Unnecessary variables

Another particularly dangerous property of inverse MLR is that the quality of the model fit (expressed as RMSEE or r) must improve as the number of variables used in the model increases. A mathematical proof of this property will not be presented here, but it makes intuitive sense that the ability to explain changes in the Y-variable is improved as one has more X-variables to work with. This leads to the temptation to overfit the model, through the use of too many variables. If the number of variables is already sufficient for determining the Y-property in the presence of interfering effects, then the addition of more unnecessary variables only presents the opportunity to add more noise to the model and make the model more sensitive to unforeseen disturbances. A discussion on overfitting, as well as techniques for avoiding it, is provided in Section 8.3.7. 

Variable elimination is the name given to the process by which unhelpful or unnecessary variables are removed from a data set. One means by which a variable may be judged is from the information it contains. If the standard deviation of the variable is very small, then it does not contain much information and is thus not likely to be useful in the construction of models. Another common situation is that a variable may contain only a small number of different values, an extreme case being where the values are the same for all compounds in the set except one. If a variable such as this is used in the construction of a model then it may appear to be useful but is usually only serving to identify, and thus explain, the response value for that single compound. An example of this is shown in Table 7.2, which contains values of receptor binding and computed properties for a set of quinuclidine-based muscarinic receptor agonists (Saunders et al., 1990). For some of the compounds (6, 7, 8, and 12) the substitution pattern means that there is not, in fact, an... 

Getting a differential equation for E. Solving the set of Maxwell equations in order to find the electric field (for instance) requires eliminating the unnecessary variables. The first step consists of looking for the curl of the potential density from Equation H8.6 and of using the Maxwell-Ampbre equation H8.5 for replacing the curl of the electromagnetic field... 

TeMe 9.5 Summary statistics of thinned MCMC sample with unnecessary variables removed... 

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. 

Several factors were utilized in bringing formaldehyde release down. In particular, resin manufacturer executed more careful control of variables such as pH, formaldehyde content, and control of methylolation. There has also been a progressive decrease in the resin content of pad baths. The common practice of applying the same level of resin to a 50% cotton—50% polyester fabric as to a 100% cotton fabric was demonstrated to be unnecessary and counter productive (89). Smooth-dry performance can be enhanced by using additives such as polyacrylates, polyurethanes, or siUcones without affecting formaldehyde release. 

The use of a chemical agent as an anti-foam is affected by an on-off algorithm with variable dosing time and time delay. If the presence of foam is detected, then the controller first activates a delay timer. This type of foam controller works with some delay and variable dosing time. If at the end of the delay period the foam is still present, then the dosing pump is activated and chemical agent is added to the bioreactor. If the foam is still detected at the end of this period, the combined system of delay and dosing is reactivated. With this method of controller, addition of any unnecessary anti-foam is prevented. 

In order to reduce unnecessary data queries, the statistics group should be consulted early in the clinical database development process to identify variables critical for data analysis. Optimally, the statistical analysis plan would already be written by the time of database development so that the queries could be designed based on the critical variables indicated in the analysis plan. However, at the database development stage, usually only the clinical protocol exists to guide the statistics and clinical data management departments in developing the query or data management plan. 

Note that by changing the aesev variable to the aerel variable throughout Program 5.4, you can easily change the previous adverse event summary to a summary of adverse events by maximum drug relatedness. Also, if you remove the maximum severity steps, you get a typical overall summary of adverse events by body system and preferred term. Since patient medical history data are also often coded with MedDRA, patient medical history data may be summarized much like an overall summary of adverse events. However, frequently medical histories are collected in a checklist/checkbox format so that using a coding dictionary is unnecessary. 

As discussed and illustrated in the introduction, data analysis can be conveniently viewed in terms of two categories of numeric-numeric manipulation, input and input-output, both of which transform numeric data into more valuable forms of numeric data. Input manipulations map from input data without knowledge of the output variables, generally to transform the input data to a more convenient representation that has unnecessary information removed while retaining the essential information. As presented in Section IV, input-output manipulations relate input variables to numeric output variables for the purpose of predictive modeling and may include an implicit or explicit input transformation step for reducing input dimensionality. When applied to data interpretation, the primary emphasis of input and input-output manipulation is on feature extraction, driving extracted features from the process data toward useful numeric information on plant behaviors. 

The curve in Fig. 2 might represent the relationship between a response Y and a single independent variable X in a hypothetical system, and since we can see the whole curve, we can pick out the highest point or lowest, the maximum or minimum. Use of calculus, however, makes the task of plotting the data or equation unnecessary. If the relationship, that is, the equation for Y as a function of X, is available [Eq. (1)] ... 

The classification of methods for studying electrode kinetics is based on the criterion of whether the electrical potential or the current density is controlled. The other variable, which is then a function of time, is determined by the electrode process. Obviously, for a steady-state process, these two quantities are interdependent and further classification is unnecessary. Techniques employing a small periodic perturbation of the system by current or potential oscillations with a small amplitude will be classified separately. 

Like the climate system described in Chapter 7, this diagenetic system consists of a chain of identical reservoirs that are coupled only to adjacent reservoirs. Elements of the sleq array are nonzero close to the diagonal only. Unnecessary work can be avoided and computational speed increased by limiting the calculation to the nonzero elements. The climate system, however, has only one dependent variable, temperature, to be calculated in each reservoir. The band of nonzero elements in the sleq array is only three elements wide, corresponding to the connection between temperatures in the reservoir being calculated and in the two adjacent reservoirs. The diagenetic system here contains two dependent variables, total dissolved carbon and calcium ions, in each reservoir. The species are coupled to one another in each reservoir by carbonate dissolution and its dependence on the saturation state. They also are coupled by diffusion to their own concentrations in adjacent reservoirs. The method of solution that I shall develop in this section can be applied to any number of interacting species in a one-dimensional chain of identical reservoirs. 

In transforming the independent variables alone, it is assumed that the dependent variable already has all the properties desired of it. For example, if the /s are normally and independently distributed with constant variance, at least approximately, then any transformations such as described in Section VI,B,1 would be unnecessary. Under such assumptions, Box and Tidwell (B17) have shown how to transform the independent variables to reduce a fitted linear function to its simplest form. For example, a function that has been empirically fitted by... 

An initial step in addressing such situations should be the performance of an analysis of the sensitivity of a risk assessment model to changes in the variable. If the model proves relatively insensitive to conservative bounds to the variable, then further consideration of uncertainty for this variable may be unnecessary and a point estimate may suffice. 

For most antimicrobial agents, the relation between dose and therapeutic outcome is well established, and serum concentration monitoring is unnecessary for these drugs. To justify routine serum concentration monitoring, it should be established (1) that a direct relationship exists between drug concentrations and efficacy or toxicity (2) that substantial interpatient variability exists in serum concentrations on standard doses (3) that a small difference exists between therapeutic and toxic serum concentrations (4) that the clinical efficacy or toxicity of the drug is delayed or difficult to measure and (5) that an accurate assay is available. 

Long-Term Data with Small or No Change over Time and Small or No Variability In this case a statistical analysis may be considered unnecessary... 

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