THROUGHOUT THE BOOK, we estimate models to test whether the tendency of justices to support outcomes consistent with their policy preferences is constrained by either legal doctrines or a combination of doctrines and the legislative and executive branches. Here we describe the latent variable specification employed to test whether non-ideological factors affect justice behavior. Generalizing the model to include multiple non-ideological factors is straightforward. Let i = 1, …, N index individuals and v = 1, …, V index votes. The utility of actor i of voting for the conservative alternative is
whereis the spatial location of the conservative alternative, θit is the ideal point of the actor at the time of proposal t, is the non-policy value of voting for the conservative alternative, δi is the weight placed by i on non-policy values, and is a random shock. The utility of voting for the liberal alternative with spatial location of is analogous.
Letbe the utility difference between the conservative and liberal alternatives. It is
Letbe the vote cutpoint, be the vote “discrimination parameter,”1 be an observed non-ideological deference variable, and be a N(0, 1) random variable; then
Observed votes (as opposed to unobserved latent values above) are denoted by yitv. To address rotational identification (e.g., liberals can have high values or low values), conservative votes are coded as yitv= 1. The location and scale of ideal points are identified by assuming they have mean 0 and variance 1; this is equivalent to fixing two individuals at arbitrary points (see, e.g., Bafumi et al. 2005).