换";②对定量和有序自变量引入派生变量,包括"对数变换""平方根变换""指数变换""平方变换""立方变换"和"交叉乘积变换"的结果;③对定量因变量分别采取"对数变换""平方根变换""指数变换""倒数变换"和"Logistic变换";④构建回归模型时,在假定"包含截距项"与"不含截距项"的条件下,分别采取"前进法""后退法"和"逐步法"筛选自变量。得到了如下几个结论:①对定量因变量和自变量不做变量变换时,回归模型的拟合优度非常差;②根据资料所具备的条件,对定量因变量采取不同的变量变换方法,其回归模型的拟合优度是不尽相同的;③对多值名义自变量进行"哑变量变换"是常规的做法,但存在不足之处;④对定量自变量引入派生变量是非常有价值的;⑤假定回归模型中不含截距项有助于提高回归模型的拟合优度。     

提高回归模型拟合优度的策略(Ⅲ)——校正均值变换与其他变量变换

本文目的是介绍第三种提高回归模型拟合优度的策略,即校正均值变换与其他变量变换。具体方法包括以下几个方面:①对多值名义自变量采取"校正均值变换";②对定量自变量引入派生变量,包括"对数变换""平方根变换""指数变换""平方变换""立方变换"和"交叉乘积变换"的结果;③对定量因变量分别采取"对数变换""平方根变换""指数变换""倒数变换"和"Logistic变换";④构建回归模型时,在假定"包含截距项"与"不含截距项"的条件下,分别采取"前进法""后退法"和"逐步法"筛选自变量。得到了如下结论:①对定量因变量和自变量不做变量变换时,回归模型的拟合优度非常低;②根据资料所具备的条件,对定量因变量采取不同的变量变换方法,其回归模型的拟合优度是不同的;③对多值名义自变量进行"校正均值变换"是合理的,且有助于提高回归模型拟合优度;④对定量自变量引入派生变量是非常有价值的;⑤假定回归模型中不含截距项有助于提高回归模型的拟合优度。     

提高回归模型拟合优度的策略(Ⅱ)——算术均值变换与其他变量变换

本文目的是介绍第二种提高回归模型拟合优度的策略,即算术均值变换与其他变量变换。具体方法包括以下几个方面:①对多值名义自变量采取"算术均值变换";②对定量自变量引入派生变量,包括"对数变换""平方根变换""指数变换""平方变换""立方变换"和"交叉乘积变换"的结果;③对定量因变量分别采取"对数变换""平方根变换""指数变换""倒数变换"和"Logistic变换";④构建回归模型时,在假定"包含截距项"与"不含截距项"的条件下,分别采取"前进法""后退法"和"逐步法"筛选自变量。得到了如下结论:①对定量因变量和自变量不做变量变换时,回归模型的拟合优度非常差;②根据资料所具备的条件,对定量因变量采取不同的变量变换方法,其回归模型的拟合优度是不同的;③对多值名义自变量进行"算术均值变换"是合理的,且有助于提高回归模型拟合优度;④对定量自变量引入派生变量是非常有价值的;⑤假定回归模型中不含截距项有助于提高回归模型的拟合优度。     

回归建模的基础与要领(Ⅲ)——变量状态与相互间关系

本文目的是介绍回归建模的基础与要领之三,即"变量状态与相互间关系"。首先,介绍"因变量状态"与"自变量状态";其次,介绍"自变量间相互关系",即"自变量间相互独立""自变量间有线性关系"和"自变量间有非线性关系";最后,介绍"自变量与因变量间关系",包括"自变量与因变量间无任何数量关系""自变量与因变量间有间接数量关系"和"自变量与因变量间有直接数量关系"。很明显,清楚"变量状态和变量间关系"是构建合理回归模型的重要基础与要领之一。     

零膨胀Poisson分布模型回归分析

本文目的是介绍零膨胀Poisson分布模型回归分析。首先,介绍零膨胀计数资料及其零膨胀Poisson分布回归模型构建原理,包括"零膨胀Poisson分布回归模型的形式"和"零膨胀Poisson分布回归模型的求解";其次,介绍"零膨胀Poisson分布回归模型的SAS实现",包括"创建SAS数据集""呈现因变量Y的频数分布""求出因变量Y的均值和方差"和"基于全部自变量对因变量Y构建多重零膨胀Poisson分布回归模型"。本文结果提示,当计数资料为非严重过离散的零膨胀计数资料时,拟合"多重零膨胀Poisson分布回归模型",可获得满意的拟合效果。     

提高回归模型拟合优度的策略(Ⅳ)——优化计分变换与其他变量变换

本文目的是介绍第四种提高回归模型拟合优度的策略,即优化计分变换与其他变量变换。具体方法包括以下几个方面:①第一,对多值名义自变量采取"优化计分变换";②对有序自变量分别采取"单调变换"与"优化计分变换";③对定量自变量分别采取"样条变换"和"单调样条变换";④对定量因变量分别采取"样条变换""单调样条变换"和"BOX-COX变换"。全部变量变换方法组合起来共12种,共创建了12个多重非线性回归模型。依据"拟合优度评价指标"的取值,从12个回归模型中挑选出一个,即本文中的"模型1",其"均方误差平方根=0.30935、R~2=0.9586、调整R~2=0.9527"。结合本期科研方法专题同类文章的结果和结论,得出提高回归模型拟合优度的策略主要在于以下四点:①应对"定量因变量""定量自变量"和"多值有序自变量"采取合适的变量变换方法;②在拟合回归模型的过程中,应尽可能多地引入派生变量;③应假定回归模型中不含截距项;④在构建回归模型的过程中,应尽可能多地使用筛选自变量的策略,如"前进法""后退法"和"逐步法"。     

适应性回归分析(Ⅲ)——构建具有混合结构的回归模型

本文目的是通过两个实例介绍适应性回归样条算法对具有混杂结构的数据集进行回归建模的实践。当一个数据集包含多个不同的回归模型时,只要给定分类变量的具体取值,SAS中的"ADAPTIVEREG过程"可以比较准确地发掘出其内在规律,并以图形方式呈现模型对资料的拟合效果,还能呈现由"基函数"及其组合所构造出的"回归模型"。图形呈现的结果确实可以给分析者提供一些有价值的"分析线索"或"积极暗示",缩小"探索性研究的空间"。     

过离散计数资料负二项分布模型回归分析

本文目的是介绍过离散(即方差明显大于均值)计数资料负二项分布模型回归分析。首先,介绍了过离散计数资料及其负二项分布回归模型构建原理,包括"过离散计数资料负二项分布回归模型的形式"和"过离散计数资料负二项分布回归模型的求解";第二,介绍了"过离散计数资料负二项分布回归模型的SAS实现",包括:(1)"创建SAS数据集";(2)"求出因变量Y的均值和方差""检验因变量是否存在过离散现象"和"基于全部自变量对因变量Y构建多重负二项分布回归模型"。本文结果提示,在"过离散"非常严重的情况下,应使用"负二项分布回归模型"取代"Poisson分布回归模型"。否则,易得出不正确的结果和结论。     

一般计数资料Poisson分布模型回归分析

本文目的是介绍一般计数资料Poisson分布模型回归分析。首先,介绍一般计数资料及其Poisson分布模型构建原理,包括"一般计数资料Poisson分布回归模型的形式"和"一般计数资料Poisson分布回归模型的求解";其次,介绍"一般计数资料Poisson分布回归模型的SAS实现",包括"创建SAS数据集""求出因变量Y的均值和方差""检验因变量是否存在过离散现象""对过离散进行校正"和"基于全部自变量对因变量Y构建多重Poisson分布回归模型"。本文结果提示,在"过离散"不十分严重的情况下,通过在GENMOD过程的"model语句"中增加选项"dist=poisson"和"scale=deviance",可以较好地校正"过离散"导致的不良后果。     

Statistical models to estimate level of psychological disorder based on a computer rating system: An application to dementia using structured mandala drawings

The mandala has been widely accepted as an effective art therapy tool to determine a client's emotional or psychological status and to treat associated disorders. The authors apply a computer system to estimate participants’ levels of dementia based on the elements in the structured mandala drawing. A regression model was formulated whose dependent variable is the level of dementia scored by a test, and the independent (explanatory) variables are the elements in the structured mandala. These dependent variables were analyzed with the computer system. The consistency between the test score and the computer system's estimated score was verified statistically. Also, another regression model was formulated to estimate the probability of severe dementia. This model classified the level of dementia into one of two categories, severe or not, by representing it as an indicator dependent variable. In both models, the important independent variables were selected by stepwise regression, and the relative magnitudes of their effects were compared by standardized regression. The system was found to provide art therapists with useful information on the stages of a patient's advancing dementia. These methods were also determined to be applicable to estimating the level and the severity of other psychological disorders.     

A statistical approach to comparing the effectiveness of several art therapy tools in estimating the level of a psychological state

An approach using a statistical method has been proposed to compare the effectiveness of several art therapy tools in estimating the level of a psychological state, which includes various symptoms and disorders. For each of the art therapy tools, a regression model is developed, whose dependent variable (to be explained) is the level of a psychological state. Various elements in drawings are considered as independent (explaining) variables, some of which are evaluated by the computer systems for art therapy assessments. A set of independent variables “well” explaining the dependent variable is determined by the stepwise regression. The effectiveness of art therapy tools is analyzed and measured in a comparable quantitative term, and thus can be compared with other tools. In this paper, the approach has been applied to three widely used art therapy tools in estimating the level of dementia. The same method can be adopted as a predictor of a psychological state of an individual.     

The logistic regression analysis of psychiatric data

Logistic regression is presented as the statistical method of choice for analyzing the effects of independent variables on a binary dependent variable in terms of the probability of being in one of its two categories vs the other. The method, which must be applied by computer, is illustrated on data from the DSM-III field trials. The dependent variable is treatment with behaviourally-oriented psychotherapy vs treatment with psychoanalytically-oriented psychotherapy, and the independent variables are several patient and clinician characteristics. Like ordinary multiple regression, the method is shown capable of analyzing categorical as well as continuous independent variables. Unlike ordinary multiple regression when applied to binary data, logistic regression analysis necessarily yields estimated probabilities that lie between 0 and 1. The measure of association derived from logistic regression analysis, the odds ratio, is defined. Methods for making inferences about it are presented and illustrated.     

非配对设计二值资料一水平多重Logistic回归分析

本文的目的是介绍非配对设计二值资料一水平多重Logistic回归模型的构建与求解方法。基于SAS软件分别对以列联表和数据库形式呈现的定性资料进行全面分析,并得出了4个对提高模型拟合优度很有价值的结论:第一,若资料以列联表形式呈现,应拟合"加权"Logistic回归模型;第二,若资料中包含定量自变量,不适合将其定性化;第三,若资料中包含定量自变量,应依据定量自变量和二值自变量产生出派生自变量;第四,若资料中有定性自变量时,必须将多值名义或有序自变量进行哑变量变换,不需要依据二值自变量产生出派生自变量。     

Children's reasons for living, self-esteem, and violence.

Attitudes toward violence and reasons for living in young adolescents with high, moderate, and low self-esteem were examined. The authors devised an Attitudes Toward Violence questionnaire; the Rosenberg's Self-esteem Scale (RSE) and the Brief Reasons for Living in Adolescents (BRFL-A) was used to assess adaptive characteristics. The independent variables were gender and self-esteem. The dependent variables were total Reasons for Living score and Attitudes Toward Violence score. Participants included 138 boys and 95 girls, ages 11 to 15 years (M = 13.3) from a city middle school. The results showed that for the dependent variable attitudes toward violence, main effects were found for both gender and self-esteem. For the dependent variable reasons for living, a main effect was found for self-esteem but not for gender. An inverse relationship was found between violence and reasons for living. Being male and low self-esteem emerged as predictors of more accepting attitudes toward violence. Low self-esteem was significantly related to fewer reasons for living.     

Children's Reasons for Living,Self-esteem,and Violence

Attitudes toward violence and reasons for living in young adolescents with high, moderate, and low self-esteem were examined. The authors devised an Attitudes Toward Violence questionnaire; the Rosenberg's Self-esteem Scale (RSE) and the Brief Reasons for Living in Adolescents (BRFL-A) was used to assess adaptive characteristics. The independent variables were gender and self-esteem. The dependent variables were total Reasons for Living score and Attitudes Toward Violence score. Participants included 138 boys and 95 girls, ages 11 to 15 years (M = 13.3) from a city middle school. The results showed that for the dependent variable attitudes toward violence, main effects were found for both gender and self-esteem. For the dependent variable reasons for living, a main effect was found for self-esteem but not for gender. An inverse relationship was found between violence and reasons for living. Being male and low self-esteem emerged as predictors of more accepting attitudes toward violence. Low self-esteem was significantly related to fewer reasons for living.     

Modified regression model for the Logan plot.

Logan's graphical model is a robust estimation of the total distribution volume (DVt) of reversibly bound radiopharmaceuticals, but the resulting DVt values decrease with increasing noise. The authors hypothesized that the noise dependence can be reduced by a linear regression model that minimizes the sum of squared perpendicular rather than vertical (y) distances between the data points and fitted straight line. To test the new method, 15 levels of simulated noise (repeated 2,000 times) were added to synthetic tissue activity curves, calculated from two different sets of kinetic parameters. Contrary to the traditional method, there was no ( P > 0.05) or dramatically decreased noise dependence with the perpendicular model. Real dynamic 11C (+) McN5652 serotonin transporter binding data were processed either by applying Logan analysis to average counts of large areas or by averaging the Logan slopes of individual-voxel data. There were no significant differences between the parameters when the perpendicular regression method was used with both approaches. The presented experiments show that the DVt calculated from the Logan plot is much less noise dependent if the linear regression model accounts for errors in both the x and y variables, allowing fast creation of unbiased parametric images from dynamic positron-emission tomography studies.     

Cerebral metabolic correlates of the clinical dementia rating scale in mild cognitive impairment

Mild cognitive impairment (MCI) is often a prodromal state of Alzheimer's disease (AD). Imaging studies have shown that metabolic deficits in cerebral regions known to be affected early by AD pathology are predictive of progression to AD. In the present article, the authors examine associations between clinical impairment (Clinical Dementia Rating scale sum of boxes [CDR-SB]) and regional deficits in glucose utilization in a sample of 41 patients with MCI, who underwent cerebral 18F-FDG PET for the measurement of regional glucose metabolism. A linear regression analysis with CDR-SB score as the independent variable and glucose metabolism as the dependent variable, adjusted for age, gender, and years of school education, was conducted in voxel-by-voxel fashion in SPM2. The regression analysis revealed a significant negative association between CDR-SB score and glucose metabolism in the right posterior cingulate gyrus (P < .001, uncorrected for multiple comparisons), which was independent from demographical variables. The authors conclude that clinical severity of impairments is already correlated with deficits in glucose metabolism in the stage of MCI.