1. For example, Miller (1993) rationalizes the use of a unidimensional model of legislative and presidential interaction with the fact that NOMINATE recovers a unidimensional policy space.
2. Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation
3. Maximum Likelihood Estimates in Exponential Response Models
4. We would like to establish that Lc (d, h) > Lu (d, h) and, thus, be confident that Ehdc (h; α) » E h du (h; α) for all α levels. Proof of this claim requires analysis of the convexity properties of the likelihood function and offers little intuition. Instead, we worry only about sufficiently high α's so that the recovered dimensionalities dc (h; α) and du (h; α) are those for which nearly perfect voting yields the recovered data set. Thus, the result should be interpreted as stating that the unconstrained estimate yields an underestimate of the dimensionality of the policy space if one is sufficiently concerned about not finding the dimensionality of the policy space smaller than it really is. Since α and β are inversely related, we formulate the analysis for sufficiently high α so as to pertain to the case of sufficiently low β (type II error).