Models for Ordered Outcomes Political Science 200C

Often dependent variables are ordinal, but are not continuous in the sense that the metric used to code the variables is substantively meaningful. For instance, it is customary to employ a 7-point scale when measuring party-identification in the U.S., assigning the numerals {0,...,6} to the categories {‘‘Strong Republican’’, ‘‘Weak Republican’’,..., ‘‘Strong Democrat’’}. But the metric underlying party identification is not necessarily the same as the linear metric relating the numerals zero through 6 (i.e., the real line). In substantive terms, the difference between 0 and 2 on the coded party identification scale (moving from ‘‘Strong Republican’ ’ to ‘‘Republican Leaner’’) may be quite different from the difference between 2 and 4 (‘‘Republican Leaner’ ’ to ‘‘Democrat Leaner’’), or 4 and 6 (‘‘Democrat Leaner’ ’ to ‘‘Strong Democrat’’). These variables are sometimes also called ‘‘polychotomous’ ’ (as opposed to ‘‘dichotomous’’). When such a variable appears on the left-hand side of a statistical model it is obvious that LS regression will suffer from many of the short-coming