A few days ago I saw an attempt at correlation analysis with Trump’s poll ratings. The idea was, could a predictor for his approval/disapproval be found with another data set?

This got me thinking — perhaps the best way to understand what is happening with Trump’s approval rating is to look not for correlations but at change-points. The difference is this — a correlation is a relationship between two variables, while a change-point is a distinct event that causes numbers to go up or down.

Fortunately, this kind of analysis is made possible using Bayesian inference. Bayesian is science for magic, and basically it allows us to create posterior probabilities for a hypothetical event to have occurred. It is different from traditional statistics in that it is not a pass/fail test, but rather a way of updating probabilities. It’s complicated, but for now, let’s just say that we can estimate how important a specific event was to a group of voters by how it affects future poll results.

Trump’s approval/disapproval with all voters. Red line = disapproval, blue line = approval. Rating % is at the top, while the Bayesian change-point posterior probabilities are below. The spikes in of the graph indicate when important events happened.

Changes in Trump’s approval aren’t usually gradual. Instead, they happen in short-term events that have long-term consequences on how Americans view him. First, notice the biggest posterior probability in the far left — it happened in late January. This was right after his inauguration, when an emergency press conference was created to brag about his crowd size at the inauguration.

But who, exactly was responsible for this big shift in his poll numbers? As it turns out, that was when Trump lost what few undecided Democrats there were.

Trump lost support from Democrats very early on in his administration, and hasn’t made any progress recapturing their support

The change is dramatic in his disapproval, but there is no real change in his approval. That tells us that early on in the Trump admin — within hours really — Trump had a sizable portion of Democrats, somewhere around 10%, who were undecided on his administration. He lost them an an issue practically devoid of substance. Interestingly, this only cost him among Democrats — independent voters were not all too worried about it.

Trump’s performance with independent voters. Someone tapped Trump’s approval

Independents leaned toward disapproval, but for the most part remained stable until mid-March, when disapproval, then approval, moved against Trump. Notably, there were no major policy changes at this time — this was before the AHCA failed (March 24th). This was a shift from -8 to -19 points. It is possible that Trump lost support among independents over one tweet.

What is interesting is the step-wise movement here. First, more independents began to express disapproval by March 16th. Then, he lost approval a few days later on March 21st. What is happening? Hard to say, but the most plausible scenario might be that Trump’s tendency to vent unfounded accusations on Twitter first moved undecided independents to disapproval, then moved more supportive independents to an undecided column. This suggests that Trump tweets may pose an existential risk to his support among independents. But, it is also possible that the damage was done to persuadable independents in March.

How about Republicans?

GOP has mostly been fine with Trump… …with one exception in May

On May 9th, Trump fired James Comey, the 7th Director of the FBI. His reasons for doing this were all over the map — first it was because of Comey’s treatment of Hillary Clinton in the infamous Rosenstein memo. Then, Trump undercut this in an interview with Lester Holt by saying he fired Comey because of the Russia investigation.

This did real damage to Trump among Republicans — both approval and disapproval moved at the same time. Trump went from +72 with the GOP to +64 — a distinct narrowing of his otherwise positive numbers with the Republican Party.

So, what can we learn here?

First, I would argue based on Bayesian change-point analysis that we have only three real movements in Trump’s poll numbers worth writing home about. First, he lost Democrats on day one by picking a fight with photographs of his inauguration crowd size. Second, he lost Independents based on his Obama ‘tapp’ tweets in March. And third, he lost a portion of Republicans when he fired James Comey.

Let’s take a moment and consider what didn’t alter Trump’s numbers. First, the Paris Climate Deal, DACA, the repeated rise and fall of Obamacare repeal, these things had no measurable affect on his support among the American people. I suspect they are important — but they should be considered as hardening positions, not creating them.

The final lesson that can be learned from these numbers is in the different responses between Independent and Republican voters. With Independents, we saw a 2-step process: first a portion moved to disapproval, then another portion moved away from approval. By contrast, the movement by Republicans was very sharp in the aftermath of the Comey firing. We can interpret this two ways. First, that while Independents may be hesitant to drop support when a controversial event occurs, Republicans may not be. Second, Trump is exposed to a great deal of danger with the Russia scandal and Special Counsel Robert Mueller among Republicans. This will press the same button that moderately — but substantively — shifted his numbers among the GOP.

p.s. if you use GitHub, you can work with the code here.

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