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%
Results
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
------------------------------------------------------------------------------
Explanation
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 |
|
23% |
4% |
|
30% |
5% |
|
40% |
7% |
|
50% |
9% |
|
60% |
13% |
|
70% |
18% |
|
84% |
26% |
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.
