Binding a Bottomless Barrel: Boundless Dimensions in Ideological Attitude Scales

• In Event: Advances and Challenges in the Measurement of Latent Traits

Abstract

This paper addresses a critical yet often overlooked issue in applied political science and quantitative psychology: the dimensionality of ideological attitudes as measured by policy position items. Traditional approaches to understanding mass ideology have oscillated between unidimensional and multidimensional perspectives. Proponents of unidimensional models claim that mass preferences on political issues can generally be summarized by a single, generalized left-right axis, while “multidimensionalists” advocate for acknowledging the inherent complexity in mass preferences through multiple, distinct ideological factors.
Our study reveals fundamental limitations of both perspectives. Using policy position data from the American National Election Studies and a graph-based machine-learning algorithm, we show that the optimal number of latent ideological dimensions increases indefinitely as more policy position items are selected for analysis. Unfortunately, boundless dimensional growth violates one of the fundamental assumptions of latent variable models in that more information is expected to lead to more precise measurement among a finite set of latent constructs. In other words, ideological dimensionality grows without bound as researchers select more issues measuring ideology.

At the same time, virtually all latent ideological dimensions found within large, nationally representative survey data of the American public are positively and sizable correlated with one another. While distinct enough to warrant separate spatial representation, these inter-factor correlations point to fundamental similarities shared across all latent dimensions. Paradoxically, data taken from the same individuals can thus simultaneously justify multidimensional and unidimensional perspectives.

In light of these findings, we propose that political ideology should neither strictly be understood as unidimensional or multidimensional. Rather, mass ideology exists in a hybrid state, best characterized by a (large) family of substantially related concepts. Consequently, we argue that modeling strategies based on “family resemblance” strikes a better balance between preserving the parsimony offered by unidimensional models while revealing insights unique to different constitutive sub-dimensions.

We propose two modeling alternatives heeding to the family resemblance paradigm. The first is based on a partial dimension reduction procedure (somewhat akin to principal components analysis), in which raw policy position data is re-scaled to match the underlying inter-item correlation matrix. This process results in a partially compressed ideological space which aligns respondents along major ideological axes while preserving the most important aspects of voters’ unique expressions. Preliminary results show that empirical estimates about relative distances within the resulting, partially shrunken space converge faster and show lower variance at larger item buckets compared to either strictly unidimensional or multidimensional models.

Our second approach employs Bayesian hierarchical factor modeling, allowing simultaneous estimation of multidimensional subfactors and a single, superordinate ideological dimension while fitting predictors to each. Reaching beyond traditional, maximum-likelihood-based estimation strategies, this method can empirically differentiate between effects driven by generalized (unidimensional) ideology (e.g., voting and political partisanship) and those specifically relevant to particular sub-dimensions (e.g., racial resentment, authoritarianism, income, etc.). In this way, Bayesian hyper-factor models can provide new insights about the drivers and consequences of mass ideology without strictly imposing particular modes of dimensionality.

Authors

• Philip Warncke, UNC Chapel Hill

• Flavio Azevedo, Friedrich Schiller University