Tag Archives: r graphics

An R Tutorial: Visual Representation of Complex Multivariate Relationships Using the R qgraph Package, Part Two Repost


This is a repost of the original article that was posted as an embedded PDF file.

 

Douglas M. Wiig
April 8, 2018
Abstract
This article is part of my series of articles exploring the use of R
packages that allow for visualization of complex relationships among variables.
Other articles have examined visual representations produced by
the qgraph package in both large and small samples with more than three
variables.  In this article I look specifically at the R qgraph package with a small
dataset of N=10, but a large number (14) of variables. Specifically, the R
qgraph.pca function is examined.

1 The Problem

In two previous blog posts I discussed some techniques for visualizing relationships
involving two or three variables and a large number of cases. In this
tutorial I will extend that discussion to show some techniques that can be used
on datasets with complex multivariate relationships involving three or more
variables.
In this post I will use a dataset called ‘Detroit.’ This data set was originally
used in the book ‘Subset selection in regression’ by Alan J. Miller published in
the Chapman and Hall series of monographs on Statistics and Applied Probability,
no. 40. It was also used in other research and appeared in appendix A
of ‘Regression analysis and its application: A data-oriented approach’ by Gunst
and Mason, Statistics textbooks and monographs no. 24, Marcel Dekker. Editor.
The Detroit dataset contains 14 variables and 10 cases. Each case represents
a year during the time period 1961-1973. The variables on which data was
collected are seen as possible predictors of homicide rate in Detroit during each
of the years studied.
These data are shown below

FTP UEMP MAN LIC GR CLEAR WM NMAN GOV HE WE HOM ACC ASR
260.35 11.0 455.5 178.15 215.98 93.4 558724. 538.1 133.9 2.98 117.18 8.60 9.17 306.18
269.80 7.0 480.2 156.41 180.48 88.5 538584. 547.6 137.6 3.09 134.02 8.90 40.27 315.16
272.04 5.2 506.1 198.02 209.57 94.4 519171. 562.8 143.6 3.23 141.68 8.52 45.31 277.53
272.96 4.3 535.8 222.10 231.67 92.0 500457. 591.0 150.3 3.33 147.98 8.89 49.51 234.07
272.51 3.5 576.0 301.92 297.65 91.0 482418. 626.1 164.3 3.46 159.85 13.0 55.05 30.84
261.34 3.2 601.7 391.22 367.62 87.4 465029. 659.8 179.5 3.60 157.19 14.57 53.90 17.99
268.89 4.1 577.3 665.56 616.54 88.3 448267. 686.2 187.5 3.73 155.29 21.36 50.62 86.11
295.99 3.9 596.9 1131.21 1029.75 86.1 432109. 699.6 195.4 2.91 131.75 28.03 51.47 91.59
319.87 3.6 613.5 837.60 786.23 79.0 416533. 729.9 210.3 4.25 178.74 31.49 49.16 20.39
341.43 7.1 569.3 794.90 713.77 73.9 401518. 757.8 223.8 4.47 178.30 37.39 45.80 23.03

The variables are as follows:
FTP – Full-time police per 100,000 population
UEMP – % unemployed in the population
MAN – number of manufacturing workers in thousands
LIC – Number of handgun licenses per 100,000 population
GR – Number of handgun registrations per 100,000 population
CLEAR – % homicides cleared by arrests
WM – Number of white males in the population
NMAN – Number of non-manufacturing workers in thousands
GOV – Number of government workers in thousands
HE – Average hourly earnings
WE – Average weekly earnings
HOM – Number of homicides per 100,000 of population
ACC – Death rate in accidents per 100,000 population
ASR – Number of assaults per 100,000 population
[J.C. Fisher ”Homicide in Detroit: The Role of Firearms”, Criminology, vol.14,
387-400 (1976)]

2 Analysis
As I have noted in previous tutorials, social science research projects often start
out with many potential independent predictor variables for a given dependent
variable. If these are all measured at the interval or ratio level, a correlation
matrix often serves as a starting point to begin analyzing relationships among
variables. In this particular case a researcher might be interested in looking at
factors that are related to total homicides. There are many R techniques to
enter data for analysis. In this case I entered the data into an Excel spreadsheet
and then loaded the file into the R environment. Install and load the following
packages:
Hmisc
stats
qgraph
readxl (only needed if importing data from Excel)

A correlation matrix can be generated using the cor function which is contained
in the stats package. To produce a matrix using all 14 variables use the
following code:
#the data file has been loaded as ’detroit’
#the file has 14 columns
#run a pearson correlation and #run a pearson correlation and put into the object ’detcor’
detcor=cor(as.matrix(detroit[c(1:14)]), method=”pearson”)
#
#round the correlation matrix to 2 decimal places for better viewing
round(detcor, 2)
#
#The resulting matrix will be displayed on the screen

Examination of the matrix shows a number of the predictors correlate with the
dependent variable ’HOM.’ There are also a large number of inter-correlations
among the predictor variables. This fact makes it difficult to make any generalizations
based on the correlation matrix only. As demonstrated in previous
tutorials, the qgraph function can be used to produce a visual representation of
the correlation matrix. Use the following code:

#basic graph with 14 vars zero order correlations
qgraph(detcor, shape=”circle”, posCol=”darkgreen”, negCol=”darkred”, layout=”spring”)

This will produce graph as seen below:

qgraphplot1

The graph displays positive correlations among variable as a green line, and
negative as a red line. The color intensity indicates the relative strength of the
correlation. While this approach provides an improvement over the raw matrix
it still rather difficult to interpret. There are many options other than those
used in the above example that allow qgraph to have a great deal of flexibility in
creating visual representation of complex relationships among variables. In the
next section I will examine one of these options that uses principal component
analysis of the data.
2.1 Using qgraph Principal Component Analysis
A discussion of the theory behind principal component exploratory analysis is
beyond the scope of this discussion. Suffice it to say that it allows for simplification
of a large number of inter-correlations by identifying factors or dimensions
that individual correlations relate to. This grouping of variables on specific factors
allows qgraph to create a visual representation of these relationships. An
excellent discussion of the theory of PCA along with R scripts can be found in
Principal Components Analysis (PCA), Steven M. Holland Department of Geology,
University of Georgia, Athens, GA, 2008.
To produce a graph using the ’detcor’ correlation matrix used above use the
following code:

#correlation matrix used is ’detcor’
#qgraph with loadings from principal components
#basic options used; many other options available
qgraph.pca(detcor, factor=3, rotation=”varimax”)
#this will yield 3 factors
This code produces the output shown below:

pcaplot

As noted above the red and green arrows indicate negative and positive loadings
on the factors, and the color intensity indicates the strength. The qgraph.pca
function produces a useful visual interpretation of the clustering of variables relative
to the three factors extracted. This would be very difficult if not impossible
with only the correlation matrix or the basic qgraph visual representation.
In a future tutorial I will explore more qgraph options that can be used to
explore the Detroit dataset as well as options for a larger datasets. In future
articles I will also explore other R packages that are also useful for analyzing
large numbers of complex variable interrelationships in very large, medium, and
small samples.
** When developing R code I strongly recommend using an IDE such as
RStudio. This is a powerful coding environment and is free for personal use as
well as being open source software. RStudio will run on a variety of platforms.
If you are developing code for future publication or sharing I would also recommend
TeXstudio, a LaTex based document development environment which is also free for personal use. This document was produced using TeXstudio 2.12.6
and RStudio 1.0.136.

 

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Ternary Diagrams Using R: An Example Using Election Outcomes


Ternary Diagrams Using R:  An Example Using Election Outcomes

A tutorial by D. M. Wiig

In part one of this tutorial I discussed creating a ternary diagram using a simple data frame that contained five hypothetical cases. In this tutorial I will expand on that foundation by creating a more informative ternary diagram using live data.

A useful application of this package in social science research is creating a visual display of parliamentary election outcomes. Specifically we can use a ternary graph to examine the distribution of seats in the British House of Commons over a period of time. Since the UK uses a proportional system to allocate seats in the House of Commons there can be a variety of outcomes in any given national election.

Since 1945 general elections in the UK have produced a division of seats among the Labour, Conservative, and various minor parties. To demonstrate how this division of seats can be shown over time data was collected for all of the general elections from the years 1945 to 2015. These data show the percentage of the popular vote won by each party and the number of seats allocated to that party based on the vote division(retrieved from http://www.ukpolitical.info).  I have created a summary table of these results as follows:

Year   Con   Lab   LD+Other   SeatsCon   SeatsLab   SeatsOther

2015  36.9  30.4      32.7                331                232                 95

2010  36.1   29         34.9                 306               258                  85

2005  35.2   32.4    32.4                 355               198                  92

2001 40.7   31.7     27.6                 412               166                   81

1997 43.2  30.7     26.1                  418               165                   76

1992  42.3 35.2     23.5                   336              271                    44

1987  42.2 30.8     27                       375             229                    48

1983  42.4  27.6    26.9                    397             209                   27

1979  43.9 36.9    15.8                     339             268                    28

1974  39.2 35.8    21.8                   319             276                     39

1974  37.1 37.9    20.1                  301             296                     38

1970  46.4   43       8.6                   330             287                    19

1966  47.9 41.9     8.5                   363             253                     25

1964  44.1 53.4   11.2                  317             304                   22

1959  49.4  43.8    5.9                    365           258                    19

1955  49.7  46.4       0                     344            277                   18

1951  48    48.8        2.5                 321            295                   18

1950  46.1 43.5       9.1                315             297                   22

1945  47.8 39.8         1                  393            213                    57

The UK has a two party dominant system with a number of minor parties that regularly contest elections. As indicated above, a proportional representation method of allocating seats is used so these minor parties are able to gain some representation in the Commons. For readers interested in learning more about political parties in the UK there are a number of resources readily available at various online and other sources.

For purposes of this example I have added the popular vote of all minor parties together in the ‘LD+Other’ column, and the number of seats gained in the ‘SeatsOther’ column. By plotting the three variables ‘SeatsCon’, ‘SeatsLab’, and ‘SeatsOther’ by year on a ternary diagram we can visualize any changes in the mixture of seats won for the three groups. Before working through this tutorial make sure that you have the ggplot, ggplot2, and ggtern packages loaded into your R environment.

I originally created the table shown above using Excel and then imported it into R studio for analysis. If you are not using R studio you can enter the data via the R data editor as shown in the previous tutorial, or put the data into an Excel or LibreOffice spreadsheet and import it into R using the read.spss() function that I have discussed in earlier tutorials. You can also use any other method that you are familiar with to get the data into your R environment.

Once the data set is loaded use the following code to create the ternary diagram. Note that in this diagram we are using the base code as shown in the first tutorial with some additions that make the diagram easier to interpret such as the vector arrows and legend. The code segment is:

################################################### #create ternary plot using seats allocated by party for each election #uses enhanced formatting for easier interpretation #results of #ggtern function are placed in ‘plot for rendering ################################################### plot <- ggtern(data = ukvotedata, aes(x = SeatsCon, y = SeatsLab, z = SeatsOther)) +geom_point(aes(fill = Year), size = 4, shape = 21, color = “black”) + ggtitle(“Proportion of Seats Won 1945-2015”) + labs(fill = “Year”) + theme_rgbw() + theme(legend.position = c(0,1), legend.justification = c(0, 1)) ###################################################

To show the diagram simply use:

################################################### #now plot the diagram ################################################### plot ###################################################

The resulting ternary diagram is:

ukfinalplot

Each point on the graph represent the relative division of seats for each of the 19 elections in the table. The shading represents the year with the darkest being 1945 and the lightest 2015. The diagram clearly shows the trend toward more minor party representation and a move away from the two major parties over time. Indeed coalition governments resulted in several of the more recent elections due to the increase in minor party influence.

My purpose here is not to discuss UK politics but to show how ternary diagrams can be used in a social science application. With the many additions and extensions that are being added to the ggtern package it can be a very power device for graphical analysis.