Relative Importance of Variables

Experience has followed an iterative pattern in playing the model exercises against field measurements. Usually, the first indication of the relative importance of variables is seen in bodies of observational data. The next step is to build a model on the basis of either intuition or a deterministic physical equation that reflects the trends seen in the data. The model is then used for the range of conditions in the data base, and uncertainties as to the correctness or completeness of the model become evident. The questions that arise can usually be answered only through further field experimentation. Thus, the models themselves are used in the design of both laboratory and field experiments that will ultimately provide a basis for the improvement of the modeling art. 

The relative importance of variability and uncertainty can be quantified. This information can be used to determine whether further research would be useful (e.g., when uncertainty is much more important than variability) and to target that research. When variability is the dominant source of uncertainty, further research will be of limited use and the assessment should proceed to decision making. 

In addition, the relative importance of variables and responses already identified will likely shift during development activities. 

Finally it is worth noting that linear combinations of the original variables may provide better and more effective classification rules than the original variables themselves. Principal components are often employed in pattern recognition and are always worth examining. However, the interpretation of the classification rule in terms of relative importance of variables will generally be more confusing. 

The following relative importance of variables was found temperature > pressure > input power > space velocity. 

Numerous workers have studied simulated weathering. Brown et al. (26) and Frankenfeld (27) conducted two-year studies under Coast Guard contract on the weathering of oil and devised some effective rapid simulation methods that could be the basis for future standardized methods. Ahmadjian et al. (28) studied simulated weathering by infrared spectroscopy. Flanigan et al. (29) investigated the effects of several methods of laboratory weathering on the results of various analytical methods. They also attempted to separate the relative importance of variables such as dissolution, evaporation, photooxidation, etc. as to their effects. Dissolution and evaporation were the variables that most affected GC and IR photooxidation most affected fluorescence. 

Under the optimized reaction conditions, the relative importance of variable reaction volume and reaction ratio AIB was confirmed. No significant difference in materials properties was found upon changing of the reaction volume under optimized reaction conditions as illustrated in Figure 5.16/4. In contrast, the variation in ratio AIB had a pronounced effect (see Figure 5.16B) as predicted by the descriptor analysis. 

Many operating variables, such as sample volume, flow rate, column length, and temperature, must be considered when performing any separation. The relative importance of these variables for Toyopearl HW-55F resin columns has been specifically evaluated. For example. Fig. 4.47 shows the relationship between column efficiency, or height equivalent of a theoretical plate (HETP),... 

The relative importance of each indicator will vary according to the type, quantity, end quality, variety and value of the product and the capital cost, flexibility and required utilization level of the plant. Three variables will serve most industrial processes ... 

For the RF system, the development was not as far advanced. There were still difficulties in making acceptable-quality foams, and significant factors and ranges had not been determined. There was also no clear indication of the relative importance of formulation and process variables. For these reasons, it was considered appropriate to execute a screening experiment to identify key variables. 

On the other hand, MCCC considers the influence of the variation of one parameter on model output in the context of simultaneous variations of all other parameters. In this situation, is smaller than 1 in absolute value and its size depends on the relative importance of the variation of model output due to the parameter of interest and the variation of model output given by the sum total of all sources (namely, the variability in all structural parameter values plus the error variance). 

Because variables in models are often highly correlated, when experimental data are collected, the xrx matrix in Equation 2.9 can be badly conditioned (see Appendix A), and thus the estimates of the values of the coefficients in a model can have considerable associated uncertainty. The method of factorial experimental design forces the data to be orthogonal and avoids this problem. This method allows you to determine the relative importance of each input variable and thus to develop a parsimonious model, one that includes only the most important variables and effects. Factorial experiments also represent efficient experimentation. You systematically plan and conduct experiments in which all of the variables are changed simultaneously rather than one at a time, thus reducing the number of experiments needed. 

On the other hand, the merits of such insights are obvious. It would become possible to evaluate the relative importance of surface and bulk mechanisms of PT. The transition from high to low proton mobility upon dehydration could be related to molecular parameters that are variable in chemical synthesis. It could become feasible to determine conditions for which high rates of interfacial PT could be attained with a minimal amount of hghtly bound water. As an outcome of great practical value, this understanding could direct the design of membranes that operate well at minimal hydration and T > 100°C. 

Models should be developed to understand the relative importance of other variables as they affect plant dose-response. These include, but are not limited to, climatic, edaphic, biotic, and genetic factors. Considerable information is available, but there are many gaps, and no comprehensive programs are in progress to determine how these factors act and interact to affect a plant s response. 

The major benefit of 2nd-order Monte Carlo analysis is that it allows analysts to propagate their uncertainty about distribution parameters in a probabilistic analysis. An analyst need not specify a precise estimate for an uncertain parameter value simply because one is needed to conduct the simulation. The relative importance of our inability to precisely specify values for constants or distributions for random variables can be determined by examining the spread of distributions in the output. If the spread is too wide to promote effective decision making, then additional research is required. 

Sensory. Although the basis for multivariate analysis was developed in the early 1900 s, its use in sensory analysis is relatively recent. These types of statistics, however, have been valuable in dealing with two fundamental problems which occur in sensory testing. First there are difficulties encountered when one attempts to breakdown complex sensory parameters into single semantic terms which can be rated, and second it is difficult to achieve the goal of every panelist having the same internal understanding of each term. Approaches to minimize these difficulties included 1) evaluation of semantic terms used by the panel to determine if the variables are unique or can be condensed to a new set of unique variables 2) evaluation of the panelists use of semantic terms to determine inconsistencies as well as the relative importance of the terms to food quality or discrimination.(8)... 

Multiple r2 values of 0.9346 and 0.9280 were obtained for these equations of capacity and stability, respectively. The relative importance of each respective partial regression coefficient was determined by comparison of B values (32). These evaluations indicate that the most important variables in the two models for foam capacity and stability are soluble protein, soluble and insoluble carbohydrate and ash, and insoluble fiber. 

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