Ordered categorical variable

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. 

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

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

Throughout this chapter we use two example data sets. The first is a real data set from a PK study in 73 individuals with an average of ten observations per individual. Each individual was studied on one to seven occasions. The second example is a simulated data set with an ordered categorical response variable and is described in greater detail in Section 7.4.7. 

Jonsson (25) showed from a simulation study that the use of the standard mixed effects modeling approach may produce biased parameter estimates when ordered categorical data with a skewed distribution are analyzed using the Laplacian method. Increasing interindividual variability and skewness in the distribution of the data increase the bias associated with the estimation of those parameters. The conse-... 

An alternative method to treating time as a categorical variable is to treat time as a continuous variable and to model time using a low-order polynomial, thereby reducing the number of estimable parameters in the model. In this case, rather than modeling the within-subject covariance the between-subject covariance is manipulated. Subjects are treated as random effects, as are the model parameters associated with time. The within-subject covariance matrix was treated as a simple covariance structure. In this example, time was modeled as a quadratic polynomial. Also, included in the model were the interactions associated with the quadratic term for time. 

Application of PLS-DA differs somewhat to criterion based methods such as LDA. In this case, a PLS regression model is built to predict the categorical variable (0 and 1 in our case). The predicted values vary around 0 and 1. In order to turn this regression model into a discriminant model, it is necessary to choose a threshold, so that any predicted values above the threshold would be classified as belonging to class 1 (plastic) and all predicted values below the threshold would be classified as belonging to class 0 (cheese). It is common to apply a threshold value of 0.5 when the class values are in the [0,1] range and the number of spectra in each class is equal. However, when the number of spectra in each class is not the same, an alternate threshold may be required. This is usually selected by trial and error. 

In order to explore the dose-response pattern of the full-scale IQ-PbB association we have used PbB as categorical variable with five levels (< 14.9,15.0-24.9, 25.0-34.9, 35.0-44.9, and > 45.0 /ig/dl). The full-scale IQ difference between the two extreme PbB levels was 11.1 units (Figure 5). After allowance for the covariates of the optimal model the full-scale IQ difference was 9.1 units. A consistent decrease of the IQ by PbB was noted in levels higher than 25.0 jUg/dl. 

Here you see the column definitions for PROC REPORT. Treatment, Gender, and Race are defined as ACROSS variables in order to get their categorical values to span columns as wanted. 

Input variables are controllable, uncontrollable and disturbance variables. Controllable variables or factors X1 X2,..., X are variables, that can be directed or that can affect the research subject in order to change the response. They can be numerical (example temperature) or categorical (example raw material supplier). Uncontrollable variables Z1 Z2,..., Zp are measured and controlled during the experiment but they cannot be changed at our wish. They can be a major cause for variability in the responses. Other sources of variability are deviations around the set points of the controllable factors, plus sampling and measurement error. Furthermore, the system itself may be composed of parts that also exhibit variability. Disturbance, non controlled variables Wi, W2,..., Wq are immeasurable and their values are randomly changed in time. 

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