Frames, like word meanings, are complex psychological entities that are difficult to identify. However, if the contexts in which a word occurs provide some information about its framing, we can exploit that information by exploring the distances or similarities of those contexts vis-à-vis those of certain manually selected words which we take to be prototypically associated with particular frames. For instance, if terror is framed as an act of war rather than a crime, then, on average, the contexts in which the word terror occurs should be more similar to the contexts in which the word war occurs than to those in which the word crime occurs. This is the assumption at the core of the method we present in this paper. More specifically, we assume that the semantic content of a word can be approximated by observing the words that it frequently co-occurs with [15,16].

LSA is a collective term for a family of methods aimed at operationalizing this intuition by deriving a measure of similarity between words from their co-occurrence behavior in a collection of documents. Technically, words are associated with vectors in a high-dimensional space. The most commonly used measure in this framework is the cosine between the associated vectors: A high cosine (i.e., low angle) indicates positively correlated co-occurrence profiles, hence by assumption semantic similarity. Within the LSA family, our method is based on the Wordspace paradigm [18,25] (see Figure 1 for a general overview of how a semantic space is generated within the paradigm. Text S1 provides details and differences with other LSA-style methods). Figure 2 presents a schematic outline of our method of analysis, as described in more detail below.

Since we are interested in the individual occurrences (tokens) of a given word (type), we use the word vectors to derive context vectors for all occurrences of the target word (such as terror or abortion). Formally, the context vector for a given token is the normalized sum of the word vectors associated with the words surrounding it within a text window of a certain fixed width. A similar method was first applied in word-sense discrimination [20]. Analogously, we hypothesize that differences in framing of a given word can be observed and measured in terms of the context vectors of its occurrences. To this end, the collection of context vectors for all occurrences of the target word can be divided up along various independent variables. Furthermore, because vector similarities are represented as simple scalars, differences in framing can be explored using standard methods for statistical hypothesis testing (e.g., by computing a t-statistic comparing the distances between context vectors representing uses of terror and war before and after September 11^th, 2001).

Although the context vectors we compare are associated with concrete words like terror and war, our similarity measure is different from a simple co-occurrence count or other measures of collocational strength. What we are interested in is a relationship between regions in a densely populated vector space. The particular words we choose to represent frames -war in our example – are merely convenient identifiers for such regions. Consequently, our analysis of the framing of terror yields qualitatively similar results whether the framing term is war, fight, or military, even though the pattern of direct co-occurrence of the term terror with these words varies considerably.

The first corpus we use is intended to track changes in issue frames among the debates of policy elites, here U.S. Senators. It includes transcripts of all speeches given on the floor of the U.S. Senate from 1989 to June of 2006 [13,14]. It is composed of 229,527 speeches totaling over 125 million transcribed words.

Our second corpus can be used to identify issue frames in the mass media and observe their development over time. That corpus is a collection of New York Times articles from 1987 to 2007, available from the Linguistic Data Consortium [26]. It is comprised of 1,855,658 articles totaling over 4 billion words.

We prepared the corpus for analysis using Infomap [27] to generate a semantic space from the corpus, and derived word vectors for the 20,000 most frequent non-stopwords in the corpus. (Text S1 provides more information on this process.)

Next, we identified all of the contexts in which the words of interest and their possible frames occur. This resulted in 3,147 contexts for terror, 27,863 for crime, and 59,686 for war, 10,954 for abortion, 17,203 for choice, 48,665 for life, 11,470 for woman, and 9,168 for mother. In the New York Times analysis, this resulted in 62,561 contexts for abortion, 109,682 for choice, 566,764 for life, 222,623 for woman, and 261,562 for mother.

For each of these contexts we computed a context vector to be used in the analysis. Context vectors were calculated based on word vectors in a semantic space generated from the same corpus. Each context vector was computed using vector addition over a window of 15 words before and 15 words after the target word, a window size that was chosen because it allows a substantial portion of context to be used. After the application of vector addition the vectors were normalized to a length of 1 by dividing each vector by its length so that the length of the resulting vector would not affect further calculations.

To calculate the semantic distance we averaged the cosines between all of the vectors representing the target term on the one hand, and those representing its possible frames for each year. Importantly, since the first dimension of the vectors resulting from Singular Value Decomposition is always positive and correlated with the frequency of the term, we omitted the first dimension when computing the cosines [28]. Statistical analysis was conducted using ANOVAs.

Our first example is the framing of terror as a war after September 11^th, 2001. While this framing has become highly salient in recent political discourse, Lakoff [29] suggests that initially there was another, competing frame – terror as a crime. In our analysis we investigated whether terror was framed in terms of war rather than crime after the events of 9/11. Following Lakoff’s analysis, we hypothesized that we should see a significant decrease in the distance between the context vectors of terror and war after 2001 compared to previous years. In contrast, we have no such expectation in the case of terror and crime.

We computed context vectors for the occurrences of the target word terror and its two hypothesized frames war and crime in our corpus. We then computed the mean distance between terror and each of war and crime for each year (Figure 3). As predicted, the distance between the vectors for terror and war is significantly reduced after 2001 (M_<2001 = 0.1363, SD_<2001 = 0.001, M_>2001 = 0.1301, SD_>2001 = 0.0001; F(1,15) = 127.48, MSE = 0.000001, p < .0001, η²_p = .90) while the distance between the vectors for terror and crime does not show a similar reduction and in fact trends in the opposite direction (M_<2001 = 0.1383, SD_>2001 = 0.001, M_>2001 = 0.1396, SD_>2001 = 0.0006; F(1,15) = 4.06, MSE = 0.000002, p = .062, η²_p = .21). This analysis provides support for the claim that post-9/11 terror was increasingly framed in terms of war rather than crime. Interestingly, it appears that of the two, war was the stronger and more prevalent framing of terror even prior to 9/11.

It is also possible to visualize this space more generally using methods for dimensionality reduction, such as multidimensional scaling (Figure 4; see Movie S1 for a complete set in movie format). We chose to use multidimensional scaling for the visualization because it focuses on maintaining the relative distances between points in the space. This makes it particularly suitable for spatial visualization. Nevertheless, there are many other options for dimensionality reduction, including factoring methods such as the one we used to generate the semantic space (SVD).

The second example concerns the political debate on abortion in the US. Whereas the framing of terror as war became close to universal in the US political debate, especially after 2001, the topic of abortion is one which continues to polarize the political arena. The two major positions in this debate are often labeled pro-choice (mostly Democrats) and pro-life (mostly Republicans). While there are many possible terms that might be used to frame this debate, we chose to focus on the terms choice and life. The first represents the notion that an abortion should be primarily viewed through the lens of a woman’s right to choose (a position usually preferred by Democrats) while the second frames the debate in terms of the consequences to the fetus’ “right to life” (and should therefore be a frame preferred by Republicans). The mean distances by party (Figure 5) reflect this difference in position between the parties (‘choice’: M_D = 0.1389, SD_D = 0.001, M_R = 0.1388, SD_R = 0.001; ‘life’: M_D = 0.1394, SD_D = 0.001, M_R = 0.1385, SD_R = 0.002). As predicted, there is a significant interaction between the party and frame used (F(1,17) = 17.91, MSE = 0.0000002, p = < .001, η²_p = .51).

The difference in framing should also be evident in the ways in which the parties refer to women undergoing the procedure [30]. That is, a focus on the effects of the procedure on the baby might be strengthened by referring to such individuals as mothers. In contrast, the term woman is more neutral with regards to the procedure. We therefore predicted that the framing of abortion by Republicans will be closer to their use of the term mother than for Democrats, but that no such differences will be found with regards to the term woman. The mean distances by party (Figure 6) support this prediction – Democrats are less likely to speak about abortion using terms associated with mother than Republicans (‘mother’: M_D = 0.1373, SD_D = 0.002, M_R = 0.1348, SD_R = 0.004; ‘woman’: M_D = 0.1365, SD_D = 0.002, M_R = 0.1359, SD_R = 0.003; Interaction term: F(1,17) = 11.33, MSE = 0.0000013, p < .01, η²_p = .40).

In political science, issue frames are generally defined as a focus on a single dimension of an issue [5]. This definition suggests that the two linguistic frames (choice/life and woman/mother) are, in actuality, manifestations of a single issue frame. The “pro-choice” frame corresponds to choice-woman, the “pro-life” frame to life-mother. That is, a preference for framing abortion in terms of life should also result in a preference to frame it in terms of mother. If this is the case, then there should be a positive correlation between the changes that these preferences undergo over time.

We tested this hypothesis by calculating a “frame preference” index for each of the two frames for each party and year. As predicted, the two indices show a significant positive correlation (r(35) = .52, p < .05). Therefore we can conclude that the two frames are not independent, but rather represent two facets of a single overarching frame of abortion.

There has been an extensive debate over media influence and bias [30]. Experimental research has shown that the media can shape opinion not only through explicit commentary, but also through issue frames [5,24]. We can investigate suggested media framing directly using our method. Here we focus on coverage in the New York Times, which is typically viewed as a relatively liberal newspaper, i.e. leaning towards a “pro-choice” position. Figure 7 presents the mean distances from abortion for the 4 terms we explored above. The results provide support for the claim that, at least in the New York Times, journalists frame abortion in terms of choice and are less likely to use terms that imply motherhood in these contexts (‘choice’: M = 0.1394, SD = 0.0007; ‘life’: M = 0.1406, SD = 0.0003; F(1,17) = 76.84, MSE = 0.0000002, p<.0001, η²_p = .82; ‘woman’: M = 0.1405, SD = 0.0003; ‘mother’: M = 0.1417, SD = .0003; F(1,17) = 241.295, MSE = 0.00000005, p<.0001, η²_p = .93). An analysis of the correlation of the frame preference indices similar to that conducted earlier results in a similarly positive correlation (r(17) = .50, p < .05). This provides further evidence supporting the hypothesis that a single issue frame is underlying the observed preferences for both linguistic frames.