“Politimetrics” (Gurr 1972), “polimetrics,” (Alker 1975), “politometrics” (Hilton 1976), “political arithmetic” (Petty [1672] 1971), “quantitative Political Science (QPS),” “governmetrics,” “posopolitics” (Papayanopoulos 1973), “political science statistics” (Rai and Blydenburgh 1973), “political statistics” (Rice 1926). These are some of the names that scholars have used to describe the field we now call “political methodology.”1 The history of political methodology has been quite fragmented until recently, as reflected by this patchwork of names. The field has begun to coalesce during the past decade; we are developing persistent organizations, a growing body of scholarly literature, and an emerging consensus about important problems that need to be solved.

The ID3 algorithm is an inductive artificial intelligence technique that generates classification trees. These trees are similar to those used in simple expert systems; with ID3 they are generated by machine rather than using human experts. This article applies a bootstrapped ID3 to the Butterworth data set on interstate conflict management. By generating a number of classification trees from randomly selected subsets of the complete data set, the variables that most effectively predict the outcome of the conflict management effort are identified, and the degree of unpredictability in the data is estimated from the accuracy of the classification tree in predicting cases not in the training set. The original set of 38 independent variables can be reduced to 5 or less with almost no loss of accuracy; classification trees using these variables have 95–100 percent accuracy when fitted to the entire data set and an average accuracy of 50–60 percent in predicting new cases in split-sample tests. Unlike many existing statistical techniques, the classification tree is a plausible model of human inductive knowledge representation since it is compatible with the cognitive constraints of the human brain.

Two-stage least squares (2SLS) is a statistical procedure that is used to correct for simultaneity bias and errors in variables. When applied to certain kinds of models, however, 2SLS is itself susceptible to bias as a result of random and nonrandom measurement error in the data. Using data from the 1980 Center for Political Studies panel, I show how different assumptions about measurement error produce radically different impressions about the reciprocal relationship between party identification and presidential performance evaluations.

Ordinary intuition about the relative exogeneity of demographic variables in a linear regression model is used to illustrate a general problem that can arise in statistical models for purely cross-sectional surveys: while the model that represents intuition is compatible with formal exogeneity criteria, the compatibility depends on information about variation over time with respect to each individual that a purely cross-sectional data collection lacks. That lack of information implies that the model usually used to represent the effects of demographic variables in cross-sectional surveys is seriously misspecified. The same limitation affects any specification motivated by ideas about temporal processes. The assumptions needed to translate ideas about temporal processes into a purely cross-sectional model are then identified, and found to include incredibly strong assumptions of homogeneity and stationarity. The difficulty of the assumptions appearing to be so extreme, the discussion then considers the possibility of a concept of causality that does not rely on variation over time, by briefly examining Lewin's field theory. The extent to which current survey practice draws on temporal ideas even in pure cross-sections is then indicated, with reference to The American Voter's image of a “funnel of causality.”

This article describes a computationally simple, statistically consistent, reasonably efficient, and statistically informative generalized least squares (GLS) estimator for a general class of nonlinear, multidimensional scaling (MDS) models including the “ideal-point” models of voters' and legislators' behavior proposed by Melvin Hinich, Keith Poole, and others. Unlike other methods, the method described in this article provides a statistical framework for testing a wide range of hypotheses about these models including their functional form, their dimensionality, and the values of specific parameters. The Hinich ideal-point model is estimated using this method. It fits the data remarkably well compared to a standard factor analysis model that does not provide a reasonable fit to the data. This has the substantive implication of suggesting that voters base their voting decisions upon ideal-point dimensions like liberalism-conservatism and not upon factor analysis dimensions like competence and leadership.

This article demonstrates how the selection of cases for study on the basis of outcomes on the dependent variable biases conclusions. It first lays out the logic of explanation and shows how it is violated when only cases that have achieved the outcome of interest are studied. It then examines three well-known and highly regarded studies in the field of comparative politics, comparing the conclusions reached in the original work with a test of the arguments on cases selected without regard for their position on the dependent variable. In each instance, conclusions based on the uncorrelated sample differ from the original conclusions.

In political science research these days, the R2 is out of fashion. A chorus of our best methodologists sounds notes of caution, at varying degrees of pitch. Berry and Feldman (1985, 15) remark in their popular regression monograph: “A researcher should be careful to recognize the limitations of R2 as a measure of goodness of fit.” In their more general statistics text, Hanushek and Jackson (1977, 59) claim that “one must be extremely cautious in interpreting the R2 value for an estimation and particularly in comparing R2 values for models that have been estimated with different data sets.” Perhaps the most pointed attack comes from Achen (1982, 61), who argues that the R2 “measures nothing of serious importance.” His contention is that it should be abandoned, and the standard error of the regression (SEE) substituted as a goodness-of-fit measure. Developing these lines of inquiry further, King (1986) provides the latest set of criticisms. Accordingly, “In most practical political science situations, it makes little sense to use [the R2]” (King 1986, 669). And, concerning the “proportion of variance explained” definition more particularly, “it is not clear how this interpretation adds meaning to political analyses.” (King 1986, 678).

Two quite different statistical specifications lead to conventional regression computations. Under the first, usually called unconditional regression, the independent variables are assigned a distribution, and the sampling distributions of parameters are computed over it, not just over the variation in the disturbance. Then the multiple squared coefficient of correlation, R2, is a substantively meaningful quantity with a population value. In such cases, it is certainly meaningful to estimate R2 and to use the resulting estimate for the usual descriptive and inferential purposes.

The nature of most social scientific work, however, generates data poorly described by the first specification. The second specification, conditional regression, is usually more helpful, and for that reason, it overwhelmingly predominates in econometric textbooks. Under it, sampling distributions are conditioned on the observed values of the independent variables. Then, R2 is a purely descriptive quantity with little substantive content. It is not a parameter, and it will vary meaninglessly across samples even when the underlying statistical law is unchanged. By contrast, the standard error of estimate (SEE) lacks these difficulties, and is a far better statistic for assessing goodness of fit.

Lewis-Beck and Skalaban are persuasive where unconditional regression is concerned. But their argument encounters serious difficulties in the far more common situation in which conditional regression applies. Their blurring of the distinction between the two situations explains why their seemingly persuasive logic leads them astray.

In an interesting and provocative article, Michael Lewis-Beck and Andrew Skalaban make an important contribution by emphasizing several philosophical issues in political methodology that have received too little attention from methodologists and quantitative researchers. These issues involve the role of systematic, and especially stochastic, variation in statistical models. After briefly discussing a few points of disagreement, hoping to reduce them to points of clarification, I turn to the philosophical issues. Examples with real data follow.