Constructing legislative networks in R using incidentally and backbone

Political networks come in many forms that can be distinguished by both their nodes (politicians, institutions, states, etc.) and their edges (alliance, opposition, collaboration, etc.; Victor et al., 2017; Knoke, 1994; Knoke et al., 2021). In this article, I focus on one type of political network: networks of legislators in the US Congress, connected by ties of ideological alignment, political alliance, and legislative collaboration inferred from their bill (co-) sponsorship activities. These types of networks have provided insight into a range of congressional phenomena, including polarization (e.g., Neal, 2020), bipartisanship (e.g., Rippere, 2016), legislative effectiveness (e.g., Tam et al., 2010), and gender roles (e.g., Neal et al., 2022). In this section, I provide a brief overview of the legislative process in the US Congress, and of the logic of legislative co-sponsorship networks.

The US Congress is composed of two chambers: the Senate that contains 100 Senators with 2 representing each state, and the House of Representatives that contains 435 Representatives with the size of each state's delegation depending on its population size. For example, in 2020 Alaska had a population under 1 million and was represented by a single Representative, while California had a population of nearly 40 million and was represented by 52 Representatives. During each two-year session of Congress, these legislators meet to create new federal laws following a multi-step legislative process illustrated in Figure 1 (Smith and Riddick, 1948; Frishberg, 1976).

Figure 1

The process begins when a legislator introduces a bill for consideration in their own chamber. This individual is known as the bill's sponsor, while other members of the same chamber can express support for the legislation by joining the bill as a co-sponsor. Upon introduction, the Congressional Research Service classifies the bill into one of 32 broad policy areas, such as “Education” or “Commerce”; a complete list with descriptions is available at https://www.congress.gov/help/field-values/policy-area. The newly introduced bill is debated, revised, and possibly voted on in the originating chamber. If the bill passes in the originating chamber, it is then debated, revised, and possibly voted on in the other chamber. If the bill passes both chambers, it is sent to the President, who may sign it into law, not sign it, or veto it. As Figure 1 illustrates, there are many ways for a bill to fail, and few ways for it to become a law.

This represents a simplified version of a complex process that can involve a wide range of political and procedural maneuvers. However, three features of this process are particularly important in the context of constructing legislative networks. First, a bill's sponsor is the first person named in the bill, but is not necessarily the bill's primary author or strongest supporter. Therefore, there may be little practical difference between a bill's sponsor and its co-sponsors. Second, legislators may introduce four distinct types of legislation, however only bills and joint resolutions can become law, while simple resolutions and concurrent resolutions are used only for procedural or ceremonial matters. Therefore, bills and joint resolutions are more consequential. Finally, while all bills have a sponsor and possibly cosponsors, most bills are never voted on, even in the originating chamber. Therefore, the (co-)sponsorship process provides substantial information, while the voting process provides relatively limited information.

A co-sponsorship network can be constructed from information on legislators' bill sponsorship activities. In a co-sponsorship network, two legislators are connected when they have (co-)sponsored the same bills. Formally, bill sponsorship data can be represented as an incidence matrix I where I_ik=1 if legislator i (co-)sponsored bill k. Multiplying this matrix by its transpose (i.e., I×I′; bipartite projection) yields a legislator network represented as an adjacency matrix A, where A_ij indicates the number of bills that both legislator i and legislator j (co-)sponsored. The political network literature contains numerous examples of, and theorizing about, co-sponsorship networks not only in the US Congress (Neal, 2014, 2020; Neal et al., 2022; Aref and Neal, 2020, 2021; Ringe et al., 2017; Fowler, 2006a, 2006b; Kirkland and Gross, 2014; Rippere, 2016; Tam et al., 2010; Zhang et al., 2008), but also in US state legislatures (Bratton and Rouse, 2011; Clark and Caro, 2013; Kirkland, 2011, 2014), and in legislative bodies around the world (Aleman and Calvo, 2013; Baller, 2017; Fischer et al., 2019; Micozzi, 2014; Briatte, 2016).

Under most circumstances it would be impractical to collect network data directly from legislators because they are busy, and because they may have strategic motivations that lead them to misrepresent their true political relations. Therefore, most legislative networks are measured indirectly through secondary data. Many such indirect measurement approaches exist, but co-sponsorship networks offer advantages over many of the alternatives. First, legislators' political ties could be inferred from their shared committee memberships (e.g., Porter et al., 2005). However, committee assignments are often made by party leadership based on seniority and other strategic considerations, whereas legislators' decisions about which bills to sponsor are more independent. Second, legislators' ties could be inferred from their shared roll call votes (e.g., Andris et al., 2015). However, roll call votes are taken on only a small subset of bills, whereas information about sponsorship is available for all bills. Finally, legislators' ties could be inferred from their co-participation in press and other events (e.g., Desmarais et al., 2015). However, there is no comprehensive database of legislators' event participations, whereas bill sponsorship is an official act recorded by the legislative body.

Although co-sponsorship networks offer many practical advantages over alternative approaches to measuring legislators' political networks, it is important to be clear what they measure. The interpretation of a co-sponsorship networks depends on the depth of inference a researcher is able to justify making from the non-network data on bill sponsorship. Directly (i.e., without making any inferences), edges in a co-sponsorship network measure whether or how often two legislators (co-)sponsor the same bills. By making an initial but relatively plausible inference, these edges might be interpreted as representing legislators' ideological or policy alignment because they identify cases where legislators supported common causes. A deeper inference might contend that the edges represent political alliances, while a still deeper inference might view them as representing active collaboration in the legislative process (Kirkland, 2011). These deeper inferences, while potentially plausible, are still inferences that go beyond the data. For example, it is possible that two legislators with similar policy agendas would sponsor the same set of bills, but would do so with no knowledge (and thus no alliance or collaboration) of the other.

The backbone package can be installed in R from CRAN with install.packages(“backbone”) and loaded for use with library(backbone) (Neal, 2022a). The backbone package provides a range of functions for extracting the backbone of networks, including bipartite projections such as co-sponsorship networks. While many of these functions are potentially relevant for political networks, here I focus on the sdsm() function, which implements the stochastic degree sequence model, because this model will often be the most useful for bill sponsorship data (Neal, 2014; Neal et al., 2021).

The basic format of the function is:

sdsm(

B,

alpha=0.05,

signed=FALSE,

mtc=“none”,

class=“original”,

narrative=FALSE

)

The sdsm() function takes an incidence matrix or bipartite igraph object B as its input, constructs its weighted bipartite projection, then identifies and retains only the statistically significant edges. In the context of a co-sponsorship network, it takes data on which legislators sponsored which bills, constructs a weighted co-sponsorship network, then yields an unweighted network in which legislators are connected if they co-sponsored statistically significantly more bills together than expected at random. This model's statistical test controls for the fact that some legislators (co-)sponsor many bills while others (co-)sponsor few, and for the fact that some bills have many (co-)sponsors while others have few.

The alpha parameter specifies the statistical significance level used to test each edge. By default, the function performs a one-tailed statistical test because it is evaluating whether a pair of legislators co-sponsored significantly more bills together than expected at random. The signed parameter can be used to modify this behavior. When signed=TRUE, the function instead returns a signed network in which legislators are connected by a positive edge if they co-sponsored more bills than expected at random, and are connected by a negative edge if they cosponsored fewer bills than expected at random. When a signed network is returned, the function performs a two-tailed statistical test.

The mtc parameter specifies whether a multiple test correction should be applied to the edge-wise statistical tests. The function must conduct many independent statistical tests – one for each edge – which can inate the Type-I error rate. By default, no correction is performed. However, any of the methods implemented in R's p.adjust() function can be specified. These methods offer options to control the familywise error rate (FWER) or false discovery rate (FDR).

The class parameter specifies the desired format of the output. By default, the output will take the same form as the input. For example, if an incidence matrix is supplied then an adjacency matrix will be returned, and if a bipartite igraph object is supplied then a unipartite igraph object will be returned.

Finally, the narrative parameter specifies whether the function should display manuscript suggested text and citations. By default, this information is not displayed to avoid cluttering the R console with unnecessary output, but can be useful for new users or for facilitating reporting of a final analysis.

The prior examples focus on constructing networks where the edges identify legislators who sponsor more bills together than expected at random, and thus might be interpreted as alignment, alliance, or collaboration. However, we can also construct signed networks that capture both alliances and antagonisms.

We begin by obtaining the data using:

B <- incidence.from.congress(

session=116,

types=c(“s”, “sjres”),

format=“igraph”)

Here, we focus on the highly contentious 116th session of the Senate, which took place in the second half of Donald Trump's presidency. By default, we include bills addressing all policy areas.

Next, we construct the network from these data using N <- sdsm(B, signed=TRUE). Here, we specify signed=TRUE to indicate that we want a signed network where pairs of legislators who (co-) sponsor more bills together than expected at random are connected by a positive edge, but pairs of legislators who (co-)sponsor fewer bills together than expected at random are connected by a negative edge.

Figure 5 shows the resulting network. In this signed network, positive edges are green, while negative edges are red. We observe that the network is polarized into two distinct groups, which here closely match political party affiliations. The majority of positive “alliance” ties are within group, a pattern that Neal (2020) called “weak polarization.” However, because this is a signed network, we can also observe that many negative “antagonism” ties are located between the two groups, a pattern that Neal (2020) called “strong polarization.” The extent of strong polarization can be characterized by the signed network's degree of structural balance, which can be measured using the triangle index T (Aref and Wilson, 2018). Here T=0.937, indicating that 93.7% of all triangles are structurally balanced, and suggesting a very high level of strong polarization. In this context, the strong polarization visible in Figure 5 means the Senate is characterized by both within-party alliances and cross-party antagonisms.

Figure 5

The incidentally package offers tools for generating and analyzing incidence matrices and bipartite networks (Neal, 2022b), while the backbone package offers tools for extracting the backbone of networks (Neal, 2022a).

This article has demonstrated how these two packages can be used together to construct customized legislative networks of co-sponsorship in the US Congress, by session, by chamber, by bill type, by bill policy area, that are binary or signed.

To summarize the code required, a basic Senate igraph network can be constructed using:

senate <- sdsm(incidence.from.congress(session=<session number>, types=c(“s”, “sjres”), format=“igraph”))

Similarly, a basic House of Representatives igraph network can be constructed using:

house <- sdsm(incidence.from.congress (session=<session number>, types=c(“hr”, “hjres”), format=“igraph”))

The examples in this article illustrate ways that options can be used to modify these basic commands to construct more specialized networks, for example, that focus on bills pertaining to specific policies or that contain both positive and negative political ties.

These methods offer one practical option for researchers wishing to study legislative networks. However, they are subject to some important limitations. First, co-sponsorship networks are only one type of political network, and their interpretation as reecting meaningful political relationships such as alliance or collaboration requires a careful theoretical rationale. Second, the incidentally package currently provides access only to data from the US Congress starting in 2003.

Some of these limitations identify directions for future software development. For example, future versions of incidentally may include functions to obtain bill sponsorship data from other legislative bodies. Functions of these packages that are not demonstrated in this article also highlight directions for future research. For example, while this article has focused on constructing networks among legislators, these packages can also be used to construct networks among bills. Following the approach used by Doreian and Mrvar (2019) to study the US Supreme Court, such bill networks may provide insight into legislators' logical consistency.