2.1 Notation and Problem Setup

Consider a collection of $N$ text documents, indexed by $i=1,\ldots ,N$ , where each document contains a sequence of terms. These documents could be any of a number of forms such as news articles posted online, blog posts, or entire books, and each document in the dataset need not be of the same form. Together, these $N$ documents comprise a corpus, and the set of $V$ unique terms used across the corpus defines the vocabulary. Each term in the vocabulary is typically a unique, lowercase, alphanumeric token (i.e., a word, number, or punctuation mark), though the exact specification of terms may depend on design decisions by the analyst (e.g., one may choose to include as terms in the vocabulary all bigrams observed in the corpus in addition to all observed unigrams). Because the number and composition of features which may be extracted from text is not well-defined, documents are generally regarded as “unstructured” data in the sense that their dimension is ex ante unknown.Footnote ¹ To address this issue, we impose structure on the text through a representation, $X$ , which maps each document to a finite, usually high-dimensional, quantitative space.

To make principled comparisons between groups of documents within the corpus, we borrow from the notation and principles of the Rubin causal model (RCM) (Holland Reference Holland1986). Under the RCM, each document has an indicator for treatment assignment (i.e., group membership), $Z_{i}$ , which equals 1 for documents in the treatment group and 0 for documents in the control group. Interest focuses on estimating differences between these groups on an outcome variable, which, under a causal view, would take the value $Y_{i}(1)$ if document $i$ is in the treatment group and $Y_{i}(0)$ if document $i$ is in the control group. These outcomes may be separate from the text of the document (e.g., the number of times a document has been viewed online) or may be a feature of the text (e.g., the length of the document or level of positive sentiment within the document).Footnote ² Credible and precise causal inference revolves around comparing treated and control documents that are as similar as possible. However, in observational studies, $Z_{i}$ is typically not randomly assigned, leading to systematic differences between treatment and control groups. Matching is a strategy that attempts to address this issue by identifying samples of treated and control documents that are comparable on covariates in order to approximate the random assignment of $Z_{i}$ (i.e., to satisfy $Z_{i}\bot \!\!\!\bot (Y_{i}(0),Y_{i}(1))|X_{i}$ ) (Rubin Reference Rubin1973a; Rosenbaum Reference Rosenbaum2002; Rubin Reference Rubin2006). Under this key assumption of “selection on observables,” which states that all covariates that affect both treatment assignment and potential outcomes are observed and captured within $X$ , comparisons of outcomes between matched samples can be used to obtain unbiased estimates of the quantities of interest (Rosenbaum Reference Rosenbaum2002). For example, in our second application examining the effects of a medical intervention, we argue that matching on both a set of numerical covariates and the text content of the patients chart allows us to identify two groups of patients, one treated and one not, that are similar enough on pretreatment variables such that any systematic differences in their outcomes can be plausibly attributed to the impact of the intervention.

These causal inference tools can be used more broadly, however, to produce clearly defined comparisons of groups of units even when a particular intervention is not well-defined. For example, Silber et al. (Reference Silber, Rosenbaum, Ross, Ludwig, Wang, Niknam, Mukherjee, Saynisch, Even-Shoshan and Kelz2014) introduce template matching as a tool for comparing multiple hospitals that potentially serve different mixes of patients (e.g., some hospitals have a higher share of high-risk patients). The core idea is to compare like with like: by comparing hospitals using an effective “score card” of patients, we can see which hospitals are more effective, on average, given a canonical population. In general, we focus on this general conception of matching, recognizing that often in text there is no treatment that could, even in concept, be randomized. For example, a comparison of style between men and women could not easily be construed as a causal impact. Nevertheless, the framing and targeting of a controlled comparison, a framing inherent in a causal inference approach, can still be useful in these contexts. This broader formulation of matching is used in our first application in Section 5, investigating different aspects of bias in newspaper media.

2.2 Promises and Pitfalls of Text Matching

Matching methods generally consist of five steps: (1) identify a collection of potential confounders (covariates) that would compromise any causal claims if they were systematically different across comparison groups; (2) define a measure of distance (or similarity) to determine whether one unit is a good match for another; (3) match units across comparison groups according to the chosen distance metric; (4) evaluate the quality of the resulting matched samples in terms of their balance on observed covariates, possibly repeating the matching procedure until suitable balance is achieved; (5) estimate treatment effects from these matched data (Stuart Reference Stuart2010). Different choices at each step of this process produce an expansive range of possible configurations. For instance, there are distance metrics for scalar covariates (Rubin Reference Rubin1973b), for multivariate covariates summarized through a univariate propensity score (Rosenbaum and Rubin Reference Rosenbaum and Rubin1983, Reference Rosenbaum and Rubin1985), and multivariate metrics such as the Mahalanobis distance metric (Rubin Reference Rubin1978; Gu and Rosenbaum Reference Gu and Rosenbaum1993).

Similarly, there is a large and diverse literature on matching procedures (Rosenbaum Reference Rosenbaum2002; Rubin Reference Rubin2006), and the choice of procedure depends on both substantive and methodological concerns. Some procedures match each unit in the treatment group to its one “closest” control unit and discard all unused controls (e.g., one-to-one matching with replacement), while other procedures allow treated units to be matched to multiple controls (e.g., ratio matching; Smith Reference Smith1997) and/or matching without replacement (e.g., optimal matching; Rosenbaum Reference Rosenbaum1989). Match quality is often evaluated with a number of diagnostics that formalize the notion of covariate balance such as the standardized differences in means of each covariate (Rosenbaum and Rubin Reference Rosenbaum and Rubin1985). Unfortunately, determinations of what constitutes “suitable” balance or match quality are often based on arbitrary criteria (Imai, King, and Stuart Reference Imai, King and Stuart2008; Austin Reference Austin2009), and assessing whether a matching procedure has been successful can be difficult. That being said, if and when a suitable set of matches is obtained, one can then typically analyze the resulting matched data using classic methods appropriate for the type of data in hand. Stuart (Reference Stuart2010) outlines a number of common analytical approaches.

The rich and high-dimensional nature of text data gives rise to a number of unique challenges for matching documents using the standard approach described above. From a causal inference perspective, in many text corpora, there is going to be substantial lack of overlap, that is, entire types of documents in one group that simply do not exist in the other groups. This lack of overlap is exacerbated by the high-dimensional aspect of text: the richer the representation of text, the harder it will be to find documents similar along all available dimensions to a target document (D’Amour et al. Reference D’Amour, Ding, Feller, Lei and Sekhon2017). This makes the many design decisions required to operationalize text for matching such as defining a distance metric and implementing a matching procedure especially challenging. Distance metrics must be defined over sparse, high-dimensional representations of text in a manner that captures the subtleties of language. If these representations are overly flexible, standard matching procedures can fail to identify good (or any) matches in this setting due to the curse of dimensionality.

Lack of overlap can come from substantive lack of overlap (the documents are inherently different) and also aspects of the text representation that are not substantive (this is akin to overfitting the representation model). Ideally, a good representation and distance metric will preserve the former but not the latter. All of the matching procedures discussed in this work can be thought of as carving out as many high-quality matches as they can find, implicitly setting parts of the corpus aside to have good comparisons across groups. This is in effect isolating (Zubizarreta, Small, and Rosenbaum Reference Zubizarreta, Small and Rosenbaum2014) a focused comparison within a larger context. In a causal context, this can shift the implied estimand of interest to only those units in the overlap region. For further discussion of the approaches commonly used to address overlap issues, see, for example, Fogarty et al. (Reference Fogarty, Mikkelsen, Gaieski and Small2016), Dehejia and Wahba (Reference Dehejia and Wahba2002) and Stuart (Reference Stuart2010).

Despite its complexities, the rich nature of text data also provides an opportunity in that it lends itself to more straightforward, intuitive assessments of match quality than are typically possible with quantitative data. Specifically, while it is difficult to interpret the quality of a matched pair of units using numerical diagnostics alone due to being high-dimensional, the quality of a matched pair of text documents is generally intuitive to conceptualize. With text data, human readers can quickly synthesize the vast amount of information contained within the text and quantify match quality in a way that is directly interpretable. Thus, when performing matching with text data, final match quality can be established in a manner that aligns with human judgment about document similarity. This is a version of “thick description,” discussed in Rosenbaum (Reference Rosenbaum2010, pg. 322). This also allows for comparing different matching methods to each other in order to find methods that, potentially by using more sparse representations of text or more structured distance measures, can simultaneously find more matched documents while maintaining a high degree of match quality.

2.3 Different Types of Text-Based Confounding

Text is quite multifaceted, but that does not necessarily mean that the researcher needs to attend to all aspects of the text in order to appropriately control for any confounding. Generally, matching with text is to control some latent feature of the text that is believed to potentially confound the relationship between group membership and outcome of interest. But how complex such a feature is can vary, and, depending on what the researcher wishes to control for, one might approach matching using explicitly calculated features of the text or something less explicit, such as the methods described in this work. We next discuss this spectrum of options.

In the simpler cases, one may wish to control for some feature identifiable as, for example, a set of related words. For instance, in the medical study described in Section 5.2, a patient’s degree of frailty (i.e., healthiness or lack thereof) is a potentially confounding factor that is not measured numerically but is indicated in the text data through several key terms or phrases (e.g., “wheelchair bound”). If all such text-based indicators for the underlying construct of interest can be identified ex ante based on subject matter expertise and/or substantive theory, then it may be possible to directly quantify the latent variable by applying some hand-coded decision rules to the text.Footnote ³ In this circumstance, we may simply calculate these features for our documents and use classic matching methods from there to find groups of documents well balanced in their prevalence of our hand-constructed, numerical covariates.

It is the cases where such a direct coding of the features of interest is not possible that are the focus of this paper. For example, many studies may have important confounding features that are inherently subjective (e.g., a hospitalized patient’s level of optimism or a news story’s partisan content). This introduces two difficulties: first, how to consider whether a match is of low or high quality, and, second, how to ensure that the measure of quality is in fact aligned with the difficulty to capture latent, potentially confounding, features of interest. To illustrate, in Section 5.1, we control for a feature of news articles that is both latent and subjective: the story being covered. Since there are many different stories covered across all news articles, this confounding feature is a high-dimensional categorical variable. As such, while there may be keywords which perfectly identify any one story, such as the flight numbers of plane crashes or the names of important figures, a complete list of all such keywords cannot feasibly be compiled.

It is contexts such as these where we hope matching on more general representations of text, which can be constructed without extensive manual coding efforts, will still allow for principled comparisons between groups of documents. That being said, we also recognize that automated methods for evaluation of text may not be appropriate in certain settings. We therefore encourage researchers to perform validation experiments that rely on human evaluation to verify that the text-matching process is controlling for aspects of text that may violate the critical “selection on observables” assumption.

3.1 Text Representations

The representation of a text document transforms an ordered list of words and punctuation into a vector of covariates and is the most novel necessary component of matching with text. To choose a representation, the researcher must first formulate a definition for textual similarity that is appropriate for the study at hand. In some cases, all of the information about potential confounders captured within the text data may be either directly estimable (e.g., frequency of a particular keyword) or may be plausible to estimate using a single numerical summary (e.g., the primary topic of a document estimated using a topic model). In other cases, such a direct approach may not be possible.

The most common general representation of text is as a “bag-of-words,” containing unigrams and often bigrams, collated into a term-document matrix (TDM); the TDM may also be rescaled according to term frequency–inverse document frequency (TF–IDF) weighting (Salton and McGill Reference Salton and McGill1986; Salton Reference Salton1991). Without additional processing, however, these vectors are typically very long; more parsimonious representations involve calculating a document’s factor loadings from unsupervised learning methods like factor analysis or STM (Roberts, Stewart, and Airoldi Reference Roberts, Stewart and Airoldi2016) or calculating a scalar propensity score for each document using the bag-of-words representation (Taddy Reference Taddy2013). Finally, we also consider a Word2Vec representation (Mikolov et al. Reference Mikolov, Sutskever, Chen, Corrado, Dean, Burges, Bottou, Ghahramani and Weinberger2013; Le and Mikolov Reference Le, Mikolov, Xing and Jebara2014), in which a neural network embeds words in a lower-dimensional space and a document’s value is the weighted average of its words.

Overall, when choosing a representation, researchers need to consider what aspects of the text are confounding the outcome. Generally, when the objective is to identify exact or nearly exact matches, we recommend using text representations that retain as much information in the text as possible. In particular, documents that are matched using the entire term vector will typically be similar with regard to both topical content and usage of keywords, while documents matched using topic proportions may only be topically similar. When the aspects of text are more targeted or specific, simply directly computing the relevant covariates constructed by hand-coded rules may be the best option. That being said, one might imagine that generally matching on the content of the text—as represented by the specific words and phrases used—will frequently capture much of what different researchers in different contexts may view as the necessary component for their selection on observables assumption. Clearly, this is an area for future work; as we see more matching with text in the social sciences, we will also see a clear picture as to what structural aspects of text are connected to the substantive aspects of text that researchers find important.

3.2 Distance Metrics

Having converted the corpus into covariate representations, the second challenge is in comparing any two documents under the chosen representation to produce a measure of distance. The two main categories of distance metrics are exact (or coarsened exact) distances and continuous distances. Exact distances consider whether or not the documents are identical in their representation. If so, the documents are a match. Coarsened exact distance bins each variable in the representation and then identifies pairs of documents which share the same bins. If the representation in question is based on a TDM, these methods are likely to find only a small number of high-quality matches, given the large number of covariates that all need to agree either exactly or within a bin. The alternative to exact distance metrics is continuous distance metrics such as Euclidean distance, Mahalanobis distance, and cosine distance. Counter to exact and coarsened exact metrics, which identify matches directly, these metrics produce scalar values capturing the similarity between two documents.

3.3 Matching Procedures

After choosing a representation and a distance metric, the choice of matching procedure often follows naturally, as is the case in standard matching analyses. Exact and coarsened exact distance metrics provide their own matching procedure, while continuous distance metrics require both a distance formula and a caliper for specifying the maximum allowable distance at which two documents may be said to still match. The calipers may be at odds with the desired number of matches, as some treated units may have no control units within the chosen caliper, and may subsequently be “pruned” by many common matching procedures. Alternatively, researchers may allow any one treated unit to match multiple controls or may choose a greedy matching algorithm.

4.1 Measuring Match Quality

In standard applications of matching, if two units that are matched do not appear substantively similar, then any observed differences in outcomes may be due to poor match quality rather than the effect of treatment. The usual best practice is to calculate the overall balance between the treatment and control groups, which is typically measured by the difference-in-means for all covariates of interest. If differences on all matched covariates are small in magnitude, then the samples are considered balanced and thus, typically, well-matched.

As previously discussed, standard balance diagnostics typically fail to capture meaningful differences when applied to covariates that are summary measures of text. Further, due to the curse of dimensionality in these settings, it is likely that the comparison groups will have imbalances on at least some (and probably many) covariates. To measure match quality, we therefore rely on a unique property of text: its ease of interpretability. A researcher evaluating two units that have been matched on demographic covariates, for example, may be unable to verify the quality of a matched pair. However, depending on what aspects of text the researcher is substantively attempting to match on, human coders who are tasked with reading two matched text documents are typically capable of quantifying their subjective similarity when properly instructed. We leverage this property to measure match quality using an online survey of human respondents, where match quality is defined on a scale of 0 (lowest quality) to 10 (highest quality).

To obtain match quality ratings, we conducted a survey experiment using Amazon’s Mechanical Turk (MTurk) and the Digital Laboratory for the Social Sciences (DLABSS) (Enos, Hill, and Strange Reference Enos, Hill and Strange2016). Online crowd-sourcing platforms such as these have been shown to be effective for similarity evaluations in a number of settings (Mason and Suri Reference Mason and Suri2012). For instance, a study by Snow, O’Connor Jurafsky (Reference Snow, O’Connor, Jurafsky, Ng, Lapata and Tou Ng2008) who tasked nonexpert human workers on MTurk with five natural language evaluations reported a high degree of agreement between the crowd-sourced results and gold-standard results provided by experts. In the present study, respondents were first informed about the nature of the task and then given training on how to evaluate the similarity of two documents. After completing training, participants were then presented with a series of eleven paired newspaper articles, including an attention check and an anchoring question, and asked to assign a similarity rating. For each question, participants were instructed to read both articles in the pair and rate the articles’ similarity from zero to ten, where zero indicates that the articles are entirely unrelated and ten indicates that the articles are covering the exact same event. Snapshots of the survey are presented in Appendix C in the Supplement.

We might be concerned that an online convenience sample may not be an ideal population for conducting this analysis and that their perceptions of article similarity might differ from the overall population or from trained experts. To assess the reliability of this survey as an instrument for measuring document similarity, we leverage the fact that we performed two identical pilot surveys prior to the experiment using respondents from two distinct populations and found a high correlation ( $\unicode[STIX]{x1D70C}=0.85$ ) between the average match quality scores obtained from each sample. Additional details about this assessment are provided in Appendix D in the Supplement. We take note that these populations, MTurkers and DLABSS respondents, are both regularly used as coders to build training datasets for certain tasks in machine learning; the hallmark of these tasks is that they are easily and accurately performed by untrained human respondents. We argue that this task of identifying whether two articles discuss related stories falls squarely in this category, and our intercoder reliability test (described in Appendix D in the Supplement) supports this argument.Footnote ⁸

In an ideal setting, for each unique matched pair identified using the procedure described above, we would obtain a sample of similarity ratings from multiple human coders. Aggregating these ratings across all pairs in a particular matched dataset would then allow us to estimate the average match quality corresponding to each of the 130 procedures considered, with the quality scores for the 13 procedures that identified no matches set to zero. Though this is possible in principle, to generate a single rating for each unique matched pair requires that a human coder read both documents and evaluate the overall similarity of the two articles. This can be an expensive and time-consuming task. Thus, in this study, it was not possible to obtain a sample of ratings for each of the 32,133 unique pairs.

Instead, we took a stratified, weighted sample of pairs such that the resulting sample would be representative of the population of all 32,133 unique matched pairs as well as the population of 2,778,607 pairs of documents that were not identified by any of the matching procedures. Specifically, the sample was chosen such that each of the 130 matching procedures that identified a nonzero number of matches would be represented by at least four pairs in the experiment. For each stratum, the sampling weights for each pair were calculated proportional to the estimated match quality of that pair, calculated using a predictive model trained on human-coded data from a pilot experiment. We also sampled an additional 50 unique pairs from the pool of 2,778,607 pairs not identified by any matching procedures.

Ratings obtained from these pairs can be used to obtain a reference point for interpreting match quality scores. The resulting sample consisted of 505 unique pairs ranging the full spectrum of predicted match quality scores. Each respondent’s set of nine randomly selected questions were drawn independently such that each pair would be evaluated by multiple respondents. Using this scheme, each of the 505 sampled pairs was evaluated by between six and eleven different participants (average of nine). Question order was randomized, but the anchor was always the first question, and the attention check was always the fifth question.

We surveyed a total of 505 respondents. After removing responses from fifty-two participants who failed the attention check,Footnote ⁹ all remaining ratings were used to calculate the average match quality for each of the 505 sampled pairs evaluated. These scores were then used to evaluate each of the 130 combinations of methods considered in the evaluation, where the contribution of each sampled pair to the overall measure of quality for a particular combination of methods was weighted according to its sampling weight. This inferential procedure is described more formally in Appendix E of the Supplement.

4.3 Evaluating Text-Matching Methods

In our applied examples, we find that text representations that use the TDM or Word2Vec embeddings paired with cosine distance achieve the best results in terms of maximizing predicted match quality and the quantity of matches identified. However, we stress that these results may not generalize to other applied settings. Applied researchers interested in performing text matching in their own analyses should therefore conduct their own systematic evaluations to determine which representations and distance metrics work best in their domains.

When attempting to control for textual confounding in a given setting, we recommend that researchers first implement a suite of text-matching procedures that includes a diverse set of representations and distance metrics. Matches identified by the different methods can then be compared to determine which procedure is most suitable for the given application. If there is substantial overlap across all methods, it may be that no evaluation is necessary. However, in most cases, the sets of matched pairs identified by each procedure will largely diverge. In this case, we recommend performing a formal evaluation, for instance using experimentation, to determine which methods most accurately and precisely capture the confounding features of interest.

Recall from our discussion in Section 2.3 that if important textual confounders can be easily extracted from the observed text data (e.g., by constructing indicator variables for a set of key terms), then these more general text-matching methods may not be necessary, strictly speaking. Rather, the approach we have described aims to create matched pairs of documents that contain similar information. This is akin to viewing mean balance as a proxy for covariate balance in classic matching. In cases where some confounding factors can be directly measured from the text, we recommend that researchers incorporate these variables into standard covariate balance assessments. After controlling for these variables, text-matching methods can then be applied to adjust for any remaining differences in the text that are not directly measurable.

If potential confounding truly hinges on the more complex and latent aspects of text, however, then one could ideally leverage human judgment to manually evaluate all possible matched pairs of documents. In our case, for example, we could, given unlimited resources, ask human coders to read through the entire corpus of news articles and label them according to which stories they cover. Even untrained human coders could reliably perform this type of evaluation. Such a task, of course, is generally not feasible, but we hope the methods described here provide an accurate and efficient approximation.

As we have seen, we can evaluate the success of human evaluation experiments by inverting the full human-coding procedure to generate a test: we identify a set of possible matches using automated text-matching methods and then present a carefully constructed sample of them to trained human coders. These human coders can then evaluate the sampled pairs of matched documents to determine which matches are systematically the most similar with regard to the targeted aspects of text. Using this information, we can then see how different automated measures of match quality align with human judgment about which matches are subjectively “best”. The general intuition behind this process is simple: to find documents that are descriptively similar using automated methods, we should first learn how humans evaluate text documents and what internal criteria they use to determine textual similarity. We can then identify machine methods that most closely mirror these qualitative decision rules. These insights can then be used to build a predictive model for match quality that approximates human judgment and allows us to make precise and efficient comparisons across large collections of text documents.

Thus, the human-coding task is of utmost importance, requiring both careful pretesting and substantial guidance to ensure the human coders attend to the aspects of text deemed most important as potential confounders. In particular, the primary concern is instructing the human coders to accurately and consistently evaluate similarity along the latent dimension of interest which may be challenging or impossible for human evaluators to reliably code in some contexts. For example, even two experienced medical doctors may systematically disagree in their readings of patient data such as X-rays (Steiner et al. Reference Steiner, MacDonald, Liu, Truszkowski, Hipp, Gammage, Thng, Peng and Stumpe2018). In such a scenario, it may still be possible to obtain reliable evaluations from experts and/or human coders with sufficient domain knowledge. This strategy is implemented in our second application, described in Section 5.2, where the latent dimension of interest considers whether a pair of matched doctor notes characterizes two patients whose conditions are equally severe. However, in other cases, human evaluations simply may not serve as a reliable ground truth to which automated text match quality may be compared. While the observed text may still offer important information about potential confounders in these cases, automated text-matching methods cannot be properly validated using this framework.

5.1 Decomposing Media Bias

While American pundits and political figures continue to accuse major media organizations of “liberal bias,” scholars, after nearly two decades of research on the issue, have yet to come to a consensus about how to measure bias, let alone determine its direction. A fundamental challenge in this domain is how to disentangle the component of bias relating to how a story is covered, often referred to as “presentation bias” (Groseclose and Milyo Reference Groseclose and Milyo2005; Gentzkow and Shapiro Reference Gentzkow and Shapiro2006; Ho et al. Reference Ho and Quinn2008; Gentzkow and Shapiro Reference Gentzkow and Shapiro2010; Groeling Reference Groeling2013), from the component relating to what is covered, also known as “selection bias” (Groeling Reference Groeling2013) or “topic selection.” In particular, systematic comparisons of how stories are covered by different news sources (e.g., comparing the level of positive sentiment expressed in the article) may be biased by differences in the content being compared. We present a new approach for addressing this issue by using text matching to control for selection bias.

We analyze a corpus consisting of $N=9903$ articles published during 2013 by each of the thirteen popular online news outlets.Footnote ¹² These data were collected and analyzed in Budak, Goel, and Rao (Reference Budak, Goel and Rao2016) and are posted on the Deep Blue Data repository offered by the University of Michigan (Budak, Goel, and Rao Reference Budak, Goel and Rao2019). The news sources analyzed here consist of Breitbart, CNN, Daily Kos, Fox News, Huffington Post, The Los Angeles Times, NBC News, The New York Times, Reuters, USA Today, The Wall Street Journal, The Washington Post, and Yahoo. In addition to the text of each article, the data include labels indicating each article’s primary and secondary topics, where these topics were chosen from a set of fifteen possible topics by human coders in a separate evaluation experiment performed by Budak, Goel, and Rao (Reference Budak, Goel and Rao2016).

The data also include two human-coded outcomes that measure the ideological position of each article on a 5-point Likert scale. Specifically, human workers tasked with reading and evaluating the articles were asked “on a scale of 1–5, how much does this article favor the Republican party?”, and similarly, “on a scale of 1–5, how much does this article favor the Democratic party?”Footnote ¹³

To perform matching on this data, we use the optimal procedure for identifying articles that cover the same underlying story identified by our prior evaluation experiment: cosine matching on a bounded TDM.Footnote ¹⁴ Because in this example we have a multivalued treatment with thirteen levels, each representing a different news source, we follow the procedure for template matchingFootnote ¹⁵ described in Silber et al. (Reference Silber, Rosenbaum, Ross, Ludwig, Wang, Niknam, Mukherjee, Saynisch, Even-Shoshan and Kelz2014) to obtain matched samples of 150 articles from each news source. Briefly, the template matching procedure first finds a representative set of stories across the entire corpus and then uses that template to identify a matched sample of similar articles within each source that collectively cover this canonical set of topics. This allows us to identify a subset of articles within each source that are all similar to the same template and therefore similar to each other.

Before matching, our estimates of a news source’s average favorability are a measure of overall bias, which includes biases imposed through differential selection of content to publish as well as biases imposed through the language and specific terms used when covering the same content. The matching controls selection biases due to some sources selecting different stories that may be more or less favorable to a given party than other stories. Differences in estimated favorability on the matched articles can be attributed to presentation bias. The difference between estimates of average favorability before matching (overall bias) and estimates after matching (presentation bias) therefore represents the magnitude of selection biases imposed by the sources. Large differences between prematched and postmatched estimates indicate a stronger influence of selection bias relative to presentation bias.

Figure 3 shows the average favorability toward Democrats (blue) and Republicans (red) for each news source overall and the average favorability among the template matched documents. Arrows begin at the average score before matching and terminate at the average score after matching. The length of the arrows is the estimated magnitude of the bias of each source that is attributable to differences in selection.

Figure 3. Estimates of average favorability toward Democrats (blue) and Republicans (red) for each source both before and after matching.

Before discussing the pattern of shifts, we first look at overall trends of favorability across sources. First, overall sentiment toward Republicans generally hovers around 2.8–3.1, slightly less, on average, than the partisan neutrality of $x=3$ , which corresponds to a response of “neither favorable nor unfavorable.” The one exception is the Daily Kos, which is unfavorable. Other sources (the Huffington Post, the NY Times, and the LA Times) are at the low end of this range, indicating some negative sentiment. For the Democrats, there is somewhat more variation, however, with Breitbart being the least favorable, followed by Fox and WSJ, and the Daily Kos being the most favorable. Furthermore, it is primarily the more extreme sources that show selection effects. Breitbart, Fox and the Washington Post, for example, all become more positive toward Democrats when we adjust for story. This suggests that they tend to select stories that are biased more toward Republicans and away from Democrats, a selection bias effect. The Daily Kos, the Huffington Post, and the New York Times show similar selection bias effects in the opposite directions. The remaining sources do not appear to be significantly impacted by controlling for selection.

We performed a series of sensitivity checks to assess the stability of our results to different specifications of the matching procedure and/or different choices of template sample. We also examine the variability due to randomly matching documents to assess how much estimation uncertainty is present in our analysis. Details of these analyses are provided in Appendix G in the Supplement. Generally, we see that estimating the selection effect of an individual source is difficult and that the magnitude of the selection effects tends to be small, indicating that the choice of what stories to cover is not driving the overall favorability ratings. In other words, most differences in favorability appear to be driven by presentation bias.

5.2 Improving Covariate Balance in Observational studies

In our second application, we demonstrate how text matching can be used to strengthen inferences in observational studies with text data. Specifically, we show that text matching can be used to control for confounders measured by features of the text that would otherwise be missed using traditional matching schemes.

We use a subset of the data first presented in Feng et al. (Reference Feng, McSparron, Kien, Stone, Roberts, Schwartzstein, Vieillard-Baron and Celi2018), which conducted an observational study designed to investigate the causal impact of bedside transthoracic echocardiography (TTE), a tool used to create pictures of the heart, on the outcomes of adult patients in critical care who are diagnosed with sepsis. The data were obtained from the Medical Information Mart for Intensive Care (MIMIC) database (Johnson et al. Reference Johnson, Pollard, Shen, Li-wei, Feng, Ghassemi, Moody, Szolovits, Celi and Mark2016) on 2401 patients diagnosed with sepsis in the medical and surgical intensive care units at a Massachusetts Institute of Technology university hospital located in Boston, Massachusetts. Within this sample, the treatment group consists of 1228 patients who received a TTE during their stay in the ICU (defined by time stamps corresponding to times of admission and discharge) and the control group is composed of 1173 patients who did not receive a TTE during this time. For each patient, we observe a vector of pretreatment covariates including demographic data, lab measurements, and other clinical variables. In addition to these numerical data, each patient is also associated with a text document containing intake notes written by nursing staff at the time of ICU admission.Footnote ¹⁶ The primary outcome in this study was 28-day mortality from the time of ICU admission.

Because the treatment in this study was not randomly assigned, patients in the treatment and control groups may differ systematically in ways that affect both their assignment to treatment versus control and their 28-day mortality. For instance, patients who are in critical condition when admitted to the ICU may die before treatment with a TTE being considered. Similarly, patients whose health conditions quickly improve after admission may be just as quickly discharged. Therefore, in order to obtain unbiased estimates of the effects of TTE on patient mortality, it is important to identify and appropriately adjust for any potentially confounding variables such as the degree of health at the time of admission.

We apply two different matching approaches to this data: one that matches patients only on numerical data and ignores the text data, and one that matches patients using both the numerical and text data. In the first procedure, following Feng et al. (Reference Feng, McSparron, Kien, Stone, Roberts, Schwartzstein, Vieillard-Baron and Celi2018), we match treated and control units using optimal one-to-one matching (Hansen and Klopfer Reference Hansen and Klopfer2006) on estimated propensity scoresFootnote ¹⁷ . We enforce a propensity score caliper equal to 0.1 standard deviations of the estimated distribution, which discards any treated units for whom the nearest control unit is not within a suitable distance. In the second approach, we perform optimal one-to-one text matching within propensity score calipers. Intuitively, this procedure works by first, via the calipers, reducing the space of possible treated–control pairings in a way that ensures adequate balance on numerical covariates. By then performing text matching within this space to select a specific match given a set of candidate matches all within the calipers, we obtain matched samples that are similar with respect to all observed covariates, including the original observed covariates and any variables that were not recorded during the study but can be estimated by summary measures of the text.

Identifying the optimal text-matching method here requires careful consideration of how text similarity should be defined and evaluated in this medical context. Here, the ideal text-matching method is one that matches documents on key medical concepts and prognostic factors that could both impact the choice of using TTE as well as the outcome (i.e., potential confounders) that are captured within the text data. Unlike in the previous application, these features cannot be reliably evaluated by nonexpert human coders due to the domain expertise and familiarity with medical jargon necessary to make comparisons between medical documents. Thus, to perform a systematic evaluation of text-matching methods in this study, we adopt an information retrieval approach for comparing medical texts that has been widely applied in the biomedical literature (Aronson Reference Aronson2001; Zeng et al. Reference Zeng, Tse, Divita, Keselman, Crowell, Browne, Goryachev and Ngo2007).

In particular, by consulting with medical professionals, we first obtained a mapping of the texts to a set of clinically meaningful concepts that could be used to characterize ICU patients. Following the approach of MacLean and Heer (Reference MacLean and Heer2013), we then calculated the Jaccard similarity over this mapping between matched pairs of documents as an omnibus measure of match quality. We treat these scores as a working gold standardFootnote ¹⁸ for this particular application; these scores are based on careful consideration from domain experts who have the medical background required to extract potentially confounding information from this type of nuanced text. We therefore calculated the average pairwise Jaccard similarity achieved after matching (within propensity score calipers based on the numerical covariates) using each of 130 text-matching specifications described in Section 3. Results of this systematic evaluation indicated that the best-performing procedure uses the cosine distance calculated over a bounded TDM, where treated units whose nearest control is outside the specified caliper are discarded. See Appendix H in the Supplement for additional details.

Figure 4 shows the covariate balance between treatment and control groups on both quantitative and text-based covariates before matching, after PSM on numeric covariates alone, and after text matching using our preferred method (using cosine distance on a bounded TDM) within propensity score calipers. Here, each of the five text-based covariates represents summary measuresFootnote ¹⁹ of the observed text documents. These variables, according to medical experts consulted on this project, all could indicate potential confounds that could bias estimates of impact if not controlled. Our general text-matching methods do not directly balance these covariates; the improved balance is a consequence of matching on the overall distance metric and representation used.

Figure 4. Standardized differences in means with 95% confidence intervals between treatment and control groups on twenty-six numerical covariates and five text-based covariates (denoted by *) before matching (gray), after propensity score matching (red), and after text matching (blue).

In general, common wisdom (e.g., Imbens and Rubin (Reference Imbens and Rubin2015)) is to condition on all available data that could indicate potential confounding influences when making inferences using observational data. While PSM is able to adequately balance the numerical covariates and some of the text-based covariates most correlated with these numerical measures, it fails to sufficiently adjust for differences between treatment and control groups on a number of potential confounders captured only by the text. For instance, both the unmatched data and the matched sample generated using PSM have large imbalances between treatment and control groups on references to Lasix, a medication commonly used to treat congestive heart failure. In the unmatched sample, only 10% of treated units have documents containing references to this medication compared to 28% of control units who are associated with the medication. Matching on the estimated propensity scores reduces this imbalance only slightly, while cosine matching within propensity score calipers shows a considerable improvement in the balance achieved between treatment groups on this variable. Incorporating the text data into the matching procedure leads to similar improvements in balance for the other five text-based variables while also maintaining suitable overall balance on the numerical covariates.

Table 1 summarizes the survival rates in the treatment and control groups within each matched sample along with the effective sample sizes (i.e., the equivalent number of matched pairs) in the final matched samples. Generally, there appears to be some confounding, with the adjusted impacts being larger than the naïve differences. The matched sample identified using text matching is slightly larger in terms of effective sample size than simple PSM, although they are not significantly different. This increase in effective sample size highlights the efficiency of text matching; when evaluating multiple controls that are eligible matches for a single treated unit in terms of quantitative covariates, the text-based distance offers a more refined measure of pairwise similarity than distances based on the propensity score. Further, when text matching within propensity score calipers, small differences in estimated propensity scores across controls will be offset by any large differences in text. In the present application, this allows for more precise and efficient optimization of the matched sample.

Of course, conducting a matched analysis is rooted in thoughtful design. In particular, the researcher must decide which variables are important potential confounders and which are not. This is especially important when balancing the trade-offs between achieving better balance on some variables at the expense of others. The purpose of highlighting text matching in this context is to demonstrate how information from the text can also be included in these decisions about what aspects of the data to consider. If the text is deemed not informative, then of course it should not be an important consideration when matching. But, as in this case, if the text is considered to indicate significant aspects of patient condition that should be attended to, the general matching procedures we have discussed can provide a way forward. And if it is uncertain what is important, then sensitivity checks that focus balance on different groups of variables can further strengthen causal claims in these contexts.