In the Myopia Study described in Section 1.6.2, one variable that is clearly important is the initial value of spherical equivalent refraction. (SPHREQ). Repeat steps (a)– (g) of Exercise 1, but for...

In the Myopia Study described in Section 1.6.2, one variable that is clearly important is the initial value of spherical equivalent refraction. (SPHREQ). Repeat steps (a)– (g) of Exercise 1, but for 2(c) use eight intervals containing approximately equal numbers of subjects (i.e., cut points at 12.5%, 25%, ... , etc.).

The example we use to initially illustrate each of the models comes from the Low-Birth-Weight Study (see Section 1.6.2) where we form a four category outcome from birth weight (BWT) using cutpoints: 2500g, 3000g, and 3500g. This example is not typical of many ordinal outcomes that use loosely defined “low,” “medium,” or “high” categorizations of some measurable quantity. Instead, here we explicitly derived this variable from a measured continuous variable. We make use of this fact when we show how the proportional odds model can be derived from the categorization of a continuous variable. In addition, some of the exercises are designed to extend this discussion. First, we need to give some thought to the assignment of codes to the outcome variable, as this has implications on the definition of the odds ratio calculated by the various ordinal models.