Confidence intervals around proportions

So you probably learned about confidence intervals around means in your introductory statistics class. For a refresher, a confidence interval covers a particular statistic at a pre-specified rate. So if I generate 100 90% intervals around a mean, I expect that those confidence intervals would cover the true underlying mean around 90 times out of those 100. So it is a statement about the procedure overall – not any individual test.

This repeated coverage property is often not exactly what we want in statistics. But, I often find examining confidence intervals around samples to be an informative way to quantify uncertainty in estimates. For example, I have a machine learning model serving up predictions to a subsequent auditing process. I expect this to maintain a hit rate above 20%. The past week I only had a hit rate of 30/200 (15%), should I be worried? Probably not, a 95% confidence interval around that proportion is 10% to 21%.

Proportions come up so often that intro stats courses should probably talk more extensively about generating confidence intervals around them. There are many different confidence intervals for proportions, Wikipedia lists 7 different options!

I prefer where possible to use the Clopper-Pearson intervals by default. I will show an examples of generating Clopper-Pearson intervals in Excel and Python. But, another situation I have come across is I want to do these intervals entirely in SQL. For that situation, I will show how to use Agresti–Coull intervals.

Excel Clopper-Pearson

In Excel, if the A column contains the numerator, the B column contains the denominator, and if G1 has the alpha level, this brutish formula gets you the lower bound of your confidence interval;

=IF(A2=0, 0, BETA.INV($G$1/2, A2, B2-A2+1))

A here is your upper bound;

=IF(A2=B2, 1, BETA.INV(1-$G$1/2, A2+1, B2-A2))

And here is a screenshot of the filled in results:

Note for my criminology friends, you can use this for very extreme proportions as well. So say you had a homicide rate of 10 per 100,000, where the observed sample was 30 homicides in a city of 300,000. You can generate a binomial confidence interval around the proportion and then translate back to the rate per 100,000. So in that scenario, it results in a 95% confidence interval of a homicide rate of 6.7 to 14.3.

This is actually the reason I like defaulting to Clopper-Pearson. The other approximations can fail very badly for extreme tail events like this.

Python Clopper-Pearson

Here is a simple function in python to return the Clopper-Pearson intervals. This works for vectorized inputs as well (e.g. numpy arrays or pandas series).

import numpy as np
from scipy.stats import beta

def binom_int(num,den, confint=0.95):
    quant = (1 - confint)/ 2.
    low = beta.ppf(quant, num, den - num + 1)
    high = beta.ppf(1 - quant, num + 1, den - num)
    return (np.nan_to_num(low), np.where(np.isnan(high), 1, high))

And here is an example use:

hits = np.array([0, 1, 2, 3, 97, 98, 99, 100])
tries = np.array([100]*len(hits))
lowCI, highCI = binom_int(hits, tries)

Check out my prior blog post on making smoothed scatterplots on how to plot those proportion spikes in matplotlib.

SQL Agresti–Coull

So as I mentioned previously, I prefer the Clopper-Pearson intervals. This however relies on the availability of a function for the inverse beta distribution. One common situation is I just have all my tables in SQL, and I want to make a dashboard connected to a view of my tables. So the proportion of some event broken downs by days/weeks/months etc.

In that case exporting the data to python and re-uploading to the database can be a bit of a hassle, whereas creating a view is much less work. So here is an example query to calculate the proportion intervals entirely in SQL. So the initial table is a micro level table of events with 0/1 for a particular group. (This screenshot is for Access, but this should work in various databases.)

And then it is a groupby to get the original numerator, denominator, and proportion. Then a few rows calculating the adjusted proportion (add 2 to the numerator and 2*2 to the denominator), then finally this can still produce lower than 0 and higher than 1 intervals, so I cap those off.

/* This is for Access, for others may want to use SQRT() instead of SQR()
   Also may want to use CASE WHEN instead of IIF */
   SUM(Outcome) AS Num,
   COUNT(Outcome) AS Den,
   Num/Den AS Prop,
   Num + 2 AS nadj,
   Den + 2*2 as dadj,
   nadj/dadj as padj,
   2*SQR((padj/nadj)*(1 - padj)) AS zadj,
   IIF( padj < zadj, 0, padj - zadj) AS LowCI,
   IIF( (1 - padj) < zadj, 1, padj + zadj) AS HighCI
FROM ExampleData

This produces a 95% confidence interval for the final two columns. If you wanted to generate say a 99% confidence interval, you would replace the 2’s in the above table with 2.6. (In R you can do qnorm(1 - a/2), where a is 1 - confidence_level, to figure out this constant.)

What you shouldn’t use these intervals for

While I believe many applications of dashboards are well suited to including confidence intervals, confidence intervals (like p-values) are apt to be misinterpreted. One common one is that for a single 95% confidence interval, that does not mean the interval covers the true estimate with a 95% probability. This is an inference for an individual sample that is not possible in frequentist statistics – that summary would be akin to a posterior credible interval in Bayesian statistics. Confidence intervals are about the procedure, if we do this procedure over and over again, in the long run it will cover the true statistic (which we do not observe for any individual sample), according to the level we set.

Another common mistake with confidence intervals is when comparing two different intervals, them overlapping is sometimes interpreted as no difference. But this is a very conservative test (e.g. will fail to reject the null of no differences too often).

So say we were monitoring a process over time, and in October the process was 20% (40/200) and in November it was 28% (168/600). October’s confidence interval is 15% to 26%, and November’s confidence interval is 24% to 32%. So since those intervals overlap, we should conclude there are no differences correct? Not exactly, if we do a direct test for the differences in proportions (akin to a t-test of mean differences), we get a confidence interval of the difference as -14% to -1% (in R prop.test(c(40,168), c(200,600))). So in that direct hypothesis test, we would conclude October’s percent is lower than Novembers percent.

Geoff Cumming suggests that when going from individual confidence intervals to comparisons between groups, one confidence interval needs to cover the point estimate for the other group to conclude the two groups are different.

But that being said, I believe many dashboards would be improved if incorporating such confidence intervals. So although they may not always provide the test of interest, they are a good way to prevent yourself from over-interpreting noisy trends in smaller samples. In the case of comparing two intervals, for most situations I deal with, being conservative in saying this process is not showing differences is a better approach than worrying about minor fluctuations (although just depends on the use case whether that default behavior makes sense.)

So please, when reporting proportions with small samples, provide a confidence interval around those proportions!

Outliers in Distributions

If you google ‘outlier’, all of the results that come up are in terms of individual observation outliers. So if you have a set of transaction data that is 10, 20, 30, 8000, the singlet observation 8000 is an outlier. But for many situations with transaction data, you don’t want to examine individual outlier incidents, but look for systematic patterns. For example, if I am looking at healthcare insurance claims for my work, a single claim that is $100,000 is actually not that rare. But if we have a hospital that has mostly $100,000 claims for a specific treatment, whereas another with similar cases has a range of $50,000 to $100,000, that may signal there is some funny business going on.

There is no singular way to examine outliers in distribution. A plain old t-test of mean differences may make sense for some situations. But a generally more useful way IMO to think about the problem is to examine the distribution of the outcome in CDF space, as opposed to looking at particular moments of the distribution. A t-test basically only looks at the differences in means for the distributions, whereas examining the CDF we are looking for weird patterns at any point in the distribution.

Here is an example of comparing the cost of hospital stays (per length of stay), for a hospital compared to all others from the same datasource (details on the data in a sec). The way to read this graph is that at 10^3 (so $1000 per day claims) for facility 1458, we have around 20% of the claims data are below this value. For the rest of the hospital data, a larger proportion of claims are under a thousand dollars, more like 25%. Since the red line is always below the black line, it also means that the claims at this hospital are pretty much always larger than the claims at all the other hospitals.

For this example analysis, I am using data from New York State health insurance claims data (SPARC). I have posted python code to replicate here (note if you cannot access dropbox links, feel free to email and I will forward).

Here I am specifically analyzing medical, in-patient insurance claims (I dropped surgical claims) for around 300+ hospitals. There are quite a few claims in this data, over 2 million, and the majority of hospitals have plenty of claims to examine (so no hospitals with only 10 claims). I also specifically examine costs per length of stay. Initially I just examined costs, but will get to why I changed to the normalized version towards the end of the post.

Analysis of CDF Outliers

So first what I did was attempt to do a leave-one-out type stat test using the Kolmogorov-Smirnov test. This is a test that looks at the maximum vertical difference between the CDFs I showed earlier. I should have known better though. Given this large of sample size, even with multiple comparison adjustments for false discovery rate, every hospital was considered an outlier. This is sort of the curse of null hypothesis significance testing, it is either underpowered, so you get null results when things should really be flagged, or with large samples everything is flagged.

So what I did first was make a graph of all the different CDFs for each individual hospital. You can see from this plot we have a mass of the distribution that looks very similar in shape, but is shifted left or right. (Hospitals can bill different values, i.e. casemix, so can have the same types of events but have different bills, so that is normal.) But then we have a few outliers really stick out.

To characterize the central mass in this image, what I did was calculate each empirical CDF for each hospital (over 300 in this sample). Then I estimated the CDF for each hospital at a sample of points logspace distributed between $100 to $100,000. Then I took the 90% distribution between the ECDF values. This is easier to show than to say, so in the below pic the grey area is the 90% region for the CDFs. Then you can do stats to see how hospitals may fall outside that band.

So here 1320 is looking good until around 60% of the distribution, and then it is shifted right. There is a kink in the CDF as well, so this suggests really a set of different types of claims, and in that second group it is the outlier. 1320 was the hospital that had the most sample points outside of my grey coverage area, but you could also do outliers in terms of the distance between those two lines (again like a KS test stat), or in the area between those two lines (that is like a version of the Wasserstein distance only considering above/below moves). So here is the hospital that has the largest distance below the band (above the band signals that a hospital has lower claims on average):

Flat lines horizontally signal an absence of data, whereas vertical lines signal a set of claims with the exact same bill. So here we have a set of claims around $1000 per day that look normal, then an abnormal absence of data from $1,000 to $10,000. Then a large spike of claims that end up being around $45k per day.

So this is looking at the distribution relative to other hospitals, but a few examples I am familiar with look for these flat/vertical spikes in the CDF to identify fraud. Mike Maltz has an example of identifying collusion in bids. In another, Chris Stucchio identifies spikes in transaction data signaling potential fraud. Here I am just doing a test relative to other data to identify weird curves, not just flat lines though.

One limitation of this analysis I have conducted here is that it does not take into account the nature of the claims data. So say you had a hospital that specializes in cancer treatment, it may be totally normal for them to have claims that are higher value overall than a more typical hospital that spreads claims among a wider variety of types of visits/treatments. Initially I analyzed just the cost data, and it identified a few big outliers that ended up being hospice/nursing homes. So they had really high dollar value claims, but also really long stays. So when analyzing the claim per length of say, they were totally normal in that central mass.

So ultimately there could be other characteristics in the types of claims hospitals submit that could explain the weird CDF. One way to take that into account is to do a conditional model for the claims, and then do the ECDF tests on those conditional models. One way may be to look at the residuals for each individual hospital, another would be to draw a matched comparison sample. (Greg Ridgeway did this when examining police behavior in the NYPD.)

That would be like making a single comparison line (like my initial black/red line graph). So controlling the false discovery after that will be tough with larger samples (again the typical KS test, even with a matched sample, will likely always reject). So wondering if there is another machine learning way to identify outliers in CDF space, like a mashup of isolation forests and conditional density forests. Essentially I want to fit a model to draw those grey CDF bands, instead of relying on my sample of hospitals to draw the grey band in those latter plots.

Mapping attitudes paper published

My paper (joint work with Jasmine Silver, Rob Worden, and Sarah McLean), Mapping attitudes towards the police at micro places, has been published in the most recent issue of the Journal of Quantitative Criminology. Here is the abstract:

Objectives: We examine satisfaction with the police at micro places using data from citizen surveys conducted in 2001, 2009 and 2014 in one city. We illustrate the utility of this approach by comparing micro- and meso-level aggregations of policing attitudes, as well as by predicting views about the police from crime data at micro places.

Methods: In each survey, respondents provided the nearest intersection to their address. Using that geocoded survey data, we use inverse distance weighting to map a smooth surface of satisfaction with police over the entire city and compare the micro-level pattern of policing attitudes to survey data aggregated to the census tract. We also use spatial and multi-level regression models to estimate the effect of local violent crimes on attitudes towards police, controlling for other individual and neighborhood level characteristics.

Results: We demonstrate that there are no systematic biases for respondents refusing to answer the nearest intersection question. We show that hot spots of dissatisfaction with police do not conform to census tract boundaries, but rather align closely with hot spots of crime. Models predicting satisfaction with police show that local counts of violent crime are a strong predictor of attitudes towards police, even above individual level predictors of race and age.

Conclusions: Asking survey respondents to provide the nearest intersection to where they live is a simple approach to mapping attitudes towards police at micro places. This approach provides advantages beyond those of using traditional neighborhood boundaries. Specifically, it provides more precise locations police may target interventions, as well as illuminates an important predictor (i.e., nearby violent crimes) of policing attitudes.

And this was one of my favorites to make maps. We show how to take surveys and create analogs of hot spot maps of negative sentiment towards police. We do this via asking individuals to list their closest intersection (to still give some anonymity), and then create inverse distance weighted maps of negative attitudes towards police.

We also find in this work that nearby crimes are the biggest factor in predicting negative sentiment towards police. This hints that past results aggregating attitudes to neighborhoods is inappropriate, and that police reducing crime is likely to have the best margin in terms of making people more happy with the police in general.

As always, feel free to reach out for a copy of the paper if you cannot access JQC. (Or you could go a view the pre-print.)

Amending the WDD test to incorporate Harm Weights

So I received a question the other day about amending my and Jerry Ratcliffe’s Weighted Displacement Difference (WDD) test to incorporate crime harms (Wheeler & Ratcliffe, 2018). This is a great idea, but unfortunately it takes a small bit of extra work compared to the original (from the analysts perspective). I cannot make it as simple as just piping in the pre-post crime weights into that previous spreadsheet I shared. The reason is a reduction of 10 crimes with a weight of 10 has a different variance than a reduction of 25 crimes with a weight of 4, even though both have the same total crime harm reduction (10*10 = 4*25).

I will walk through some simple spreadsheet calculations though (in Excel) so you can roll this on your own. HERE IS THE SPREADSHEET TO DOWNLOAD TO FOLLOW ALONG. What you need to do is to calculate the traditional WDD for each individual crime type in your sample, and then combine all those weighted WDD’s estimates in the end to figure out your crime harm weighted estimate in the end (with confidence intervals around that estimated effect).

Here is an example I take from data from Worrall & Wheeler (2019) (I use this in my undergrad crime analysis class, Lab 6). This is just data from one of the PFA areas and a control TAAG area I chose by hand.

So first, go through the motions for your individual crimes in calculating the point estimate for the WDD, and then also see the standard error of that estimate. Here is an example of piping in the data for thefts of motor vehicles. The WDD is simple, just pre-post crime counts. Since I don’t have a displacement area in this example, I set those cells to 0. Note that the way I calculate this, a negative number is a good thing, it means crime went down relative to the control areas.

Then you want to place those point estimates and standard errors in a new table, and in those same rows assign your arbitrary weight. Here I use weights taken from Ratcliffe (2015), but these weights can be anything. See examples in Wheeler & Reuter (2020) for using police cost of crime estimates, and Wolfgang et al. (2006) for using surveys on public perceptions of severity. Many of the different indices though use sentencing data to derive the weights. (You could even use negative weights and the calculations here all work, say you had some positive data on community interactions.)

Now we have all we need to calculate the harm-weighted WDD test. The big thing here to note is that the variance of Var(x*harm_weight) = Var(x)*harm_weight^2. So that allows me to use all the same machinery as the original WDD paper to combine all the weights in the end. So now you just need to add a few additional columns to your spreadsheet. The point estimate for the harm reduction is simply the weight multiplied by the point estimate for the crime reduction. The variance though you need to square the standard error, and square the weight, and then multiply those squared results together.

Once that is done, you can pool the harm weighted stats together, see the calculations below the table. Then you can use all the same normal distribution stuff from your intro stats class to calculate z-scores, p-values, and confidence intervals. Here are what the results look like for this particular example.

I think this is actually a really good idea to pool results together. Many place based police interventions are general, in that you might expect them to reduce multiple crime types. Various harm scores are a good way to pool the results, instead of doing many individual tests. A few caveats though, I have not done simulations like I did in the WDD peer reviewed paper, I believe these normal approximations will do OK under the same circumstances though that we suggest it is reasonable to do the WDD test. You should not do the WDD test if you only have a handful of crimes in each area (under 5 in any cell in that original table is a good signal it is too few of crimes).

These crime count recommendations I think are likely to work as well for weighted crime harm. So even if you give murder a really high weight, if you have fewer than 5 murders in any of those original cells, I do not think you should incorporate it into the analysis. The large harm weight and the small numbers do not cancel each other out! (They just make the normal approximation I use likely not very good.) In that case I would say only incorporate individual crimes that you are OK with doing the WDD analysis to begin with on their own, and then pool those results together.

Sometime I need to grab the results of the hot spots meta-analysis by Braga and company and redo the analysis using this WDD estimate. I think the recent paper by Braga and Weisburd (2020) is right, that modeling the IRR directly makes more sense (I use the IRR to do cost-benefit analysis estimates, not Cohen’s D). But even that is one step removed, so say you have two incident-rate-ratios (IRRs), 0.8 and 0.5, the latter is bigger right? Well, if the 0.8 study had a baseline of 100 crimes, that means the reduction is 100 - 0.8*100 = 20, but if the 0.5 study had a baseline of 30 crimes, that would mean a reduction of 30 - 0.5*30 = 15, so in terms of total crimes is a smaller effect. The WDD test intentionally focuses on crime counts, so is an estimate of the actual number of crimes reduced. Then you can weight those actual crime decreases how you want to. I think worrying about the IRR could even be one step too far removed.


CrimCon Roundtable: Flipping a Criminal Justice PhD to an alt-academic Data Science Career

This Thursday 11/19/2020 at 1 PM Eastern, I will be participating in a roundtable for the online CrimCon event. This is free for everyone to zoom in, and here is the link to the program, I am on Stream 3!

The title is above — I have been a private sector data scientist at HMS for not quite a year now. I wanted to organize a panel to help upcoming PhD’s in criminal justice get some more exposure to potential data science positions, outside the traditional tenure track. Here is the abstract:

Tenure-track positions in academia are becoming more challenging to obtain, and only a small portion of junior faculty continue in academia to the rank of full professor. Therefore, students may opt to explore alternate options to obtain employment after their PhD is finished. These alternatives to the tenure track are often called “alt-academic” jobs. This roundtable will be focused on discussing various opportunities that exist for PhD’s in criminal justice and behavioral sciences spanning the public sector, the private sector, and non-profits/think tanks. Panelists will also discuss gaps in the typical PhD curriculum, with the goal of aiding current students to identify steps they can take to make themselves more competitive for alt-academic roles.

And here are each of the panelists bios:

Dr. Andrew Wheeler is currently a Data Scientist at HMS working on problems related to predictive modeling and optimization in relation to health insurance claims. Before joining HMS, he received a PhD degree in Criminal Justice from SUNY Albany. While in academia his research focused on collaborating with police departments for various problems including; evaluating crime reduction initiatives, place based and person based predictive modeling, data analytics for crime analysis, and developing models for the efficient and fair delivery of police resources.

Dr. Jennifer Gonzalez is the Senior Director of Population Health at the Meadows Mental Health Policy Institute, where she manages the Institute’s research and data portfolio. She earned her doctoral degree in epidemiology and a M.S. degree in criminal justice. Before joining MMHPI, Dr. Gonzalez was a tenured associate professor at the University of Texas School of Public Health, where she maintained a portfolio of more than $10 million in research funding and published more than one hundred interdisciplinary articles focused on the health of those who come into contact with—and work within—the criminal justice system.

Dr. Kyleigh Clark-Moorman is a Senior Research Associate for the Public Safety Performance Project at The Pew Charitable Trusts, a non-profit public policy organization. Kyleigh began working at Pew in 2019 and completed her PhD in Criminology and Criminal Justice at the University of Massachusetts, Lowell in May 2020. As an early career researcher, Dr. Clark-Moorman’s work has been published in Criminal Justice and Behavior, Criminal Justice Studies, and the Journal of Criminal Justice. In her role at Pew, Kyleigh is responsible for research design and data analysis focused on various criminal justice topics while also working with external partners to produce high-impact reports and analyses to raise awareness and drive public policy.

Matt Vogel is Associate Professor in the School of Criminal Justice at the University at Albany, SUNY and the Director of the Laboratory for Decision Making in Criminology and Criminal Justice. Matt regularly assists local agencies with data and evaluation needs. Some of his ongoing collaborations include assessments of racial representation on capital juries in Missouri, a longitudinal evaluation of a school-based violence reduction program, and the implementation of a police-hospital collaboration to help address retaliatory violence in St. Louis. Prior to joining the faculty at UAlbany, Matt worked in the Department of Criminology and Criminal Justice at the University of Missouri – St. Louis and held a long-term visiting appointment with the Faculty of Architecture at TU Delft (the Netherlands).

If you have any upfront questions you would like addressed by the panel, always feel free to send me a pre-emptive email (or comment below).

Regression with Simple Weights

I was reminded of this paper by Jung et al. on constructing simple rules via regression recently. So in the past few posts I have talked about how RTM (1,2) is aimed at making simple models. This is via variable selection and/or simplying the inputs to be binary yes/no. But in the end the final equation could be something like:

log(Crime) = -0.56 + 0.6923*NearbyBars + 0.329*HighDensity311

The paper linked above is about making the regression weights simple, so instead of a regression weight of 0.89728, you may just round the regression weight to 1. The Jung paper does a procedure where they use lasso regression and then round the weights. But there is a simpler approach IMO I will illustrate, just amend the lasso weights to push the coefficients to simple integers. (Also reminded by this example of using an iterative linear program to push weights to binary 0/1.)

So in lasso, you estimate your normal regression equation, but put a penalty on the weights that is typically something like lambda*(sum(abs(reg_weights)) - 1)**2. So if you have reg weights that add to more than 1, they are penalized by a particular amount (the lambda is a tuner to make the penalty higher/lower). And in the iterative algorithm to minimize your loss function plus this added penalty, it will converge to regression weights that meet the criteria of in total summing to around 1. Not exactly 1 but close.

You can however swap out that penalty term with whatever you want (or add to it additional penalties). I will show an example of using a penalty term to push regression coefficients towards integer values, creating simple regression weights.

Why Simple Models?

Dan Simpson has a good blog post of the Jung paper and why simple models are sometimes preferable (and I also have a comment why simple models like this tend to work out well for CJ datasets). But here are few quick examples why you might want a simple model results.

Example 1: If you have people in the field who are tabulating data and making quick decisions, it may be they need to use pen/paper and make a quick decision. No time to input results into a computer and pop out a prediction. Imagine a nurse in the ER, or even your general practitioner. There may be quite a bit of utility in making a simple check list that says if +4 on this scale, do a more intensive treatment.

Example 2: You have a complicated, large database. It is easier to create a simple predictive model in SQL to serve up predictions (either because of latency or because of the complexity of the data pipeline). Instead of a complicated random forest, a linear regression with simple weights will be much easier to implement.

Example 3: Transparency. Complicated models are more difficult to understand and monitor. If you have a vested interest in presenting the model to outside parties, it may make sense to sacrifice some accuracy to make the model more interpretable. Also similar to lasso, I suspect these simple weights will reduce the variance of predictions.

The reason that these simple weights work well in practice for many social science examples you could interpret either in a good light or a bad one. For the half-empty interpretation, our models are not well identified – we can literally swap out various weights in our regression equation and get near similar predictions. So it is fools errand to try to find the regression equation that describes the underlying system. But you can flip that around as well, we don’t even need to find the perfect equation, we can identify quite a few good predictive equations. And why not pick a good equation that is easier to interpret?

Pytorch Example

The example set of code here is very simple, so I will just put the python code entirely in this post. First I import my libraries I am using and change my directory.

import os
import torch
import statsmodels.api as sm
import statsmodels.formula.api as smf
import pandas as pd
import numpy as np

my_dir = r'D:\Dropbox\Dropbox\Documents\BLOG\regression_simpleweights\analysis'

Next I read in the data, which I have previously used as an example in prior blog posts on doctor visits for medicare patients. One thing to note here, is that I rescale the independent variables I am using to min/max. So the age variable instead of going from 65-90 like in the original data, now is scaled to be between 0/1. This is a problem intrinsic to lasso as well, in that you can change the scale of the input variables and it changes the weights. Here with the original data, the education variable has a tiny regression coefficient (0.2), but is highly stat significant. So without rescaling that variable, the model said to hell with your penalty and still converged to a solution of that regression weight is 0.2. If you divide the education variable by 5 though, the corresponding regression weight would change to around 1.

#Data from Stata,
#see pg 501

visit_dat = pd.read_stata('gsem_mixture.dta')
y_dat = visit_dat[['drvisits']]
x_vars = ['private','medicaid','age','educ','actlim','chronic']
#rescaling variables to 0/1
x_dat = visit_dat[x_vars]
visit_dat[x_vars] = (x_dat - x_dat.min(axis=0)) / ( x_dat.max(axis=0)  - x_dat.min(axis=0) )
x_dat = visit_dat[x_vars] #intentional not a copy

Now in the next part, I estimate the default linear regression model using statsmodels for reference. Then I stuff the results into pytorch tensors (which I will use later as default starting points for the pytorch estimates). Below is a pic of the resulting summary for the regression model (with the scaled variables, so is slightly different than my prior post).

#Estimating the same model in statsmodel
#for confirmation of the result

stats_mod = smf.ols(formula='drvisits ~ private + medicaid + age + educ + actlim + chronic',
sm_results =

#What is the mean squared error
pred = sm_results.get_prediction().summary_frame()
print( ((y_dat['drvisits'] - pred['mean'])**2).mean() )
#169513.0122252265 for sum
#46.10 for mean

#for setting default initial weights
coef_table = sm_results.params
int_ten = torch.tensor([coef_table[0]], dtype=torch.float, requires_grad=True)
coef_ten = torch.tensor(pd.DataFrame(coef_table[1:]).T.to_numpy(), dtype=torch.float, requires_grad=True)

Now creating the pytorch model is quite simple. For linear regression it is just one linear layer, and then setting the loss function to mean squared error. Then I create my own simple weight penalization factor in the simp_loss function. This takes the regression weights (not including the bias/intercept term), takes the difference between the observed weight and the rounded weight, takes the absolute value and sums those absolute values up. Then in the loop when I am fitting the model, you can see the loss = criterion(y_pred, y_ten) + 0.4*simp_loss(model) line. For the usual linear regression, it would just be the first criterion term. Here to add in the penalty term is super simple in pytorch, you just add it to the loss. (And you can incorporate additional penalities, the same way ala elastic-net. The Jung paper they put a penalty on the sum of coefficients as per the original lasso as well.)

Then the final part of the code after the loop is just putting the coefficients in a nicer data frame to print. And below the code snippet are the results.

#Now estimating OLS model with simple coefficient
#Penalities in Pytorch


model = torch.nn.Sequential( 

##Initializing weights
#with torch.no_grad():
#    model[0].weight = torch.nn.Parameter(coef_ten)
#    model[0].bias = torch.nn.Parameter(int_ten)

x_ten = torch.tensor( x_dat.to_numpy(), dtype=torch.float)
y_ten = torch.tensor( y_dat.to_numpy(), dtype=torch.float)

criterion = torch.nn.MSELoss(reduction='mean')
optimizer = torch.optim.Adam(model.parameters(), lr=1e-4)

def simp_loss(mod):
    dif = mod[0].weight - torch.round(mod[0].weight)
    return dif.abs().sum()

for t in range(100000):
    #Forward pass
    y_pred = model(x_ten)
    loss = criterion(y_pred, y_ten) + 0.4*simp_loss(model)
    if t % 1000 == 99:
        print(f'iter: {t}, loss: {loss.item()}') 
    #Zero gradients

#Making a nice dataframe of coefficients

coef_vars = ['Inter'] + x_vars
vals = list(model[0].bias.detach().numpy()) + list(model[0].weight.detach().numpy()[0,:])
res = pd.DataFrame(zip(coef_vars, vals), columns=['Var','Coef'])
print( res )

Here I did not round the coefficients, so you can see that they are not exactly integer values, but are very close. So this will result in a lower loss than taking the usual linear regression coefficients and rounding them like in the noted Jung paper. It is a more direct approach. Also note that the intercept is not close to an integer value. I did not include the intercept in my penalty term. You could if you wanted to, but for most examples I don’t think it makes much sense to do that.

But one of the things that I have noticed playing around with pytorch more is that it is very difficult to get random initialized weights to converge to the same solution. That identification problem I mentioned earlier. One way is instead of using random initialized weights, is to initialize them to some reasonable values. If you uncomment the lines with torch.no_grad(): in the above code and initialize the weights to start from the unregularized OLS solution, it converges much faster, has a slightly smaller mean square error term, and results in these effects:

So you can see in that solution it is exactly the same as rounding the initial OLS solution (ignoring the intercept again). But that may not always be the case. For example if actlim (activity limitations) and educ (education) had a very high correlation, it may be rounding both down is too big a hit to the fit of the equation, so one may go down and one go up. (You need to estimate the equation to know if things like that will occur.)

And that is all folks! While if I were sharing this more broadly, I would likely make a statsmodel like interface (and it appears they use cvxopt under the hood) instead of pytorch, it is very simple to amend pytorch to return simple weights, just add in the penalty to the loss function. Works the same way for lasso/ridge as it does for the simple weights example I give here.

Next up I want to try to figure out autograd in pytorch good enough to give standard errors for these various regression models I am estimating. While I don’t think hypothesis testing makes sense for these various models I am sharing, seeing a standard error that is very high may have prognostic value. In this case, if you had a very high standard error relative to the simple coefficient, it might suggest you should rescale the variable a different way or drop it entirely.

Also for this example, to be simple in the field it would not only need simple coefficients, but simple inputs as well. Wondering if there is a way to add in threshold layers in deep learning to automatically figure out the best way to make the inputs binary (e.g. above 70, educ below 10, etc.) instead of doing min/max scaling of the inputs.

A latent variable approach to RTM using hidden layers in deep learning

Sorry about the long title! Previously I have blogged about how to use Deep Learning to generate an RTM like model variable selection and positive constraints. Deep learning frameworks often do not rely on variable selection like that though, they more often leverage hidden layers. For social scientists familiar with structural equation modelling, these hidden layers are very much akin to formative latent variables. (More traditionally folks use reflective latent variables in factor analysis, so the latent variable causes the observed measures. This is the obverse, the observed measures cause/define the latent variable, and we find the loadings that best predict some outcome further down the stream.)

In a nutshell, instead of the typical RTM way of picking the best variable to use, e.g. Alcohol Density < 100 meters OR Alcohol Density < 500 meters, it allows both to contribute to a latent variable, call it AlcoholDens, but allows those weights to vary. Then I see how well the AlcoholDens latent variable predicts crime. I will show later in the results that the loadings are often spread out among different density/distance measures in this sample, suggesting the approach just pick one is perhaps misguided.

I’ve posted the data and code to follow along here. There are two py files, runs the main analysis, but has various functions used to build the deep learning model in pytorch. I am just going to hit some of the highlights instead of walking through bit by bit.

Some helper functions

First, last blog post I simply relied on using Poisson loss. This time, I took some effort to figure out my own loss function for the negative binomial model. Here I am using the NB2 form, and you can see I took the likelihood function from the Stata docs (they are a really great reference for various regression model info). To incorporate this into your deep learning model, you need to add a single parameter in your model, here I call it disp.

#Log likelihood taken from Stata docs, pg 11 
def nb2_loss(actual, log_pred, disp):
    m = 1/disp.exp()
    mu = log_pred.exp()
    p = 1/(1 + disp.exp()*mu)
    nll = torch.lgamma(m + actual) - torch.lgamma(actual+1) - torch.lgamma(m)
    nll += m*torch.log(p) + actual*torch.log(1-p)
    return -nll.mean()

A second set of helper functions I will illustrate at the end of the post is evaluating the fit for Poisson/Negative Binomial models. I’ve discussed these metrics before, they are just a python rewrite of older SPSS code I made.

def pred_nb(mu, disp, int_y):
    inv_disp = 1/disp
    p1 = gamma(int_y + inv_disp) / ( factorial(int_y)*gamma(inv_disp) )
    p2 = ( inv_disp / (inv_disp + mu) ) ** inv_disp
    p3 = ( mu / (inv_disp + mu) ) ** int_y
    pfin = p1*p2*p3
    return pfin
def nb_fit(mu, obs, disp, max_y):
    res = []
    cum_fit = mu - mu
    for i in range(max_y+1):
        pred_fit = pred_nb(mu=mu, disp=disp, int_y=i)
        pred_obs = (obs == i)
        res.append( (str(i), pred_obs.mean(), pred_fit.mean(), pred_obs.sum(), pred_fit.sum()) )
        cum_fit += pred_fit
    fin_fit = 1 - cum_fit
    fin_obs = (obs > max_y)
    res.append( (str(max_y+1)+'+', fin_obs.mean(), fin_fit.mean(),
                  fin_obs.sum(), fin_fit.sum()) )
    dat = pd.DataFrame(res, columns=['Int','Obs','Pred','ObsN','PredN'])
    return dat

Main Analysis

Now onto the main analysis. Skipping the data loading (it is near copy-paste from my prior RTM Deep Learning post), here are the main guts to building and fitting the RTM model.

model = dl_rtm_funcs.RTM_hidden(gen_list=[alc_set,metro_set,c311_set], 
optimizer = torch.optim.Adam(model.parameters(), lr=0.001) #1e-4

for t in range(5001):
    #Forward pass
    y_pred = model(comb_ten)
    loss_insample = dl_rtm_funcs.nb2_loss(y_ten, y_pred, model.dispersion)
    loss_insample.backward() #retain_graph=True
    if t % 100 == 0:
        loss_out = dl_rtm_funcs.nb2_loss(out_ten, y_pred, model.dispersion)
        print(f'iter {t}: loss in = {loss_insample.item():.5f}, loss out = {loss_out.item():.5f}')

And in terms of iterations, on my machine this takes less than 20 seconds to do the 5000 iterations, and it has clearly peaked out by then (both in sample 2011 and out of sample 2012).

I’ve loading the RTM model object with a few helper functions, so if you then run print( model.coef_table() ), you get out the final regression coefficients, including the dispersion term. For my negative binomial models for my dissertation, the dispersion term tended to be around ~4 for many models, so this corresponds pretty closely with my prior work.

These have interpretations as latent variables representing the effect of nearby alcohol outlets (both distance and density), metro entrances (just distance), and 311 calls for service (just density). Similar to original RTM, I have restricted the crime generator effects to be positive.

I also have another helper function, model.loadings(), that gives you a nice table. Here this shows how the original variables contribute to the latent variable. So here are the loadings for the distance to the nearest metro.

You can see that the dummy variables for met_dis_300 (meters) and smaller all contribute to the latent variable. So instead of picking one variable in the end, it allows multiple variables to contribute to the latent risk score. It may make more sense in this set up to encode variables as not cumulative, e.g. < 50 meters, < 100 meters, but orthogonal, e.g. [0,50),[50,100), etc.), but just stuck with the prior data in the same format for now. I force the loadings to sum to 1 and be positive, so the latent variables still have a very apples-to-apples comparison in terms of effect sizes.

Here are the loadings for alcohol outlets, so we have both some distance and density effects in the end.

And here are the loadings for 311 density variables:

So you can see for the last one, only the furthest away had an effect at all. Which is contra to the broken windows theory! But also shows that this is more general than the original RTM approach. If it only should be one variable the model will learn that, but if it should be more it will incorporate a wider array of weights.

Next is to check out how well the model does overall. For calibration for Poisson/Negative Binomial models, I just detach my pytorch tensors, and feed them into my functions to do the evaluations.

#Calibration for Negative Binomial predictions
pred_pd = pd.Series( y_pred.exp().detach().numpy() )
disp_val = model.dispersion.exp().item()

nb_fit = dl_rtm_funcs.nb_fit(mu=pred_pd, obs=crime_data['Viol_2011'], 
                             disp=disp_val, max_y=10)
print( nb_fit )

So this shows that the model is pretty well calibrated in terms of overall predictions. Both samples predict 83% zeroes. I predict a few more 3/4 crime areas than observed, and my tails are somewhat thinner than they should be, but only by a tiny bit. (No doubt this would improve if I incorporated more covariates, kept it simple to debug on purpose.)

We can ignore the negative binomial dispersion term and see what our model would predict in the usual Poisson case (the mean functions are the same, it is just changing the variance). To do this, just pass in a dispersion term of 1.

pois_fit = dl_rtm_funcs.nb_fit(mu=pred_pd, obs=crime_data['Viol_2011'], 
                               disp=1, max_y=10)
print( pois_fit )

You can see that the Poisson model is a much worse fit. Underpredicting zero crime areas by 6%, and areas with over 10 crimes should pretty much never happen according to the Poisson model.

We should be assessing these metrics out of sample as well, and you can see that given crime is very historically stable, the out of sample 2012 violent crime counts are similarly well calibrated.

Finally, I have suggested in the past to use a weighted ROC curve as a metric for crime counts. Here is a simple example of doing that in python.

crime_data['Weights'] = crime_data['Viol_2012'].clip(1)
crime_data['Outcome'] = crime_data['Viol_2012'].clip(0,1)

fpr, tpr, thresh = roc_curve(crime_data['Outcome'], pred_pd, sample_weight=crime_data['Weights'])
weighted_auc = auc(fpr, tpr)
print( weighted_auc ) 

So you can see the AUC is nothing to brag about here, 0.61 (it is only 0.63 in the 2011 sample). But again I am sure I could get that up by quite a bit by incorporating more covariates into the model.

A bunch of random shout outs

Busy, busy, busy! Hopefully I will have some time in the near future to write up some more data science posts. But for now, here is a small python snippet to help you build interaction variables between two sets of numpy arrays/dataframes.

import numpy as np
def np_int(a,b):
    rows = a.shape[0]
    cols = a.shape[1]*b.shape[1]
    return np.einsum('ij,ik->ijk', a, b).reshape((rows,cols))

This works for pytorch as well (just replace np.einsum with torch.einsum). So coming up (eventually) I will illustrate encoding interaction between hidden layers in a deep learning model. But for now some quicker updates.

Shout out #1: Scott Jacques has continued to push the charge for open access to criminology journals. He has two recent posts about post-prints, and how our main journal (Criminology) has an excessive policy of not allowing authors to post post prints for over two years (whereas the majority of criminology journals allow you to post immediately).

Several aspects of open science are tricky – posting pre-prints/post-prints is not. If we can come together as a group this is an easy, no cost way to greatly improve the accessibility of our work to the greater public.

Shout out #2: The folks at Police Rewired have hosted a hackathon intended to Hack Hate. It is too late to participate, but they will be displaying the results this Sunday. I have not had the chance to participate in any code hackathons, I will need to make a concerted effort in the future to give at least one a shot. (It seems hard, how can you do any work in only a day or a week or two!? But the proof is in the pudding so to speak, I’ve have seen some pretty cool things come out of various hackathons in the past.)

Shout out #3: My workplace, HMS, is involved in a data sharing collaborative called the Digital Health DRC. They also have a hackathon coming up, but this is related to Telehealth use. The Digital Health DRC is pretty cool though, it is basically a way for HMS (and several other private sector entities) to share various datasets with researchers over the globe.

The scope of HMS’s data is somewhat outside the realm of my old stomping grounds of criminology (but not entirely, a big part of my job is identifying potentially fraudulent patterns in claims data). But for folks who have a research question that could be answered using health insurance claims data, this is a good resource to look into. (HMS has pretty good coverage of Medicare claims across the US.)

Finally, I experimented a few days on the site with hosting ads. I managed to serve up a few thousand and make 10 cents. So I will turn that off for now. I debated on putting the button for folks to donate a coffee, but even that is not necessary. (I can afford the few bucks for the domain, and I use dropbox to back up my files anyway, so hosting extra materials is not a big deal.) I rather folks just take my nerdy notes and make your own cool stuff (and share them with me!) I may need to figure out a better hosting solution for images though — google photos is continuing to give me troubles I see (so if you see an image is not coming through feel free to let me know in the comments or send me an email).

Overview of DataViz books

Keith McCormick the other day on LinkedIn the other day made a post/poll on his favorite data viz books. (I know Keith because I contributed a chapter on geospatial data analysis in SPSS in Keith and Jesus Salcedo’s book, SPSS Statistics for Data Analysis and Visualization, and Jon Peck contributed a chapter as well.)

One thing about this topical area is that there isn’t a standard Data Viz 101 curriculum. So if you pick up Statistics 101 books, they will cover pretty much all the same material (normal distribution, central limit theorem, t-tests, regression). It isn’t 100% overlap (some may spend more time on elementary probability, and others may cover ANOVA), but for someone learning the material there isn’t much point in reading multiple introductory stats books.

This is not so with the Data Viz books in Keith’s picture – they are very different in content. As I have read quite a few different books on the topic over the years I figured I would give my breakdown of the various books.

Albert Cairo’s The Functional Art

While my list is not in rank order, I am putting Cairo’s book first for a reason. Although there is not a Data Viz 101 curriculum, this book is the closest thing to it. Cairo goes through in short order various cognitive aspects on how we view the world that are fundamental to building good data visualizations. This includes things like it is easier to compare lengths along a common axis, and that we can perceive rank order to color saturation, but not to a color’s hue.

It is also enjoyable to read because of all the great journalistic examples. I did not care so much for the interviews at the back, and I don’t like the cover. But if I did a data viz course for undergrads in social sciences (Cairo developed this for journalism students), I would likely assign this book. But despite being very accessible, he covers a broad spectrum of both simple graphs and complicated scientific diagrams.

For this review many of these authors have other books. So I haven’t read Cairo’s The Truthful Art, so I cannot comment on it.

Edward Tufte’s The Visual Display of Quantitative Information

Tufte’s book was the first data viz book I bought in grad school. I initially invested in it as he had a chapter on a critique of powerpoint presentations, which is very straightforward and provides practical advice on what not to do. Most of the critiques of this book are that it is mostly just a collection of Tufte’s opinions about creating minimalist, dense, scientific graphs. So while Cairo dives into the science of perception, Tufte is just riffing his opinions. His opinions are based on his experience though, and they are good!

I believe I have read all of Tufte’s other books as well, but this is the only one that made much of an impression on me (some of his others go beyond graphs, and talk about UI design). I gobbled it up in only two days when I first started reading it, and so if I were stuck on an island with one book scenario I would choose this one over the others I list here (although again think Cairo’s book is the best to start with for most folks). So for scientists I think it is a good investment and an enjoyable read overall.

Nathan Yau’s Visualize This

Of all the books I review, Yau’s is the only how-to actually make graphs in software. Unfortunately, much of Yau’s programmatic advice was outdated already when it was published (e.g. flash was already going by the wayside). So while he has many great examples of creating complicated and beautiful data visualizations, the process he outlines to make them are overly complicated IMO (such as using python to edit parts of a pre-made SVG map). It is a good book for examples no doubt, and maybe you can pick up a few tricks in terms of post editing charts in a vector graphics program, such as Illustrator or Inkscape (most examples are making graphs in base R and then exporting to edit finishing touches).

In terms of making a how-to book it is really hard. Yau I am sure has updates on his Flowing Data website to make charts (and maybe his newer book is better). But I don’t think I would recommend investing in this book for anything beyond looking at pretty examples of data viz.

Stephen Kosslyn’s Graph Design for the Eye and Mind

The prior books all contained complicated, dense, scientific graphs. Kosslyn’s book is specifically oriented to making corporate slide decks/powerpoints, in which the audience is not academic. But his advice is mostly backed on his understanding of the psychology (he relegates extensive endnotes to point to scientific lit, to avoid cluttering up the basic book). He has as few gems of advice I admit, such as it isn’t the number of lines in a graph that make it complicated, but really the number of unique profiles. But then he has some pieces I find bizarre, such as saying pie charts are OK because they are so popular (so have survived a Darwinian survival process in terms of being presented to business people).

I would stick with Tufte’s powerpoint advice (and later will mention a few other books related to giving presentations), as opposed to recommending this book.

Alan MacEachren How maps work: Representation, visualization, and design

MacEachren’s book is encyclopedic in terms of scientific literature on design aspects of both cartography, as well as the psychological literature. So it is like reading an encyclopedia (not 100% sure if I ever finished it front to back to be honest). I would start here if you are interested in designing cognitive experiments to test certain graphs/maps. I think MacEachren pooling from cartography and psychology ends up being a better place to start than say Colin Ware’s Information Visualization (but it is close). They are both very academically oriented though.

Leland Wilkinson’s The Grammar of Graphics

I used SPSS for along time when I read this book, so I was already quite familiar with the grammar of graphics in terms of creating graphs in SPSS. That pre-knowledge helped me digest Wilkinson’s material I believe. Nick Cox has a review of this book, and for this one he notes that the audience for this book is hard to pin down. I agree, in that you need to be pretty far along already in terms of making graphs to be able to really understand the material, and as such it is not clear what the benefit is. Even for power users of SPSS, much of the things Wilkinson talks about are not implemented in SPSS’s GGRAPH language, so they are mostly just on paper.

(Note Nick has a ton of great reviews on Amazon as well for various data viz books. He is a good place to start to decide if you want to purchase a book. For example the worst copy-edited book I have ever seen is Andy Kirk’s via Packt publishing, and Nick notes how poorly it is copy-edited in his review.)

Here is an analogy I think is apt for Wilkinson’s book – if we are talking about cars, you may have a book on the engineering of the car, and another on how to actually drive the car. Knowing how pistons work in a combustible engine does not help you drive a car, but helps you build one. Wilkinson’s book is more about the engineering of a graph from an algebraic perspective. At the fringes it helps in thinking about the components of graphs, but doesn’t really give any advice about what graph to make in-and-of itself, nor what is a good graph or a bad graph.

Note that the R library ggplot2, is actually quite a bit different than Leland’s vision. It is simpler, in that Wickham essentially drops the graph algebra part, so you specify the axes directly, whereas in Wilkinson’s you just say X*Y*Z, and depending on other aspects of the grammer this may produce a 3d scatterplot, a facet gridded scatterplot, a clustered bar chart, etc. I think Wickham was right to make that design choice, but in doing so it really isn’t an implementation of what Wilkinson was talking about in this book.

Jacques Bertin’s Semiology of Graphics: Diagrams, Networks, Maps

Bertin’s book is an attempt to make a dictionary of terms for different aspects of graphs. So it is a bit in the weeds. One unique aspect of Bertin is that he discusses titles and labels for graphs, although I wouldn’t go as far as saying that his discussion leads to straightforward advice. I find Wilkinson’s grammer of graphics a more useful way to overall think about the components of a graph, although Bertin is more encyclopedic in coverage of different types of graphs and maps in the wild.

Short notes on various other books

Most of these books (with the exception of Nathan Yau’s) are not how-to actually write code to make graphs. For those that use R, there are two good options though. Hadley Wickham’s ggplot2: Elegant Graphics for Data Analysis (Use R!) was really good at the time (I am not sure if the newer version is more up to date though, like any software it changes over time so the older one I know is out of date for many different code examples). And though I’ve only skimmed it, Kieran Healy’s Data Visualization: A practical introduction is free and online and looks good (and also for those interested in criminal justice examples Jacob Kaplan has examples in R as well, Crime by the Numbers). So those later two I know are good in terms of being up to date.

For python I just suggest using google (Jake VanderPlas has a book that looks good, and his website is really good). For excel I really like Jorge Camões work (his book is Data at Work, which I don’t think I’ve read, but have followed his website for along time).

In terms of scientific presentations (which covers both graphs and text), I’ve highly suggested in the past Trees, maps, and theorems. This is similar in spirit to Tufte’s minimalist style, but gives practical advice on slides, writing, and presentations. Jon Schwabish’s book, Better Presentations: A Guide for Scholars, Researchers, and Wonks, is very good as well in terms of direct advice. I think for folks in academia I would say go for Doumont’s book, and for those in corporate environment go for Schwabish’s.

Stephen Few’s books deserve a mention here as well, such as Show me the numbers. Stephen is the only one to do a deep dive into the concept of dashboards. Stephen’s advice is very straightforward and more oriented towards a corporate type environment, not so much a scientific one (although it isn’t bad advice for scientists, ditto for Schwabish, just stating more so for an understanding of the intended audience).

I could go on forever, Tukey’s EDA, Calvin Schmid’s book on how to draw graphs with actual splines! How to lie with statistics and how to lie with maps. So many to choose from. But I think if you are starting out in a data oriented role in which you need to make graphs, I would suggest starting with Cairo’s book, then get Tufte to really get some artistic motivation and a good review of bad powerpoint practices. The rest are more advanced material for study though.

From a criminologist, we should restore voting rights

I have donated to the Southern Poverty Law Center in the past (recently my workplace, HMS, matched contributions). I no doubt do not 100% agree with their positions on every little detail (as is probably true for every organization in the criminal justice sphere) , but I believe they do good work. In particular I’ve always though that their identifying hate groups is a valuable public service, see the SPLC’s Hate Map.

They do more work than just the hate group map though. Recently they have been sending information on voter disenfranchisement. It is not uniform across states, but in many places if you have a felony conviction you have your rights to vote stripped entirely. It is even more severe in some places, in that you cannot vote if you simply owe fines or fees to the state.

I figured this would be a good blog post, as I have always had a more extreme view on this than most people. While most argue simply that individuals voting rights should be restored after an individuals imprisonment has ended, I don’t believe they should ever be stripped to begin with. Or more specifically, I believe people who are even currently incarcerated should be allowed to vote.

The reasons I have this opinion are relatively simple. First, there is no evidence that voter disenfranchisement acts as a deterrent to prevent someone from committing a crime. No one thinks, hey, I shouldn’t commit this robbery because I need to cast my ballot this fall. Restoring voting rights, even to those imprisoned, poses no threat to public safety.

The second reason I support restoring voting rights is because an important part of offender reintegration into society is to participate in civil matters. We don’t lock people up and throw away the keys, so we should take steps to help those former offenders come back and have a positive contribution to our society. What simpler way than to allow those individuals to engage in the voting process? (The foremost authority on this subject is Vesla Weaver.)

You may ask how would voting in prison work? For voting in prison the location of the vote should not count where the jail is located, but wherever the last address of the offender was before they were incarcerated. This brings up another issue, that certain state census counting procedures count individuals incarcerated at the location of the prison. This results in gerrymandering, where typically rural areas with prisons get more electoral representation, even though for the most part those individuals have no voting rights.

I believe we would be better off as a nation if not only everyone was allowed to vote, but that everyone did vote.