Showing papers on "Ordinal regression published in 1974"

Nominal and Ordinal Bivariate Statistics: The Practitioner's View

Abstract: The menu of statistics used in the analysis of bivariate tables of nominal and ordinal data is substantial, including among others C, y, D, dyx.dxy, Vp, K, ka, Xb, k, Q, T, two kinds of Ta and Tb, Tc and V, not to mention x2 and other significance tests. This bewildering array is more satisfactory to those who invent statistics than to those who use them, either as analysts or as consumers of political analysis. In choosing a measure of relationship between two attributes, it is necessary to consider more than their mathematical or statistical qualities. The level of measurement of the variables, the number of categories, the substantive meaning of the data, the analyst's purpose, whether testing significance in a sample or measuring association in a population, the proposition being investigated (whether it implies necessary or sufficient consequences or both), and the usefulness of statistics as communication devices (particularly whether they are familiar and understandable to the readership), are among the criteria for selecting measures.

The Use of Ordinal Statistics in Causal Analysis of Correlations

Abstract: phenomena is not to say that every research effort is engaged in "hypothesis testing." Indeed, whole studies and programs of research can be exploratory and directed toward discovery rather than confirmation. But the essence of a rational empirical discipline is to make assertions about phenomena and support or refute these with systematic empirical evidence. So, sooner or later the question of evidence for or against hypotheses comes up. And even in exploratory research, one develops and provisionally accepts or rejects countless small hypotheses on the basis of evidence. But all this does not affect the essential issue: the fact is, the fundamental problem of ordinal multivariate analysis remains unsolved, and we do not know what an ordinal multivariate relation is.

On “Ordinal Path Analysis”

Abstract: In a recent paper Smith proposes a solution to the longstanding problem of multivariate analysis with ordinal data, but it is argued that Smith has not dealt adequately with the question of empirically relevant interpretation and that the problem remains unsolved. It is proposed further that the fundamental difficulty obstructing work on the problem is the lack of a clear, precise formulation of multivariate ordinal relations and hypotheses. In a recent paper Smith (1972) attempts to develop and apply a technique of path analysis for ordinal variables based on an analogy with metric path analysis. However, there appear to be some difficulties with Smith's treatment of ordinal variables that raise doubts about his claim to have demonstrated that path analysis can be done in terms of interpretable

On Ordinal Prediction Problems

Abstract: One limitation in building empirically testable models in sociology is that many familiar statistical techniques such as least-squares regression analysis require interval-level measurements while sociologists often have only ordinal-level measurements. Fortunately there do exist statistical techniques that use ordinal measurements. In this article we consider several types of prediction procedures which use ordinal data, as input, including individual ordinal prediction procedures and pairwise ordinal prediction procedures. The latter were studied by Wilson (1971) who claimed that ordinal variables could neither be used to build empirically testable models nor to state substantive propositions rigorously. But his claims are weakened because (1) he states, but fails to prove, that a particular loss function is the only one that can be used in pairwise ordinal prediction procedures, (2) he ignores alternative types of ordinal prediction procedures, and (3) his main mathematical theorem is in error. We consider his arguments, salvage his theorem, and display a similar theorem for individual ordinal prediction procedures. We argue that, for the three reasons mentioned, Wilson's results do not show that it is unprofitable to use ordinal variables in prediction procedures. Finally we consider a generalized individual ordinal prediction procedure in which one ordinal variable is only useless for predicting a second ordinal variable if the two variables are statistically independent. The construction of empirically testable mathematical models is becoming increasingly important in sociological research. These models can yield precise and succinct information about complex social processes. But many popular statistical techniques such as leastsquares regression analysis require interval-level measurements while sociologists unfortunately often have only ordinal-level measurements.' Thus the temptation arises to treat ordinal variables as interval variables in order to apply familiar techniques. Debate has arisen over the appropriateness of using interval-level statistics with ordinal measurements. On the one hand Labowitz (1967; 1970) appeared to demonstrate empirically that the product-moment correlation is not greatly affected by random assignment (using a uniform distribution) of integer values to rank-order categories when the range of the values and the number of categories are both large. Similarly, Boyle (1970) and Leik and Gove (1969) demonstrate the utility of using the technique of causal modeling with ordinal variables. Finally, Good (1973) demonstrates that the correlation between two variables is not much affected by substituting powers of one of the variables for that variable unless the powers are very high. On the other hand, Mayer (1970; 1971), Vargo (1971), and Schweitzer and Schweitzer (1971) have argued mathematically that in extreme cases treating an ordinal variable as an interval variable can have disastrous consequences. In a recent article Wilson (1971) claims that ordinal variables cannot be used to build empirically testable models. The main purpose of the present article is to show that his arguments contain three flaws. First, although his comments appear to apply to the overall prob: The authors would like to acknowledge the helpful criticisms of the referees, and partial support from the Department of Health, Education and Welfare Grants ROI GM 18770 and R03 MH 21454. 1 For convenience we recall the definitions of nominal, ordinal, and interval scales of measurement. Nominal scales, or names, are such that only equality is relevant, and they are therefore invariant under all permutations. For ordinal scales or measurements, only inequalities and equalities are relevant, and they are therefore invariant under all (strictly) monotonic transformations. For interval scales, only ratios of differences. are relevant, and they are therefore invariant under all affine transformations. For a more extended discussion see, for example, Lea (1972).