Jiří Militký

Detection of single influential points in OLS regression model building

Identifying outliers and high-leverage points is a fundamental step in the least-squares regression model building process. Various influence measures based on different motivational arguments, and designed to measure the influence of observations on different aspects of various regression results, are elucidated and critiqued here. On the basis of a statistical analysis of the residuals (classical, normalized, standardized, jackknife, predicted and recursive) and diagonal elements of a projection matrix, diagnostic plots for influential points indication are formed. Regression diagnostics do not require a knowledge of an alternative hypothesis for testing, or the fulfillment of the other assumptions of classical statistical tests. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high-leverages, which cause many problems in regression analysis. This paper provides a basic survey of the influence statistics of single cases combining exploratory analysis of all variables. The graphical aids to the identification of outliers and high-leverage points are combined with graphs for the identification of influence type based on the likelihood distance. All these graphically oriented techniques are suitable for the rapid estimation of influential points, but are generally incapable of solving problems with masking and swamping. The powerful procedure for the computation of influential points characteristics has been written in Matlab 5.3 and is available from authors.

New methodology of influential point detection in regression model building for the prediction of metabolic clearance rate of glucose

Abstract Identifying outliers and high-leverage points is a fundamental step in the least-squares regression model building process. The examination of data quality involves the detection of influential points, outliers and high-leverages, which cause many problems in regression analysis. On the basis of a statistical analysis of the residuals (classical, normalized, standardized, jackknife, predicted and recursive) and diagonal elements of a projection matrix, diagnostic plots for influential points indication are formed. The identification of outliers and high leverage points are combined with graphs for the identification of influence type based on the likelihood distance. The powerful procedure for the computation of influential points characteristics written in S-Plus is demonstrated on the model predicting the metabolic clearance rate of glucose (MCRg) that represents the ratio of the amount of glucose supplied to maintain blood glucose levels during the euglycemic clamp and the blood glucose concentration from common laboratory and anthropometric indices. MCRg reflects insulin sensitivity filtering-off the effect of blood glucose. The prediction of clamp parameters should enable us to avoid the demanding clamp examination, which is connected with a higher load and risk for patients.

Multiparametric curve fitting XIV. Modus operandi of the least-squares algorithm MINOPT.

Hybrid least-squares algorithm MINOPT for a nonlinear regression is introduced. MINOPT from CHEMSTAT package combines fast convergence of the Gauss-Newton method in a vicinity of minimum with good convergence of gradient methods for location far from a minimum. Quality of minimization and an accuracy of parameter estimates for six selected models are examined and compared with different derivative least-squares methods of five commercial regression packages.

Some graphical aids for univariate exploratory data analysis

Abstract The main parts of exploratory data analysis (EDA) are discussed. For data presentation the quantile plot and quantile-box plot are proposed. Special techniques for empirical probability density construction and empirical quantile-quantile plot creation are described. Some graphically oriented methods for selection of optimum power transformations are presented. These graphical aids in EDA are demonstrated on Hinkleys well known data.

Use of the mean quadratic error of prediction for the construction of biased linear models

Abstract The main practical problems caused by multi-collinearity are reviewed. The biased estimators based on the generalization of principal components for avoiding multi-collinearity problems are described. The mean quadratic error of prediction criterion is used for the selection of suitable bias. Some advantages of biased regression are demostrated on the problem of intercept estimation in a polynomial model.

Assessment of the mean-value of 17-hydroxypregnenolone in the umbilical blood of newborns by the exploratory analysis of biochemical data

The main aim of data analysis in biochemical metrology is the extraction of relevant information from biochemical data measurements. A system of extended exploratory data analysis (EDA) based on the concept of graphical tools for sample data summarization and exploration is proposed and the original EDA algorithm in S-Plus is available on the Internet at http://www.trilobyte.cz/EDA. To check basic assumptions about biochemical and medical data is to examine the independence of sample elements, sample normality and homogeneity. The exact assessment of the mean-value and the variance of steroid levels in controls is necessary for the correct assessment of the samples from patients. Data examination procedures are illustrated by a determination of the mean-value of 17-hydroxypregnenolone in the umbilical blood of newborns. For an asymmetric, strongly skewed sample distribution corrupted with outliers the best estimate of location seems to be the median. The Box-Cox transformation improves a sample symmetry. The proposed procedure gives reliable estimates of a mean-value for an asymmetric distribution of 17-hydroxypregnenolone when the arithmetic mean can not be used.

Computer estimation of dissociation constants. Part VI. Diagnostics in regression analysis of absorbance-pH curve

Nonlinear regression program DCMINOPT is introduced for numerical analysis of a set of {A, pH} data expressing a dependence of absorbance of a mixture of variously protonated light-absorbing species L, LH,..., LHR on pH. Efficiency of the program has been examined on simulated A-pH data corrupted with artificial (generated) errors namely for a case of closely overlapping protonation equilibria. An accuracy and precision of parameters estimates have been examined and compared with those determined by another three standard algorithms DCFIT, DCMINUIT and PSEQUAD. Goodness-of-fit test brings various regression diagnostics, 3D-plots and statistical measures enabling to test and prove a reliability of a regression process and accuracy and precision of parameter estimates.

Data analysis in the chemical laboratory Part 1. Analysis of indirect measurements

Abstract Response quantities of analytical chemistry investigations of, for instance, concentration or content of substances, viscosity, stability constants or solubility, can be obtained as a non-linear transformation of directly measured quantities or signals. The goal of the indirect mesurements analysis is estimation of basic statistical parameters of analytical results from the known non-linear transformation and from the statistical parameters of measured variables. The analysis is based on Taylor series expansion, two-point approximation and Monte Carlo simulation. An algorithm may be applied on any chemical, physical, biological or medical result.

Multiparametric curve fitting XV: statistical analysis and goodness-of-fit test by the least-squares algorithm MINOPT

Estimation of nonlinear regression quality leads to examination of quality of parameter estimates, a degree of fit, a prediction ability of model proposed and quality of experimental data. Statistical analysis serves for computation of confidence intervals of parameters and confidence bands, the bias of parameters and bias of residuals. Goodness-of-fit test examines classical residuals using various diagnostics and identifies influential points. Mentioned topics of nonlinear model building and testing contained in MINOPT program from CHEMSTAT package are illustrated.