基于多群体遗传算法的非线性最小二乘估计

由于非线性模型参数估计理论广泛使用的传统牛顿类算法对初值的敏感性,以及简单遗传算法易陷入局部最优的问题,提出了一种多群体遗传算法,它采用多个群体执行遗传算法搜索解,并且能根据各个群体在较少迭代次数中找到的最优解动态调整参数域,提高了遗传算法的性能及搜索到的解是全局最优解的可靠性.实验结果表明:新的算法是一种有效的非线性系统模型参数估计方法.     

Comparison of hot rolled steel mechanical property prediction models using linear multiple regression,non-linear multiple regression and non-linear artificial neural networks

Abstract

In the manufacture of rolled steel from a hot strip mill, the final mechanical properties, such as yield strength, ultimate tensile strength and elongation to fracture, are important requirements specified by the customer. The use of mathematical modelling techniques such as multiple regression analysis, or computational developments such as artificial neural networks, can result in the creation of acceptably accurate predictive models. However, the accuracy of any predictive model will depend on the quality of data used in its creation, and thus a brief statistical analysis of the mechanical property data used for model development is discussed. In the present paper a comparison of the application of linear multiple regression, non-linear multiple regression and non-linear neural networks is made for various steel families using data taken from the Corus Port Talbot hot strip mill. A statistical summary of their relative predictive errors is given, and although all three are comparable, the non-linear, black box approach of a suitably structured neural network provides overall more accurate predictive models than the use of linear or non-linear multiple regression.     

Multivariate analysis of variance by multiple regression methods.

Discusses multivariate analysis of variance as a general case of familiar multiple regression analysis. A consequence of this approach is a unified treatment of multivariate analysis of variance which can be used by psychologists who are generally familiar with multiple regression approaches to univariate analysis of variance. It is suggested that the generality of the approach permits solutions consistent with any of the several available strategies for dealing with problems of unequal and disproportionate cell frequencies. Inherent in the multiple regression formulation is the otherwise not so obvious fact that univariate analysis of variance results are an integral part of the multivariate solution and that both are important for understanding complex data. Methods of interpreting multivariate analysis of variance results in complex factorial experimental designs are discussed. (32 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Meta-analysis of multiple outcomes by regression with random effects

Earlier work showed how to perform fixed-effects meta-analysis of studies or trials when each provides results on more than one outcome per patient and these multiple outcomes are correlated. That fixed-effects generalized-least-squares approach analyzes the multiple outcomes jointly within a single model, and it can include covariates, such as duration of therapy or quality of trial, that may explain observed heterogeneity of results among the trials. Sometimes the covariates explain all the heterogeneity, and the fixed-effects regression model is appropriate. However, unexplained heterogeneity may often remain, even after taking into account known or suspected covariates. Because fixed-effects models do not make allowance for this remaining unexplained heterogeneity, the potential exists for bias in estimated coefficients, standard errors and p-values. We propose two random-effects approaches for the regression meta-analysis of multiple correlated outcomes. We compare their use with fixed-effects models and with separate-outcomes models in a meta-analysis of periodontal clinical trials. A simulation study shows the advantages of the random-effects approach. These methods also facilitate meta-analysis of trials that compare more than two treatments.     

轧机特性的回归与参数估计

本文对ＡＧＣ系统中的轧机特性问题进行了研究，介绍了本钢热连轧ＡＧＣ系统中使用的轧机特性回归模型和参数估计方法，并给出实际控制效果。     

Sample size and multiple regression analysis.

Despite the development of procedures for calculating sample size as a function of relevant effect size parameters, rules of thumb tend to persist in designs of multiple regression studies. One explanation for their persistence may be the difficulty in formulating a reasonable a priori value of an effect size to be detected. This article presents methods for calculating effect sizes in multiple regression from a variety of perspectives and also introduces a new method based on an exchangeability structure among predictor variables. No single method is deemed superior, but rather examples show that a combination of methods is likely to be most valuable in many situations. A simulation provides a 2nd explanation for why rules of thumb for choosing sample size have persisted but also shows that the outcome of such underpowered studies will be a literature consisting of seemingly contradictory results. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Magnitude estimation of perceived odor intensity: Empirical and theoretical properties.

Four subjects judged the odor intensities of 7 pyridine concentrations and a blank. Computer simulations of a judgment model were compared with the empirical data. The model generates data patterns that closely mimic empirical findings. The following patterns were confirmed: (a) A power function relates magnitude estimates and concentration with an exponent in the range of 0.7 to 1.0. (b) The exponent fluctuates so that the level constant is negatively correlated with the exponent. (c) The standard deviation of the responses is a negatively accelerated function of the mean. (d) The skewness of the responses is relatively high for low concentrations and declines toward zero with increasing concentration. (e) The correlation between responses to successive stimuli is highest when successive concentrations are similar. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

From multiple regression analysis to logistic model, proportional hazard model and log linear model. Its concept and application

Recently logistic model, proportional hazard model and log linear model have been used frequently in the medical literatures. Here, each model is reviewed briefly from basics to its application, pointing out pitfalls in its application, some of which are common to any regression analysis. The logistic model is especially useful for the analysis of retrospective data where odds ratio is utilized to evaluate the outcome probability. On the other hand, proportional hazard model is useful when we analyze censored data, utilizing hazard function. Log linear model has been used where contingency table has more than three independent variables, the situation where its applicability in clinical medicine is wide. Familiarity with these statistical methods would enable us to evaluate data more effectively and efficiently and ultimately to read literature more easily.     

Control of halo error: A multiple regression approach.

Comments on an article by F. J. Landy et al (see record 1981-00274-001) that suggests a method for excluding halo variance in rating scales. It is argued that this approach may result in excluding true variance. The present article presents a conceptualization of the halo effect in terms of a suppressor variable. Accordingly, a multiple regression approach for the treatment of halo variance is suggested. (13 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation

MOTIVATION: The simulation of biochemical kinetic systems is a powerful approach that can be used for: (i) checking the consistency of a postulated model with a set of experimental measurements, (ii) answering 'what if?' questions and (iii) exploring possible behaviours of a model. Here we describe a generic approach to combine numerical optimization methods with biochemical kinetic simulations, which is suitable for use in the rational design of improved metabolic pathways with industrial significance (metabolic engineering) and for solving the inverse problem of metabolic pathways, i.e. the estimation of parameters from measured variables. RESULTS: We discuss the suitability of various optimization methods, focusing especially on their ability or otherwise to find global optima. We recommend that a suite of diverse optimization methods should be available in simulation software as no single one performs best for all problems. We describe how we have implemented such a simulation-optimization strategy in the biochemical kinetics simulator Gepasi and present examples of its application. AVAILABILITY: The new version of Gepasi (3.20), incorporating the methodology described here, is available on the Internet at http://gepasi.dbs.aber.ac.uk/softw/Gepasi. html. CONTACT: prm@aber.ac.uk     

Faculty ratings and student grades: A university-wide multiple regression analysis.

Studied the relationship between grades professors give their students and ratings those students give their professors, using multivariate techniques and a large sample size (2,360 of 2,449 course sections taught in the spring semester of 1973) to avoid weaknesses of previous studies. Results show the following: (a) Only one factor was present among the 8 rating items; (b) the correlation between average student grade in each course section and average student rating of the teacher of that section was .35; (c) average grade was the best predictor of average rating; and (d) when average grade was added to several other available predictors, it significantly improved the multiple correlation from .25 to .39. Findings suggest that students' grades probably do influence their ratings of faculty, accounting for about 9% of the total variance. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Parametric statistics and levels of measurement: Factorial designs and multiple regression.

Let Y be a continuous, ordinal measure of a latent variable Θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable Θ even when the standard normality and equality of variance assumptions hold. If Y is a continuous, ordinal measure of a latent variable Θ; X?,…, Xn are continuous, ordinal measures of latent variables Φ?,…, Φn; and the observed measures have a multivariate normal distribution, then a multiple regression analysis of the observed criterion measure Y and predictors X?,…, Xn can be used to test hypotheses about multivariate associations among the latent variables. Furthermore, the predicted values Y′ are unbiased estimates of quantities that are monotonically related to predicted values on the latent criterion variable Θ. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Developmental and individual differences in pure numerical estimation.

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergartners and 1st, 2nd, and 3rd graders were presented problems involving the numbers 0-100; in Experiment 2, 2nd and 4th graders were presented problems involving the numbers 0-1,000. Parallel developmental trends, involving increasing reliance on linear representations of numbers and decreasing reliance on logarithmic ones, emerged across different types of estimation. Consistent individual differences across tasks were also apparent, and all types of estimation skill were positively related to math achievement test scores. Implications for understanding of mathematics learning in general are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Power and sample size calculations for studies involving linear regression

This article presents methods for sample size and power calculations for studies involving linear regression. These approaches are applicable to clinical trials designed to detect a regression slope of a given magnitude or to studies that test whether the slopes or intercepts of two independent regression lines differ by a given amount. The investigator may either specify the values of the independent (x) variable(s) of the regression line(s) or determine them observationally when the study is performed. In the latter case, the investigator must estimate the standard deviation(s) of the independent variable(s). This study gives examples using this method for both experimental and observational study designs. Cohen's method of power calculations for multiple linear regression models is also discussed and contrasted with the methods of this study. We have posted a computer program to perform these and other sample size calculations on the Internet (see http://www.mc.vanderbilt.edu/prevmed/psintro+ ++.htm). This program can determine the sample size needed to detect a specified alternative hypothesis with the required power, the power with which a specific alternative hypothesis can be detected with a given sample size, or the specific alternative hypotheses that can be detected with a given power and sample size. Context-specific help messages available on request make the use of this software largely self-explanatory.     

Visual field progression: comparison of Humphrey Statpac2 and pointwise linear regression analysis

BACKGROUND: Humphrey Statpac2 "glaucoma change probability analysis' is a widely available analysis technique to aid the clinician in the diagnosis of glaucomatous visual field deterioration. A comparison of this technique with the more recently described pointwise linear regression analysis (PROGRESSOR) is given. METHODS: Series of visual field data from a group of nine eyes of nine patients with normal-tension glaucoma were selected. Each series had 16 fields with mean follow-up of 5.7 years (SD 0.6 years). Statpac2 "glaucoma change probability analysis' was used to define test locations that had unequivocally deteriorated in the last three fields of each series. The accuracy of both Statpac2 and PROGRESSOR in providing early detection of these deteriorated locations was assessed. RESULTS: The sensitivity and specificity of the two techniques in predicting deteriorated locations were similar when a rate of luminance sensitivity loss of faster than 1 dB/year (2 dB/year for outer locations beyond 15 deg of eccentricity) with a slope significance of P < 0.10 was used as the regression definition of deterioration. The difficulties of comparing two techniques in the early diagnosis of field progression without a true external standard for field loss are illustrated. CONCLUSIONS: PROGRESSOR closely emulates the performance of Statpac2 in detecting sensitivity deterioration at individual test locations. This new technique, which uses all available data in a field series and gives the rate of sensitivity loss at each location, may provide a clinically useful method for detecting field progression in glaucoma.     

Children's numerical estimation: Flexibility in the use of counting.

Tested the hypothesis that increased skill and strategy use in counting would be associated with greater accuracy in estimation. 61 children in kindergarten and Grades 1 and 3 played a game of "darts" on a microcomputer in which they had to estimate the ordinal position of a point along a vertical line segment on which only the endpoints were numerically labeled. Each S was presented with 21 trials, representing all possible target positions along the line segment. Ss were asked to report how they made their estimates and also were given an inventory of forward- and backward-counting skills. Results show developmental differences in accuracy of estimation, fluency in counting, and sophistication of self-reported strategy use. Third graders were very accurate at estimating targets at both ends of the line segment and also relatively accurate at middle-range targets, whereas younger Ss were accurate only within the small range of target positions. It appears that the older Ss' flexibility in adjusting the direction and starting point of their counting sequences provided them an advantage in estimating ordinal number. Results are discussed in terms of the relationship between children's counting skills and mathematical understanding. (28 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)