Regression influence analysis

Ikawa K, Eshima N, Morikawa N, Kawashima H, Izumi T, Takeyama M. Influence of concomitant anticonvulsants on serum concentrations of clonazepam in epileptic subjects an age- and dose-effect linear regression model analysis. Pharm Pharmacol Commun 1999 5 307-10. 

Regression analysis includes not only the estimation of model regression parameters, but also the calculation of goodness of fit and -> goodness of prediction statistics, regression diagnostics, residual analysis, and influence analysis [Atkinson, 1985]. 

In the following, several approaches to constructing a regression model will be tested on some simple example data sets. In these examples, traditional second-order calibration is not possible, as there is no causal or direct relationship between specific measured variables and the responses. The purpose of this example is mainly to illustrate the relative merits of different calibration approaches on different types of data, whereas the model building (residual and influence analysis) itself is not treated in detail. 

In the described MC simulation, the action of several simultaneous sources of variation is considered. The explanation of the different time courses of parameter influence on volume size between sensitivity and MCCC analyses lies in the fact that classic sensitivity analysis considers variations in model output due exclusively to the variation of one parameter component at a time, all else being equal. In these conditions, the regression coefficient between model output and parameter component value, in a small interval around the considered parameter, is approximately equal to the partial derivative of the model output with respect to the parameter component. 

More than just a few parameters have to be considered when modelling chemical reactivity in a broader perspective than for the well-defined but restricted reaction sets of the preceding section. Here, however, not enough statistically well-balanced, quantitative, experimental data are available to allow multilinear regression analysis (MLRA). An additional complicating factor derives from comparison of various reactions, where data of quite different types are encountered. For example, how can product distributions for electrophilic aromatic substitutions be compared with acidity constants of aliphatic carboxylic acids And on the side of the parameters how can the influence on chemical reactivity of both bond dissociation energies and bond polarities be simultaneously handled when only limited data are available ... 

For NO2 the recommended values of am and ap (benzoic acid scale) in the IUPAC document79 are 0.73 and 0.78, respectively, compared with the traditional values of 0.71 and 0.78, respectively (Section III.B). When these values are used for correlations of processes taking place in other than highly aqueous media, the possibility of specific solvent effects should be borne in mind. The fact that the 0 values of NO2 are very much at the upper end of the scale for commonly used substituents means that they exert a strong influence in regression analysis and there is danger of their biassing a correlation unduly. 

Multilinear Regression Analysis. As an entry to the problem we have selected simple gas phase reactions involving proton or hydride ion transfer which are influenced by only a few effects and for which reactivity data of high accuracy are available. In these situations where a larger set of numerial data are available multilinear regression analysis (MLRA) was applied. Thus, the simplest mathematical form, a linear equation is chosen to describe the relationship between reactivity data and physicochemical factor. The number of parameters (factors) simultaneously applied was always kept to a minimum, and a particular parameter was only included in a MLRA study if a definite indication of its relevance existed. 

A dramatic departure of ozone measurements from total oxidant measurements has b Mi reported for the Houston, Texas, area. Side-by-side measurements suggested that either method was a poor predictor of the other. Consideration was given to known interferences due to oxides of nitrogen, sulfur dioxide, or hydrogen sulfide, and the deviations still could not be accounted for. In the worst case, the ozone measurements exceeded the national ambient air quality standard for 3 h, and the potassium iodide instrument read less than 15 ppb for the 24-h period. Sulfur dioxide was measured at 0.01-0.04 ppm throughout the day. Even for a 1 1 molar influence of sulfur dioxide, this could not explain the low oxidant values. Regression analysis was carried out to support the conclusion that the ozone concentration is often much higher than the nonozone oxidant concentration. 

Martin H) has written a perceptive analysis of the possible ways in which an ionized species may behave in various models and contribute to or be responsible for a given activity. QSAR studies that have dealt with ion-pair partitioning include a study of fibrinolytics ( ) and the effect of benzoic acids on the K ion flux in mollusk neurons ( ). Schaper (10) recently reanalyzed a large number of absorption studies to include terms for the absorption of ionized species. Because specific values were not available for log Pj, he let the relation between log Pi and log P be a parameter in a nonlinear regression analysis. In most cases he used the approximation that the difference between the two values is a constant in a given series. This same assumption was made in the earlier studies (, ) Our work suggests that the pKa of an acid can influence this differential (see below). The influence of structure on the log P of protonated bases or quaternary ammonium compounds is much more complex (11,12) and points out the desirability of being able to easily measure these values. 

The composition of the Portland cement in the concrete can also influence the effectiveness of both calcium chloride and calcium nitrate and a regression analysis [26] for data for 10 cements produced the equation... 

The effects of both alkyl and aryl substituents can be observed in the two-component tautomeric equilibria of 3-alkyl-l-aryl-2,3-dihydro-177-naphth[l,2-r ][l,3]oxazines containing C-3-epimeric naphthoxazines 52B-58B and 52G-58C (Scheme 7). The influence of the Meyer parameters (V ) of the alkyl substituents on the epimerization constants (K d ( r= [B]/[G]) can be characterized by Equation (3). Multiple linear regression analysis of log A)r according to Equation (4) leads to the conclusion that these equilibria are also influenced significantly by the inductive effect of substituent Y 0.48) <2004JOC3645>. 

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