Strategy and tactics for graphic multiples in Stata

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Strategy and tactics for graphic
multiples in Stata

• Nicholas J. Cox
• Department of Geography
• Durham University, UK

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Comparison

• Many useful graphs compare two or more sets of
  values, and so can be thought as of multiples.
• Often there can be a fine line between richly
  detailed graphics and busy, unintelligible
  graphics that lead nowhere.
• In this presentation I survey strategy and
  tactics for developing good graphic multiples in
  Stata.

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Strategies what to do

• superimpose (on top) or juxtapose (alongside)?
• plot different versions or reductions of the data
• transform scales for easier comparison
• linear reference patterns
• backdrops of context

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Tactics details of what to do

• over() and by() options and graph combine
• kill the key or lose the legend if you can
• annotations and self-explanatory markers

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Datasets visited

• James Shorts collation from the transit of Venus
• Florence Nightingales data on deaths in the
  Crimean War
• deaths from the Titanic sinking
• Grunfeld panel data
• admissions to Berkeley
• hostility in response to insult or apology
• fluctuations in Arctic sea ice

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Original programs discussed

• catplot (SSC)
• devnplot (SSC)
• qplot (Stata Journal)
• sparkline (SSC)
• spineplot (SJ)
• stripplot (SSC)
• tabplot (SSC)

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• Categorical comparisons

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Berkeley admissions data

• A classic dataset covers admissions to six
  graduate majors by gender at UC Berkeley.
• At first sight, females were discriminated
  against.
• But there is an underlying interaction major by
  major, females generally do well, yet their
  acceptance rates are worse on more popular
  majors.
• This is an example of an amalgamation paradox
  named for E.H. Simpson (1922) but known to K.
  Pearson (18571936) and G.U. Yule (18711951).

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Berkeley data references

• The original reference was Bickel, P.J., E.A.
  Hammel and J.W. OConnell. 1975. Sex bias in
  graduate admissions Data from Berkeley. Science
  187 398404.
• The Berkeley data were discussed as an example
  for Stata in Cox, N.J. 2008. Spineplots and
  their kin. Stata Journal 8 105121.

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A simple problem?

• The structure of the data is already well known.
  The challenge is how best to present it.
• There are three categorical variables
• major (anonymously A, B, C, D, E, F)
• gender (male, female)
• decision (accept, reject)
• so the data are just 24 frequencies.

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Bar chart

• Many researchers would reach first for a bar
  chart.
• Here is a slightly non-standard example, produced
  by tabplot (SSC), which is for one-way, two-way
  or three-way bar charts.
• One feature here is showing numbers too in a
  hybrid of graph and table.
• A cosmetic detail is toning down the use of
  colour. Large blocks with strong colours are
  unsubtle.

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Mosaic plot or spineplot

• The previous bar chart omitted the frequencies.
  We can show them using a mosaic plot or
  spineplot.
• The proportions of both variables are shown,
  giving marginal and conditional distributions.
• Areas of tiles are proportional to raw
  frequencies. Departures from independence are
  easily seen.
• The program here is spineplot.

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Drilling down

• The bar chart and spineplot do a fair job of
  showing the gross breakdown with four percents.
• (Two are redundant.)
• Predictably, both would be rejected as trivial by
  many journal reviewers, but both could be useful
  for presentations.
• But clearly we need to drill down to see the
  patterns for different majors.

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More detailed bar chart

• Stacking bars is a standard strategy, but the
  result is immediately much more complicated.
• Showing all the detail does not always help.
  Focusing more sharply on the response of interest
  is a way forward.
• In general there is no need for alphabetical
  order. Here majors A to F are already ordered by
  admission rate.

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Dot chart

• Dot charts as advocated by W.S. Cleveland remain
  under-used by comparison with bar charts.
• In Stata that usually means graph dot.
• By using marker position alone, rather than bar
  length, they are less busy and thus ease more
  detailed comparison.
• Here it is easier to identify that female
  admission rates are higher for four majors and
  lower for the other two.

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Details for dot charts

• Open symbols (e.g. ? not ?) tolerate overlap much
  better than closed symbols. ? can even be
  combined with whenever nearly equal values are
  possible.
• Legends (keys) are at best a necessary evil.
  Self-explanatory or at least memorable
  symbolisation is to be prized wherever it is
  possible. Using blue for males and pink for
  females is a simple example.

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A scatter plot?

• Many statistically-minded people find the idea of
  bar charts trivial, but their practice not very
  helpful. Where is the scatter plot, they cry?
• Plotting admission rate against number of
  applicants re-introduces a crucial aspect, size
  of major. This allows identification of positive
  correlation for males and negative correlation
  for females, hence the paradox.
• This is currently my favourite plot for these
  data.

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Previously

• In an earlier version of this plot I had
  admissions versus applications, both raw
  frequencies.
• Reference lines here are lines through the origin
  such as y x and y 0.5x for 100 and 50
  admission rates.
• But it is simpler to plot admission rates. Then
  the reference lines are horizontal.

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Slogans the banal in search of the profound

• Focus as far as possible on the response or
  outcome, the variable you most want to explain.
• Linear reference patterns are good and horizontal
  patterns better.
• Omit what is unimportant and keep what is
  important.
• Even for a very simple problem, it is rare that a
  single graph meets all needs.

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• Continuous comparisons

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Hostility change

• Results of an experiment reported by Atkinson, C.
  and J. Polivy. 1976. Effects of delay, attack,
  and retaliation on state depression and
  hostility. Journal of Abnormal Psychology 85
  570576.
• Male and female subjects were made to wait and
  then either were insulted or received an apology.
  
• Half were given a chance to retaliate by
  negatively evaluating the experimenter.
• Hostility was measured before and after the
  experiment.

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Variables in hostility study

• Response
• Change in hostility, a difference of scores
  and so approximately continuous
• Predictors all binary
• Treatment insult, apology
• Gender male, female
• Retaliation allowed yes, no

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ANOVA-type problems What to plot?

• Change in hostility is adequately modelled by a
  simple linear model, using analysis of variance.
• What to plot for similar analyses is key here.
• Box plots (with medians etc.) are surprisingly
  common even when comparison of means is the
  central question.
• Plotting means with standard errors or confidence
  intervals is also common, but what about the
  detail omitted?

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devnplot (SSC)

• devnplot (SSC) is named for its emphasis on
  plotting deviations. Deviations are measured from
  any level you care to specify, but deviations
  from means are the default.
• devplot was too ugly and deviationplot too
  long.
• Quantile enthusiasts will see it as a way to plot
  ordered quantiles side by side. Compare quantile
  or qplot (SJ).

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devnplot syntax

• The syntax resembles standard modelling syntax,
  response named first and any predictors
  following.
• With one variable named we get in essence a
  quantile plot for that variable, a plot of the
  ordered values versus an implicit cumulative
  probability scale.
• The scaffolding emphasising that each value can
  be represented by a deviation from a level might
  seem redundant, but bear with me.

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Adding predictors to the syntax

• You can specify either one or two predictors.
• The result is a quantile plot for each subset,
  namely a category or combination of categories.
• An undocumented upper limit arising from a limit
  in graph is 20 subsets, but more than 20 would
  likely be too busy any way.
• A third binary predictor can be shown indirectly
  by a separate() option.

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devnplot virtues

• The display serves well in showing variation
  within subsets as well as variation between.
• Interactions can be seen.
• The scaffolding (in subtle gray) helps to tie the
  values of a group together visually.
• The separate() option is best used to highlight a
  few unusual or interesting cases.

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Waterfall plots

• Similar plots have been called waterfall plots,
  especially in clinical oncology.
• But watch out waterfall plots (or charts) have
  at least two quite different meanings elsewhere,
  in business and physical science contexts.
• Sometimes the jungle of plot names is just a
  confounded nuisance.

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James Short and the transit of Venus (1763)

• Short collated and corrected observations made by
  various astronomers during the transit of Venus
  in 1761.
• The parallax here is the angle subtended by the
  earths radius, as if viewed and measured from
  the surface of the sun.
• The data will be published and discussed in Stata
  Journal 13(3).

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Deviation plot

• A deviation plot adjusts to the differing sample
  sizes.
• Here deviations are relative to 25 trimmed means
  (otherwise known as midmeans or interquartile
  means). Boxplot fans can think that they average
  values within the box.
• The context here of careful precise measurement
  does not rule out the occasional mild or even
  strong outlier.

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Quantile plots

• Deviation plots (waterfall plots, if you prefer)
  are in essence quantile plots.
• qplot from SJ can
• superimpose through its over() option
• or juxtapose through its by() option.
• How well does that compare?

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devnplot or qplot?

• I prefer devnplot here, although qplot has useful
  options too, including flexibility over axis
  scales.
• For example, if we plot against standard normal
  quantiles, normal (Gaussian) distributions will
  follow straight lines.

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Strip plot

• An alternative display is a strip plot or dot
  plot. (Many other names exist.)
• Here it takes on the flavour of a histogram but
  with markers or point symbols for each value.
  Some binning allows stacking.
• stripplot from SSC offers an alternative to
  official Statas dotplot.

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Histograms or box plots?

• Many statistical people would start almost
  automatically with histograms or box plots for
  such data. How do they compare?
• You can judge for yourself.
• A specific problem with histograms is keeping the
  amount of scaffolding down. It is easy to lose
  valuable real estate in axis and title
  information.

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How did we do that?

• The main trick here is moving the subtitles to
  the left. It only works here because they are so
  short, but accept good fortune, however it
  comes.
• The incantation is
• subtitle(, ring(1) pos(9) nobox nobexpand)

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Box plots

• Box plots do work fairly well, but they just
  leave out too much detail for my taste.
• If the details are accessible, you can decide for
  yourself whether they are trivial.

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• Timed comparisons

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Time series

• Comparisons of time series are an especially
  rich, and especially challenging, area of
  statistical graphics.
• The widespread term spaghetti plot hints
  immediately at the difficulties.
• As always, we want to combine a grasp of general
  patterns with access to individual details.

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sparkline

• The Grunfeld data (webuse grunfeld) are a classic
  dataset in panel-based economics.
• Ten companies were monitored for 193554.
• This can be an example for sparkline (SSC).
• The name sparkline was suggested by Edward Tufte
  for intense text-like graphics. Time series are
  the most obvious example.

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Vertical and horizontal

• By default sparkline stacks small graphs
  vertically.
• If several graphs are combined, it is typical to
  cut down on axis labels and rely on differences
  in shape to convey information.
• Horizontal stacking is also supported, which can
  be useful for archaeological or environmental
  problems focused on variations with depth or
  height.

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Nightingales data

• Florence Nightingale (1820-1910) is well
  remembered for her nursing in the Crimean war and
  less so as a pioneer in data analysis.
• Her most celebrated dataset is often reproduced
  using her polar diagram, but is easier to think
  about as time series.
• Zymotic (loosely, infectious) disease mortality
  dominates other kinds, so much so that a square
  root scale helps comparison. (A logarithmic scale
  over-transforms here.)

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Sparkline?

• A sparkline display is useful to show relative
  shape, such as times of peaks.
• We see that seasonality is only part of what is
  being seen. The harsh winter of 18545 coincided
  with some of the hardest battles of the war.

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Arctic sea ice

• Another time series example concerns seasonal
  variation in Arctic sea ice for 2002-13, just 12
  annual series.
• The usual spaghetti plot shows the similarity of
  series well, but makes comparing them difficult.
  Although some people try using a key or legend,
  that rarely works well beyond a very few series.
• Separating out the series runs into the opposite
  problem.

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Combine backdrop as context

• So, use both ideas
• Plot all data as a backdrop
• (subdued, say using grayscale).
• Plot each series within its context
• (with stronger colour, thicker line).
• See for discussion Cox, N. J. 2010. Graphing
  subsets. Stata Journal 10 670681.

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• Cross-fertilisation

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Titanic data

• The Titanic sank in 1912. Statistically, we want
  to explain fraction survived in terms of age, sex
  and class of those on board.
• A standard graph is a stacked or divided bar
  graph, but it lacks punch. The command used was
  catplot (SSC).
• So, we end with something rather different,
  produced with devnplot.

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