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Statistical Analyses of the House Freedom Caucus and the Search for a New Speaker

Flag of the United States of AmericaWith Speaker John Boehner resigning, Kevin McCarthy quitting before the vote for him to be Speaker, and a possible government shutdown in the works, the Freedom Caucus has certainly been in the news frequently! Depending on your political bent, the Freedom Caucus has caused quite a disruption for either good or bad. 

Who are these politicians? The Freedom Caucus is a group of approximately 40 Republicans in the U.S. House of Representatives. You may also know this group as the “Hell No” caucus, and they are a key part of the fractured Republican House. In all of the articles and blogs I’ve read, they are described an extremely conservative, far-right group. This extreme conservatism is generally considered to be the defining characteristic.

However, in the Republican presidential race, we’ve seen that the usual debate over the candidates’ conservative credentials has been overshadowed by the outsiders. In other words, there’s an assessment of each candidate’s conservativeness as well as their establishmentarianism.

Is there evidence that an establishment/anti-establishment split is also a factor among the Republicans in the House of Representatives and their search for a new Speaker of the House? In this blog post, I’ll use data and statistical analyses to test these hypotheses!

Data for these Analyses

I obtained the data for these analyses from voteview.com. This group runs an algorithm that uses roll call votes to estimate each politician’s conservativeness and their support of the party establishment. I added a variable that identifies Freedom Caucus membership using the information in this Wikipedia article.

For these data, higher conservative scores indicate that the politician is more conservative. Higher establishmentarianism scores indicate that the politician is more supportive of the establishment while lower scores indicate an anti-establishment position.

Scatterplot of the House Republicans

Graphing the data is always a good place to start for any analysis. The scatterplot below displays a point for each Republican member of the House by their Establishment and Conservativeness scores. The data points that are further right are more conservative. The points that are closer to the bottom are more anti-establishment. Red points identify members of the Freedom Caucus.

Scatterplot of House Republicans

The graph shows that not all members of the Freedom Caucus are extremely conservative. Some are right in the middle! However, all members of the Freedom Caucus are at least on the right half of the graph. These members are also in the bottom, anti-establishment half, which keeps the door open for the hypothesis that we'll test. 

Binary Logistic Regression

Let’s test this formally with statistics. To do this, I’ll use binary logistic regression in Minitab statistical software because the response variable is binary. The Republican House members can only either belong to the Freedom Caucus (Yes) or not (No).

Response information table for binary logistic regression

The Response Information table displays general information about the analysis. There are 36 members of the Freedom Caucus out of 247 House Republicans in the analysis.

Deviance table for binary logistic regression

The Deviance Table is like the ANOVA table in a linear regression analysis. This table shows us that both the Conservativeness and Establishmentarianism of the politicians are very statistically significant (p = 0.000). We can conclude that changes in the values of these two predictors are associated with changes in the probability that a politician is a member of the Freedom Caucus.

The interaction between the two predictors is insignificant and I did not include it in the final model.

Graph the Results to Understand the Binary Logistic Regression Model

The easiest way to understand these results is to graph them. When you fit a variety of model types in Minitab 17, the analysis stores that model in the worksheet. You can then use a variety of handy features to quickly and easily explain what your model really means.

The graph below displays the probabilities associated with the values of the two predictors. The highest probabilities for Freedom Caucus membership are in the bottom right for politicians who are both very conservative and very anti-establishment.

Contour plot of the probability of belonging to the Freedom Caucus

In the main effects plot below, Minitab graphs the effect of each variable independently while the other variable is held constant.

Main effects plot of conservativeness and establishmentarianism

On the Conservativeness side, the graph shows that as a politician becomes more conservative (by moving right), their probability of membership in the Freedom Caucus increases. In fact, the probability really starts to shoot up fast around a score of 0.5. On the Establishmentarianism side, as a politician becomes more anti-establishment (by moving left), their probability of Freedom Caucus membership also increases at an increasing rate.

Collectively, the statistical analyses show that membership in the Freedom Caucus is not as simple as being on the far right end of the political spectrum. Instead, this group has a mixture of very conservative and anti-establishment sentiment driving their actions. Understanding this multidimensional fracture in the Republican Party helps explain why it is so difficult to form a more cohesive caucus and to choose a new Speaker of the House.

When Kevin McCarthy refused to run for Speaker, many called on Paul Ryan as the ideal candidate to unify the House Republicans. Although Ryan appears to have declined this call to duty, he provides a notion of what the ideal Speaker looks like in this new environment.

To compare McCarthy to Ryan across both characteristics, I standardized their raw scores to account for any differences in the scaling of the two variables. The table shows their Z-values, which is the number of standard deviations that each politician falls from the House Republican mean for each variable.

  Conservatism Establishmentarianism
McCarthy -0.169 0.549
Ryan 0.496 -1.180

Compared to McCarthy, Ryan has a moderately more conservative score, but he is notably more anti-establishment. This larger difference indicates which way the political winds are blowing!

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