Categorical variables

The nature of the performance metric, y, is determined by the characteristics of the specific process under analysis. Since we are particularly interested in analyzing situations where y is related to product or process quality, it is quite common to find systems where a categorical variable y is chosen to classify and evaluate their performance. This may happen due to the intrinsic nature of y (e.g., it can only be measured and assume qualitative values, such as good, high, and low ), or because y is derived from a quantization of the values of a surrogate continuous measure of performance (e.g., y = good if some characteristic z of the product has value within the range of its specifications, and y= bad, otherwise). 

In Section IV we considered a categorical performance metric y. Although that represents a common practice, especially when y defines the quality of a product or process operation, there are many instances where system performance is measured by a continuous variable. Even when y is quality-related, it is becoming increasingly clear that explicit continuous quality cost models should be adopted and replace evaluations of performance based on categorical variables. 

Both situations with categorical and continuous, real-valued performance metrics will be considered and analyzed. Since Taguchi loss functions provide quality cost models that allow the different objectives to be expressed on a commensurate basis, for continuous performance variables only minor modifications in the problem definition of the approach presented in Section V are needed. On the other hand, if categorical variables are chosen to characterize the system s multiple performance metrics, important modifications and additional components have to be incorporated into the basic learning methodology described in Section IV. 

The observation will not be included in population analysis and denominator definitions. The response is "No" when the categorical variable is a Boolean variable. The observation will be included in population analysis and denominator definitions. 

There are negative consequences when a zero result is assumed for a categorical variable. When a zero result is assumed, inferential analysis can provide an incorrect result and descriptive statistics can be skewed. 

Much like the previous demographics table example, the majority of the tables generated for clinical trial reporting compare a set of continuous and/or categorical variables across treatment groups. The purpose is to see whether therapy groups are comparable or whether they differ in some way. These kinds of tables include the following ... 

On occasion you need to perform a test for association between two categorical variables while stratifying, or controlling, for a third variable. The Cochran-Mantel-Haenszel test for association stratifies by a third variable to give proper weight to strata size. In the previous example, let s assume that you want to stratify your analysis by center to control for differences in center size. You can then run a Cochran-Mantel-Haenszel test like this ... 

The first PROC CORR sends the Pearson correlation coefficients to a data set called pearson for the continuous variables Age and Weight, while the second PROC CORR sends the Spearman correlation coefficients to a data set called spearman for the categorical variables Race and Treatment Success. The correlation coefficients are found where the TYPE variable is equal to CORR in the pearson and spearman data sets. 

FIGURE 2.3 Variable (feature) matrix X and a property vector y. The property may be a continuous number (a physical, chemical, biological, or technological property), as well as a discrete number or categorical variable defining a class membership of the objects. 

The components of discrete feature vectors may indicate the presence or absence of a feature, the number of occurrences of a feature, or a finite set of binned values such as would be found in an ordered, categorical variable. 

Moving up from binary is categorical data where there are more than two categories that form the basis of the measurement . The following are examples of categorical variables ... 

Used to test the main and interactive effects of categorical variables on a continuous dependent variable, controlling for the effects of other selected continuous variables that covary with the dependent variable. Volume 2(4). 

Safety analysis patient set was defined as all patients who received the Biod/VTs/o Batimastat OC stent, per-protocol analysis patient set was defined as all patients in the Safety analysis set who did not deviate from the protocol. Categorical variables were summarized using counts and percentages. Continuous variables were summarized using mean, standard deviation, minimum and maximum, and median for variable not showing a normal distribution. For comparison of subgroups, the unpaired two-tailed student s t-test was used. Results were considered statistically significant at P< 0.05. 

How do we set about variable selection One obvious approach is to examine the pair-wise correlations between the response and the physicochemical descriptors. One form of model building, forward stepping multiple regression, begins by choosing the descriptor that has the highest correlation with a response variable. If the response is a categorical variable such as toxic/non-toxic,... 

H., Peck, C. C., Mould, D. R. Simulation of correlated continuous and categorical variables using a single multivariate distribution. J Pharmacokinet Pharmacodyn 2006 [Epub ahead of print]. 

Attribute data were identified from the photomicrographs of each location point in the sample, and each potential categorical variable (attribute) was recorded as present or absent. Because it was desirable to determine whether the evidence at the location points was related, the data were subjected to hierarchical clustering. The measure of dissimilarity used in the project was the number of matches among attribute measurements that two location points shared. For example, two points had a dissimilarity of 0 if they matched on all attribute measurements, and at the other extreme, the two location points had a dissimilarity of 13 (the total number of measured attributes) if they did not match on any of the measurements. Each match was weighed as equally important. In addition to this intuitive measure of... 

The toxicity upon pharmaceutical treatment is often described by categorical variables that are either non-ordered (e.g., mortality dead or alive) or ordered... 

Harrell (35) developed the transcan function for performing Mis as part of his Hmisc library of miscellaneous S-Plus functions. The transcan function is a general purpose imputation function that can be used for imputing both continuous and categorical variables. The software can be accessed from his web site (http //... 

The responses measured are not continuous—pain relief is often measured as an ordered categorical variable, while time for remedication is a survival variable. 

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