Multiple correlations analysis limitations

Foaming properties can be quantitatively related to surfactant chemical structure, surfactant physical properties, and test conditions using the technique of multiple correlation analysis.(11) The current studies were restricted to linear correlation equations to permit the analyses to be performed on a small microcomputer. While non-linear equations having higher correlation coefficients than obtained herein can be developed, theoretical insights are often limited due to the complexity of the various terms of such equations. The quality of the correlations were assessed using the correlation coefficient (r ) criteria of Jaffe (12)... 

Both the use of one atmosphere foaming experiments and the technique of multiple correlation analysis have a common purpose minimizing the effort required to develop new surfactants for mobility control and other EOR applications. Proper use of these techniques with due consideration of their limitations can substantially reduce the number of experiments required to develop new surfactants or to understand the effect of surfactant chemical structure on physical properties and performance parameters. ... 

The limitation of the use of one atmosphere foaming experiments to rank order the predicted surfactant performance in permeable media rather than in quantitatively or semi-quantitatively predicting the actual performance of the surfactants under realistic use conditions has already been mentioned. Multiple correlation analysis has its greatest value to predicting the rank order of surfactant performance or the relative value of a physical property parameter. Correlation coefficients less than 0.99 generally do not allow the quantitative prediction of the value of a performance parameter for a surfactant yet to be evaluated or even synthesized. Despite these limitations, multiple correlation analysis can be valuable, increasing the understanding of the effect of chemical structure variables on surfactant physical property and performance parameters. 

Unfortunately, most of these tools are extremely expensive, and are fairly complex to deploy, requiring a database backend for alert storage. Surprisingly, they also have limited correlation capabilities, only providing a dozen or so rules as example for the development of environment-specific correlation rules. They should be viewed as a development framework for writing correlation rules. Since our correlation needs are very diverse, we could not find a platform that would allow us to run multiple correlation processes in parallel, from dynamic statistical analysis to vulnerability assessment. Also, manipulation of contextual data with interfaces to the inventory and configuration databases of the companies, was a strong requirement that no commercial tool satisfied at the time we launched the project. 

We should note that the use of the Lipari-Szabo analysis implies that relaxation data are available at multiple magnetic fields. It provides a phenomenological description of the rotational motion that can be very useful for comparing systems with similar structure. Nevertheless, one should be aware of the limits of this approach and avoid direct comparison of local or global rotational correlation times for structurally very different compounds. 

However, single-point correlations are of limited value for two reasons. The first relates to the choice of the specific parameters to be correlated. Although there are some procedures in the literature that could be used for selecting the most appropriate parameter [e.g., the quadrant analysis (16,17)], these are not easy to apply in practice and the choice is usually based on a best-result basis. Another reason is that two processes having the same value of the chosen characteristic parameter can be different in terms of their overall shape. Consequently, a quantitative IVIVC is much more informative if established using all available in vitro and in vivo raw data these are termed multiple-point or point-to-point correlations. 

The paper by Cochrane, St. Leger, and Moore (1978) typifies the issues associated with many early studies. Specifically, they relied on cross sections with multiple countries and often limited the analysis to simple correlations. Because determinants of life expectancy are multifactorial, national studies are more likely to detect differences than international studies. It is also critically important to include adequate control variables. In fact, a later study (Cremieux, Ouellette, and Meilleur 1999) based on extensive national data suggests that a 10% increase in health care spending reduces infant mortality by 0.5% for males and 0.4% for females while increasing life expectancy by half a year for males and three months for females. The current study uses similar modeling and data hence, results on the effect of pharmaceuticals reported below can be put in perspective relative to the overall effect of health care spending from that earlier research. 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

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