Evolutionary Factor Analysis of the Dynamics of Frames: Introducing a Method for Analyzing High-Dimensional Semantic Data with Time-Changing Structure

Abstract

In public discourse, meaning is constantly renegotiated. Frames and other semantic structures are co-constructed in the public debate based on the contributions of many discourse participants. Over time, they incorporate new information and interpretations. As a result, time-dependent changes occur both on the level of manifest contributions and on the level of latent structures organizing discourse into meaningful frames. This article introduces a technique capable of analyzing the changing patterns of meaning in a genuinely dynamic fashion. It applies Evolutionary Factor Analysis (EFA), a recently developed technique for treating high-dimensional data with time-changing latent structure. Using EFA, we uncover evolving patterns on different levels of abstraction within our data, which represent discourse as a detailed semantic network. We investigate specific dynamics expected within dynamic discourse (e.g., emergence, evolution, consolidation, crisis) and analyze the time-changing structure and content of meaning. The methodological innovation presented in this paper allows a detailed analysis of micro-level changes organized by latent higher-level structures: It can be transferred to a variety of social phenomena organized by structures that evolve over time (e.g., public opinion, social interaction). Rendering their dynamic behavior accessible to statistical analysis, it offers new theoretical insights into their mechanics and underlying structure.

Notes

¹Our approach is based on The Evolutionary Factor Analysis introduced by Motta (2009), which is similar to the procedure introduced by Baumgartner, De Boef, and Boydstun (2008), but differs in three important respects: First, while they construct moving windows of time points by simply summing up occurrences at successive moments, our model discounts prior events increasing with temporal distance. Second, our technique models the smooth transition from one moment to the next (optimally, with kernel smoothing), such that one dynamic factor model is estimated across all recorded time points. Their approach, by contrast, computes stationary factor models for overlapping phases and relies chiefly on a stepwise (rather than smooth) comparison of successive phase's factor solutions. Third, due to the unified, genuinely dynamic statistical modeling, our approach allows computing a range of additional parameters which are also smooth functions of time. As a consequence, our approach is capable of tracing internal changes within semantic structures on multiple levels of abstraction over time, detecting frame evolution, mergers and differentiations. It is not, as Baumgartner et al.’s (2008) strategy is, dependent on manually identifying factor solutions in different phases which are, in one way or another, sufficiently similar to call them two states of the same frame.

²We use the terms “meaning” and “interpretations” more or less interchangeably to denote the sense given to a specific phenomenon in social reality based on the available information. Meaning is thus the outcome of a interpretative process which draws upon both manifest information provided by some message and prior knowledge, which has been formed by past discourse and cultural socialization. Since meaning is idiosyncratic, it remains a latent concept in our analysis.

³Propositions are the smallest possible semantic unit that conveys information: While concepts presuppose that their semantic content is understood, propositions relate concepts to one another and thereby present the kernel of meaning construction (Baden, 2010). Propositions go beyond concept associations in that they qualify the association between the participating concepts and thereby render the association interpretable.

⁴One difficulty is that the same definition criteria can be applied to semantic structures of remarkably different scale and abstraction, depending on the precise interpretation of the ‘coherence’ requirement: With a relatively strict notion of coherence (all participating concepts relate in meaningful ways to one another, and the sum of all these relations constructs one common interpretation), frames are relatively small and highly context specific. If one takes “coherent” to mean compatible sets of background assumptions that support the interpretation, very many quite different concepts and associations may occur within one frame, which is then relatively general: One case might be Valkenburg, Semetko, and de Vreese's (1999) “generic frames,” which require coherence in the kind of information that is regarded as relevant (personal, economic, …). Another case would be Benford and Snow's (2000) “master frames,” which reflect a common ideological background, and come close to what we will call a repertoire (Donati, 1992; Wetherell & Potter, 1988)—a term borrowed from discourse analysis that expresses an agreement with regard to implicit background assumptions and overall perspective. Also Gerhards and Rucht's (2000) “master frames,” which express an agreement in the overall narrative structure (actor roles, kinds of explanations and actions) but can be used to construct substantively quite different accounts, would fit such a wide definition. Our notion of frames is closer to the strict (small) end of the continuum: To consider a set of concept associations coherent (hence, call it a frame), we require that a small set of concepts defines the core concern of the frame (they are all directly linked to each other by Gamson and Modigliani's (1987) “central organizing idea”); peripheral elements of the frame may instantiate or elaborate upon this core selectively, as long as the interpretations that arise from these elaborations do not contradict each other. For a detailed discussion, see Baden (2010).

⁵We use the expression “semantic structures” to describe any kind of pattern within discourse that conveys semantic information. Semantic structures exist in many shapes; however, this article mainly treats three kinds—concept associations, frames, and repertoires. Semantic structures are latent in that they emerge within discourse from a recurrent (manifest) use of specific concepts in characteristic constellations.

⁶Obviously, the precise meaning expressed by each dimension is less than perfectly stable but evolves over time. Consequently, it is somewhat problematic to speak of the time-changing salience of ‘the dimension’. However, to the degree that semantic evolution is a) gradual and b) observable, it is possible to identify those continuities and path-dependencies that justify talking of one, ongoing and evolving discourse.

⁷This Evolutionary Factor Analysis is not to be confused with the technique introduced under the same name by Baumgartner, De Boef, and Boydstun (2008; see footnote 1).

⁸Related matrix transformation techniques such as singular value decomposition or non-negative matrix factorization are less suitable for this approach. The latter technique prevents negative factors, thereby misrepresenting the shape of fluctuations in evolutionary discourse data. SVD is unable to recover the latent factors of a factor model, thereby limiting the opportunities for subsequent macro-level analysis.

⁹We use the trace ration as a measure of the amount of variance that q principal components account for. This value is given by the ratio between the sum of the largest q eigenvalues over all eigenvalues.

¹⁰These core concepts were identified based on their sustained pivotal role in defining a specific repertoire: They did not necessarily show the strongest loadings on a specific factor, but they had to remain consistently, over multiple extended periods, among the set of three to six concepts that defined the meaning expressed by a factor.

¹¹The macro level structure is usually predefined—postulating, for example, an ideological left-right-continuum or a taxonomy of topics (Beauchamp, 2001; Chang & Blei, 2009).