Thursday, September 10, 2020

The Removal of Montana Post Boxes: Evidence of Partisan Shenanigans

Working with Maritsa Georgiou at NBC Montana, I analyzed the removal of post boxes in the state of Montana and found that Democratic vote at the precinct level is associated with a higher probability that a post box is slated for removal. A discussion of the process by which I came to this disturbing conclusion is outlined below. You can access Maritsa's story about my analysis can be found here. Below is the memo that I wrote for her, walking through the data and analysis.

The Data

I was provided with the locations of all post boxes in the state of Montana as of August 2020 and July 2019. As of July 2019, there were 1,438 box locations. As of August 2020, 12 box locations were added since July 2019 and another 47 removed or slated for removal. 302 locations are stand alone boxes not located at post offices. 30 of these were removed or slated to be removed in August of 2020 and 3 had been added after July 2019.

Data Collection

With precinct maps available online and phone calls to county clerks throughout the state, I was able to locate the voting precinct associated with each box address. I then gathered precinct level returns from the 2018 Montana Senate election, specifically the percentage of the vote cast for Democrat Jon Tester, from the Secretary of State’s website

Next, I added county-level demographic data to each box location. This data includes the percentage of college graduates in the county, the population change over the past ten years, and the county’s population density.

Statistical Models

Unit of Analysis: Each individual box address.

Dependent Variables (What we are predicting): Dichotomous (0/1).

Was a box removed from the location? No (0), Yes (1).

Was a box added to the location? No (0), Yes (1).

Independent variables (Variables that explain box addition or removal).

Demv = Democratic Vote at the Precinct Level (Percentage ranging between 0 and 1)

Postoffice =  Indicator variable. Is the address location at a post office? (0 No, 1 Yes) This controls for box clusters around post offices.

Density: Population density at the county level as reported by the Census (People per square mile).

Pop_Change: Population change since 2010 at the county level as reported by the Census (Percentage ranging between 0 and 1).

Box_den: Total boxes in the county divided by the county population. I simply totaled all the mailbox addresses in each county and divided that by the county’s population as reported by the Census (Express as a percentage ranging between 0 and 1).

The addition of these variables controls for other factors which might reasonably be associated with the addition or removal of postal boxes. This is to be sure that there isn’t a spurious correlation with box removal and Democratic vote.

Some basic numbers:

The average Democratic vote cast where a box was removed: 64%

The average Democratic vote cast where a box was left unchanged: 46%

The average Democratic vote cast where a box was added: 49%


Table 1: Predicting Box Removal in Montana

. logit remove demv postoffice density pop_change box_den, cluster(fips3)


Iteration 0:   log pseudolikelihood = -207.40096 

Iteration 1:   log pseudolikelihood = -199.71757 

Iteration 2:   log pseudolikelihood = -176.68126 

Iteration 3:   log pseudolikelihood = -176.53519 

Iteration 4:   log pseudolikelihood = -176.53486 

Iteration 5:   log pseudolikelihood = -176.53486 


Logistic regression                             Number of obs     =      1,450

                                                Wald chi2(5)      =      13.22

                                                Prob > chi2       =     0.0214

Log pseudolikelihood = -176.53486               Pseudo R2         =     0.1488


                                 (Std. Err. adjusted for 56 clusters in fips3)


             |               Robust

      remove |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]


        demv |   3.612453   1.550089     2.33   0.020     .5743357    6.650571

  postoffice |  -1.689901   .5109666    -3.31   0.001    -2.691378   -.6884252

     density |  -.0018252   .0173632    -0.11   0.916    -.0358564     .032206

  pop_change |   2.330461   4.284481     0.54   0.586    -6.066968    10.72789

     box_den |   123.6979   173.8481     0.71   0.477    -217.0382    464.4339

       _cons |  -4.733514   1.130804    -4.19   0.000     -6.94985   -2.517179



If a variable is significant (p-value of less than .05), then this means there is a relationship between the variable and the dependent variable. The sign on the variable tells the direction of the relationship. Demv (Democratic vote cast in the precinct) is positively associated with box removal, meaning the greater the Democratic vote, the higher the probability a box gets removed. If a box is located at a post office, is it less likely to get removed (denoted by the negative sign on the variable and the fact the p-value is less than .05). Population density, Post box density, and population change are NOT significantly related to box removal. The model correctly classifies 97 percent of box removals (that’s really superb, but we also only have few cases that differ from zero).

Predicted Probabilities

To determine the magnitude of effect of Democratic vote share on the probability of a box removal, we need to generate predicted probabilities. Let’s consider Gallatin County, which has a population density of 34, a box density of .006816, a population change of 27 percent, and for a box location that is NOT outside of a post office. Now, let’s vary the Democratic vote share at the precinct level from .23 (a precinct south of Manhattan) to .84 (a precinct located near the university just south of downtown that includes a lot of students living off campus). How does the probability of a box removal change?

Table 2: Democratic Vote Share and Probability of Post Box Removal

Democratic Vote Share

Probability of a Box Removal















Caption: Other variables held to represent Gallatin County and box locations not located outside a postal facility.

Across the range of precincts in Gallatin County, the probability of postal box removal increases more than 6-fold as we move from the most Republican precincts in the county to the most Democratic.

Statistical Notes

I ran the model using a procedure know as a rare event logit given the low number of cases. The results are substantively no different—the same variables are significant. I also ran models predicting box additions and found no relationship between the predictors listed above and the probability of a box addition.