Recovering a Basic Space in R

This R (R Development Core Team, 2011) package contains software designed to recover latent dimensions (i.e. a basic space) from a numeric matrix of data. The initial development was conducted by Poole (1998), who wrote the Fortran executable that was previously used by social scientists to analyze survey data in publications such as Saiegh (2009) and Abrajano and Poole (2011). The principal purpose of the package is to facilitate the analysis of selfplacement and/or perceptual survey data by scaling stimuli into a common space. Stated differently, assume that various political actors (i.e. the stimuli) occupy positions on a continuous left-right political spectrum, and our objective is to recover estimates of those positions. This package facilitates the estimation of these positions under the assumption that survey respondents report their personal estimates of these positions with different levels of bias and scale attenuation. While intended for use with survey data, this procedure has potentially broader applications outside of social science because mathematically it can be thought of as a special case of singular value decomposition on a numeric matrix with missing data. This vignette proceeds in four steps. First, we begin with a description of the math that underlies the basic space estimator. We then provide three examples. First, we show a Monte Carlo analysis that suggests our estimator produces an accurate decomposition of our simulated data matrix even with 30 per cent of the data missing. Secondly, we show how the procedure can be applied to self-placement survey data from the 1980 National Election Survey. We conclude with an application of the model to perceptual data from the 1980 National Election Study, where various political candidates are ranked along a 7 point liberal-conservative scale.