Lord’s Equity Theorem Revisited

Lord’s (1980) equity theorem claims observed-score equating to be possible only when two test forms are perfectly reliable or strictly parallel. An analysis of its proof reveals use of an incorrect statistical assumption. The assumption does not invalidate the theorem itself though, which can be shown to follow directly from the discrete nature of the equating problem it addresses. But, surprisingly, an obvious relaxation of the problem is enough to obtain exactly the opposite result: As long as two test forms measure the same ability, they can always be equated, no matter their reliability, degree of parallelness, or even difference in length. Also, in spite of its lack of validity, the original proof of Lord’s theorem has an important interim result directly applicable to the problem of assembling a new test form pre-equated to an old form.

Modeling Equilibrium Relationships: Error Correction Models with Strongly Autoregressive Data

Political scientists often argue that political processes move together in the long run. Examples include partisanship and government approval, conflict and cooperation among countries, public policy sentiment and policy activity, economic evaluations and economic conditions, and taxing and spending. Error correction models and cointegrating relationships are often used to characterize these equilibrium relationships and to test hypotheses about political change. Typically the techniques used to estimate equilibrium relationships are based on the statistical assumption that the processes have permanent memory, implying that political experiences cumulate. Yet many analysts have argued that this is not a reasonable theoretical or statistical assumption for most political time series. In this paper I examine the consequences of assuming permanent memory when data have long but not permanent memory. I focus on two commonly used estimators: the Engle-Granger two-step estimator and generalized error correction. In my analysis I consider the important role of simultaneity and discuss implications for the conclusions political scientists have drawn about the nature, even the existence, of equilibrium relationships between political processes. I find that even small violations of the permanent memory assumption can present substantial problems for inference on long-run relationships in situations that are likely to be common in applied work in all fields and suggest ways that analysts should proceed.

No Evidence on Directional vs. Proximity Voting

The directional and proximity models offer dramatically different theories for how voters make decisions and fundamentally divergent views of the supposed microfoundations on which vast bodies of literature in theoretical rational choice and empirical political behavior have been built. We demonstrate here that the empirical tests in the large and growing body of literature on this subject amount to theoretical debates about which statistical assumption is right. The key statistical assumptions have not been empirically tested and, indeed, turn out to be effectively untestable with existing methods and data. Unfortunately, these assumptions are also crucial since changing them leads to different conclusions about voter decision processes.