[Here we examine how various demographics might be related to voting patterns in the Republican and Democratic primaries that have taken place so far, and whether one or more candidates has broad popular appeal across demographics.]

(Spoiler alert: as of mid-April, 2016, Clinton appears to have the broadest appeal across many demographics.  However, I do not mean this analysis to advocate one candidate or political party over another, I simply represent the data as it is.)

Based on the counties that have had primaries so far at the time of this writing in mid-April, 2016, we expressed the demographics of a particular county as a percentile related to all the other counties that have voted, and visualized the results in a format sometimes called a “spider-web graph”; the spokes of the circular graph correspond to various demographics and social indicators, and if a point lies on a spoke far from the center, it indicates that it lies at a higher percentile for the demographic that corresponds to that spoke.

So, for instance, if one of the spokes is  “income”, the closer towards the center of the circle on that spoke, the lower the average household income compared to other counties, and the closer to the perimeter of the circle, the higher the average income. Here is what these spokes might look like for a bunch of different demographics and variables:

There is a lot of information on display all at once in the above plot!  Let’s break it down a step at a time.  The variables corresponding to each spoke are:

• fwhite: fraction of non-hispanic whites in the population
• fover_65: fraction of the population over the age of 65
• no_high_school: fraction of the population 25 years and over without a high school diploma
• bachelors: fraction of the population 25 years and over with at least a bachelors degree
• food stamps: fraction of family households receiving food stamp assistance
• uninsured: fraction of the population without health insurance
• bankruptcies: per-capita bankruptcy rates
• mobile homes: fraction of households that consist of mobile homes
• obese: fraction of the population that is obese
• overdose: per-capita death rates by drug overdoses
• suicide rate: per-capita age-adjusted suicide rate
• pop_dens: population density
• evangelical: fraction of population regularly attending an evangelical church
• firearm_owners: fraction of households that own firearms
• fvote_2012: fraction of adult population that voted in 2012 election
• f_obama_2012: fraction of votes that went to Obama
• f_independent_2012: fraction of votes that went to an independent candidate

The blue circle on the plot represents the median values for each of the demographics and variables for all counties that have voted in the primaries so far.  The outer black circle represents the 100th percentile (basically, the county that has the highest value of that particular indicator along a spoke).  The inner dashed line is the 25th percentile, and the outer dashed line is the 75th percentile.

Now, for a particular sub-group of counties (in the case in the figure, counties that favoured Trump over any other candidate by at least 5 points in the primary), we can show, with the red line, how the demographics in those counties compare to those of all other counties.  You can see that, for example, the average median household income in counties that favoured Trump is much lower than that for all counties, because the red line dips sharply towards the center of the circle along the “income” spoke.  And there is an unusually large fraction of people in those counties who do not have a high school diploma, because the red line deviates outwards along the “no_high_school” spoke.

Let’s look at this further, in more detail…

Demographics of counties that heavily favour Trump in the Republican primaries

Here we examine the average percentiles of counties that favoured Trump over any other candidate by at least 5 percentage points in the Republican primaries, which was 47% of all counties. This is what the demographics of those counties look like, where I have added a pink band to the plot above show the 25th to 75th percentiles for those counties:

The counties that favour Trump over other candidates skew older and less hispanic, are more poorly educated, have a high fraction of families receiving food stamps, low income, a relatively large fraction of people living in mobile homes, and are generally in poorer health than average.  These counties were about average in voter participation, the percentage that voted for Obama in 2012, and the percentage that voted for an independent presidential candidate in 2012.

 Demographics of counties that heavily favour Cruz in the Republican primaries

Now let’s look at the same plot for counties that favoured Cruz by at least 5 percentage points in the Republican primaries.  This was 21% of counties:

These counties skew far more hispanic, more white, somewhat younger, higher income, and generally have better health than average, despite the very high average of people without health insurance.  The counties also skew very rural (low population density), had generally very low voter participation in 2012, and skewed very Republican in the 2012 election.

Demographics of counties that heavily favour Sanders in the Democratic primaries

Now let’s look at the counties that favoured Sanders over Clinton by at least 5 percentage points in the Democratic primaries that have occurred so far (21% of counties):

These counties skew very white, very educated, much less evangelical, high income, low percentage of uninsured, and good health (except for overdose and suicide rates, which are about average).  There was a high degree of voter participation in these counties in 2012, and they skewed Democrat and heavily Independent rather than Republican.

Demographics of counties that heavily favour Clinton in the Democratic primaries

Now let’s look at the counties that favoured Clinton over Sanders by at least 5 percentage points so far (67% of counties):

These counties skew perhaps somewhat less white than average, but for the most part are quite close the average for all other counties.

Which candidate has the broadest appeal?

As I discussed above, the candidate with the broadest appeal would be favoured by counties that are representative of the national averages in the various demographics. It would appear that, as of mid-April 2016, neither Trump nor Cruz achieves this, although Trump so far comes closer than Cruz to broader appeal; however Trump support appears to skew poorer, unhealthier, and less educated, and Cruz support appears to skew heavily rural, and evangelical.

Clinton appears to so far have far broader appeal over a wide array of demographics than Sanders (and indeed, over any other candidate).

Sources of data

• The Politico website makes available the county level election results for most of the primaries that have taken place.  They are missing the county level results for Iowa and Alaska, and Kansas and Minnesota have results by district, not counties.
• All cause and cardiovascular death rates from 2010 to 2014 from the CDC.
• Household firearm ownership is estimated using the fraction of suicides that are committed by firearm; the suicide data by cause from 2010 to 2014 is obtained from the CDC.
• Education, racial and age demographics, household living arrangements, percentage without health insurance, and income are obtained from the 2014 Census Bureau American Community Survey 5 year averages.
• Land area of counties obtained from the 2015 Census Bureau Gazetteer files.
• Religion demographics from the 2010 Census religion study
• Drug overdose mortality from 1999 to 2014 from the CDC.
• Obesity and diabetes prevalence from the CDC.

There have been 8 apparent influenza pandemics (generally agreed upon in the literature to have occurred) since 1700, and a total of 16 apparent and potential pandemics.  Influenza pandemics tend to have high mortality, which means that it would be awfully nice if we could predict when they will occur, such that we can prepare in advance.

It has been observed that 6 out of the 8 apparent influenza pandemics since 1700 (and 13 of the 16 total potential number) occurred within one year of when the number of sunspots was at a maximum or minimum (sunspot activity has an 11 year cycle, on average).  Here’s a plot that shows the pattern (you can find the sunspot data from many different sites online… for instance, here):

A total of 6 out of 8 (or 13 out of 16) perhaps seems like an awfully large fraction that occur near a high or low in sunspot activity! Indeed, there have been claims that sunspot activity can increase the chance of meteorites from outer space bringing in extraterrestrial influenza viruses (no, I’m not making that up… a 1990 paper claiming that actually appeared in Nature).

Since that initial paper, there have been several other analyses of the same data, some of which also conclude that yes, influenza pandemics appear to happen “around the time” of sunspot activity maxima and/or minima.

However, let’s take a closer look.  There were 56 sunspot extrema in the past 264 years.  The number of years within +/- one year of an extrema is thus 56*3=168.  Thus, by mere random chance, we would expect that the a pandemic would fall “near” a max or min with probability p=168/264=0.64.  The observed fraction of 0.75 (or 0.81 if you include potential pandemics too)  is higher than this.  But is it significantly higher?  In R, the binom.test(k,n,p) function returns the confidence interval on the estimate of the probability of success if we observe k successes out of n trials.  It also assesses the probability that this fraction is consistent with an assumed true probability of success, p (if the true value of p lies within the estimated confidence interval for the probability of success, there is no statistically significant evidence that they are different).

If we use binom.test(6,8,168/264), we find that the 95% confidence interval of the estimated p is [0.35,0.97].  If we include potential pandemics as well, and use binom.test(13,16,168/264), we get a confidence interval of [0.54,0.96]. The true value that we assume under our null hypothesis is p=168/264=0.64, which falls squarely within both confidence intervals.  Thus, despite claims to the contrary in the literature, there is no statistically significant evidence that sunspot cycles have anything whatsoever to do with influenza pandemics.*

In addition to this simple Binomial probability analysis, I also took a look at the distribution of the number of sunspots in pandemic and non-pandemic years using the two sample Kolomogorov-Smirnov test…. there is no statistically significant difference between the distributions.

*The reason the various papers draw the opposite conclusion is due to faulty statistical analyses.  Just like the old saying “all happy families are alike, but unhappy families are unhappy in their own way”, it is true that all good statistical analyses tend to be a lot alike, but faulty ones are usually faulty in their own unique way.  In this case, in general, the various statistical analyses didn’t account properly for the small sample sizes, and/or used statistical tests or methods inappropriate for the data.  It is well worth noting that just because something in the published literature made it past review doesn’t mean that it was a sound analysis without flaws.

Most journals in the field of mathematical epidemiology/biology require that you submit manuscripts in LaTeX format.

LaTeX is a word processing language, in which you create a document that contains directives to the latex compiler to produce a final document.  LaTeX provides many capabilities not available in Word; perhaps most important to mathematicians, LaTeX enables typesetting of complex equations that would be difficult, if not impossible in Word.

In addition, LaTeX has a reference management package called BibTeX that easily enables citation of references within your document.

In this module, we will discuss some simple examples of document formatting in LaTeX, and describe how to include figures and tables in the document, and cite references.

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As scientists, our main objective is not just to do well motivated and novel research, but also to publish that research in a timely fashion, and in a way that clearly communicates to an “educated layperson“ what is new and interesting about your research, while also providing enough detail in the paper such that an expert in your field can assess the soundness of your work.  Remember that, first and foremost, your work needs to be novel with a well posed research question, and must be an interesting and well motivated addition to the body of published literature on the topic.  If you don’t have the skills to produce a well written paper, even with a well posed research question you will have a difficult time getting your work published, and/or you will needlessly get bogged down in review.

• Learning to write (and read) a scientific paper
• Tips for making your paper easy for a reviewer to review
• Sections required in a scientific paper, and what they should contain.
• Developing skills to efficiently and quickly write up your work
• Who to include as co-authors
• Your responsibilities as a author/co-author
• Submitting your paper to a journal
• Responding to reviewer questions
• Rejection and Acceptance

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If you are looking at an archaeological site that you believe was a comprehensive ancient sky observatory, it may be possible to date the site from its alignments to celestial phenomenon.  Note that you need a site with several likely sun/moon/star alignments to do this. On this page I provide some handy R and python scripts to calculate the rise/set azimuth (assuming a flat horizon) of the Sun, Moon, and stars for a given location at a given date.

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Once you have used pyephem or an R script to calculate the rise/set azimuths of stars, the Sun and the Moon at a particular date for a particular latitude, you need to correct the calculation for horizon features.

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I am a data scientist with a diverse background visual analytics, data mining, social media analytics, machine learning, high performance computing, and mathematical and computational dynamical modeling.  As both an academic and a consultant, I have worked on a broad array of research topics in public health and the social sciences, including crime and violence risk analyses, spread of political and partisan sentiments in a society, disease modelling, and other topics in applied modelling in the social and life sciences, with over 360 publications on a wide variety of subjects. My unique trans-disciplinary skill set enables me to examine a wide range of research questions that are often of broad interest and importance to policy makers and the general public.

My work in the computational social sciences has been high impact, including an analysis of how media can incite panic in a population, and how contagion may play a role in the temporal patterns observed in mass killings in the US. The latter work has received extensive media coverage, including on BBC, CNN, NBC, CBS, FOX, NPR, Reuters, USA Today, Washington Post, Los Angeles Times, The Wall Street Journal, Huffington Post, Christian Science Monitor, Newsweek, The Atlantic, The Telegraph, The Guardian, Vox, and many other local, national, and international news agencies. The study was also profiled in Season 8, Episode 4 of Morgan Freeman’s Through the Wormhole documentary series on the Discovery Channel in 2017, “Is Gun Crime a Virus?”.

Several of my publications in computational epidemiology have also received widespread attention, including forecasts for the progression of the 2009 influenza pandemic, and the 2014 Ebola epidemic in West Africa. Both analyses correctly forecast the progression of the epidemics, and my forecast for the 2009 pandemic was discussed in a special US Senate meeting on October 23, 2009 H1N1 Flu: Monitoring the Nation’s response.

Through my consulting company, Towers Consulting LLC, I provide consulting services for industry, academia, and the public sector in quantitative and predictive analytics, modelling, statistics, and visual analytics.  Notable past and current clients include the VACCINE Department of Homeland Security Center of Excellence, Cure Violence Global, the Carter Center, George Washington University, and Disney. Prospective clients can contact me at TowersConsultingLLC@gmail.com.

On this website I share information and computational tools related to a wide range of my research topics, including visual analytics, applied statistics, and mathematical and computational modelling methods. This website also includes material related to my lectures and seminars in statistical and computational methods in the life and social sciences.

My CV is available here.