# R Tutorial: Visualizing Multivariate Relationships in Large Datasets

R Tutorial: Visualizing multivariate relationships in Large Datasets

A tutorial by D.M. Wiig

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 large datasets and complex multivariate relationships involving three or more variables.

In this tutorial I will use the R package nmle which contains the dataset MathAchieve. Use the code below to install the package and load it into the R environment:

####################################################
#code for visual large dataset MathAchieve
#first show 3d scatterplot; then show tableplot variations
####################################################
install.packages(“nmle”) #install nmle package
library(nlme) #load the package into the R environment
####################################################

Once the package is installed take a look at the structure of the data set by using:

####################################################
attach(MathAchieve) #take a look at the structure of the dataset
str(MathAchieve)
####################################################

Classes ‘nfnGroupedData’, ‘nfGroupedData’, ‘groupedData’ and ‘data.frame’: 7185 obs. of 6 variables:
\$ School : Ord.factor w/ 160 levels “8367”<“8854″<..: 59 59 59 59 59 59 59 59 59 59 …
\$ Minority: Factor w/ 2 levels “No”,”Yes”: 1 1 1 1 1 1 1 1 1 1 …
\$ Sex : Factor w/ 2 levels “Male”,”Female”: 2 2 1 1 1 1 2 1 2 1 …
\$ SES : num -1.528 -0.588 -0.528 -0.668 -0.158 …
\$ MathAch : num 5.88 19.71 20.35 8.78 17.9 …
\$ MEANSES : num -0.428 -0.428 -0.428 -0.428 -0.428 -0.428 -0.428 -0.428 -0.428 -0.428 …
– attr(*, “formula”)=Class ‘formula’ language MathAch ~ SES | School
.. ..- attr(*, “.Environment”)=<environment: R_GlobalEnv>
– attr(*, “labels”)=List of 2
..\$ y: chr “Mathematics Achievement score”
..\$ x: chr “Socio-economic score”
– attr(*, “FUN”)=function (x)
..- attr(*, “source”)= chr “function (x) max(x, na.rm = TRUE)”
– attr(*, “order.groups”)= logi TRUE
>

As can be seen from the output shown above the MathAchieve dataset consists of 7185 observations and six variables. Three of these variables are numeric and three are factors. This presents some difficulties when visualizing the data. With over 7000 cases a two-dimensional scatterplot showing bivariate correlations among the three numeric variables is of limited utility.

We can use a 3D scatterplot and a linear regression model to more clearly visualize and examine relationships among the three numeric variables. The variable SES is a vector measuring socio-economic status, MathAch is a numeric vector measuring mathematics achievment scores, and MEANSES is a vector measuring the mean SES for the school attended by each student in the sample.

We can look at the correlation matrix of these 3 variables to get a sense of the relationships among the variables:

> ####################################################
> #do a correlation matrix with the 3 numeric vars;
> ###################################################
> data(“MathAchieve”)
> cor(as.matrix(MathAchieve[c(4,5,6)]), method=”pearson”)

SES MathAch MEANSES
SES 1.0000000 0.3607556 0.5306221
MathAch 0.3607556 1.0000000 0.3437221
MEANSES 0.5306221 0.3437221 1.0000000

In using the cor() function as seen above we can determine the variables used by specifying the column that each numeric variable is in as shown in the output from the str() function.  The 3 numeric variables, for example, are in columns 4, 5, and 6 of the matrix.

As discussed in previous tutorials we can visualize the relationship among these three variable by using a 3D scatterplot. Use the code as seen below:

####################################################
#install.packages(“nlme”)
install.packages(“scatterplot3d”)
library(scatterplot3d)
library(nlme) #load nmle package
attach(MathAchieve) #MathAchive dataset is in environment
scatterplot3d(SES, MEANSES, MathAch, main=”Basic 3D Scatterplot”) #do the plot with default options
####################################################

The resulting plot is:

Even though the scatter plot lacks detail due to the large sample size it is still possible to see the moderate correlations shown in the correlation matrix by noting the shape and direction of the data points  .  A regression plane can be calculated and added to the plot using the following code:

scatterplot3d(SES, MEANSES, MathAch, main=”Basic 3D Scatterplot”) #do the plot with default options
####################################################
##use a linear regression model to plot a regression plane
#y=MathAchieve, SES, MEANSES are predictor variables
####################################################
model1=lm(MathAch ~ SES + MEANSES)    ## generate a regression
#take a look at the regression output
summary(model1)
#run scatterplot again putting results in model
model <- scatterplot3d(SES, MEANSES, MathAch, main=”Basic 3D Scatterplot”)     #do the plot with default options
#link the scatterplot and linear model using the plane3d function
model\$plane3d(model1)        ## link the 3d scatterplot in ‘model’ to the ‘plane3d’ option with ‘model1’ regression information
####################################################

The resulting output is seen below:

Call:
lm(formula = MathAch ~ SES + MEANSES)

Residuals:
Min 1Q Median 3Q Max
-20.4242 -4.6365 0.1403 4.8534 17.0496

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.72590 0.07429 171.31 <2e-16 ***
SES 2.19115 0.11244 19.49 <2e-16 ***
MEANSES 3.52571 0.21190 16.64 <2e-16 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.296 on 7182 degrees of freedom
Multiple R-squared: 0.1624, Adjusted R-squared: 0.1622
F-statistic: 696.4 on 2 and 7182 DF, p-value: < 2.2e-16

and the plot with the plane is:

While the above analysis gives us useful information, it is limited by the mixture of numeric values and factors.  A more detailed visual analysis that will allow the display and comparison of all six of the variables is possible by using the functions available in the R package Tableplots.   This package was created to aid in the visualization and inspection of large datasets with multiple variables.

The MathAchieve contains a total of six variables and 7185 cases.  The Tableplots package can be used with datasets larger than 10,000 observations and up to 12 or so variables. It can be used visualize relationships among variables using the same measurement scale or mixed measurement types.

To look at a comparisons of each data type and then view all 6 together begin with the following:

####################################################
attach(MathAchieve) #attach the dataset
#set up 3 data frames with numeric, factors, and mixed
####################################################
mathmix <- data.frame(SES,MathAch,MEANSES,School=factor(School),Minority=factor(Minority),Sex=factor(Sex)) #all 6 vars
mathfact <- data.frame(School=factor(School),Minority=factor(Minority),Sex=factor(Sex)) #3 factor vars
mathnum <- data.frame(SES,MathAch,MEANSES) #3 numeric vars
####################################################

To view a comparison of the 3 numeric variables use:

####################################################
require(tabplot) #load tabplot package
tableplot(mathnum) #generate a table plot with numeric vars only
####################################################

resulting in the following output:

To view only the 3 factor variables use:

####################################################
require(tabplot)   #load tabplot package
tableplot(mathfact)    #generate a table plot with factors only
####################################################

Resulting in:

To view and compare table plots of all six variables use:

####################################################
require(tabplot)    #load tabplot package
tableplot(mathmix)    #generate a table plot with all six variables
####################################################

Resulting in:

Using tableplots is useful in visualizing relationships among a set of variabes. The fact that comparisons can be made using mixed levels of measurement and very large sample sizes provides a tool that the researcher can use for initial exploratory data analysis.

The above visual table comparisons agree with the moderate correlation among the three numeric variables found in the correlation and regression models discussed above.  It is also possible to add some additional interpretation by viewing and comparing the mix of both factor and numeric variables.

In this tutorial I have provided a very basic introduction to the use of table plots in visualizing data. Interested readers can find an abundance of information about Tableplot options and interpretations in the CRAN documentation.

In my next tutorial I will continue a discussion of methods to visualize large and complex datasets by looking at some techniques that allow exploration of very large datasets and up to 12 variables or more.

# R For Beginners: Basic Graphics Code to Produce Informative Graphs, Part Two, Working With Big Data

R for beginners: Some basic graphics code to produce informative graphs, part two, working with big data

A tutorial by D. M. Wiig

In part one of this tutorial I discussed the use of R code to produce 3d scatterplots. This is a useful way to produce visual results of multi- variate linear regression models. While visual displays using scatterplots is a useful tool when using most datasets it becomes much more of a challenge when analyzing big data. These types of databases can contain tens of thousands or even millions of cases and hundreds of variables.

Working with these types of data sets involves a number of challenges. If a researcher is interested in using visual presentations such as scatterplots this can be a daunting task. I will start by discussing how scatterplots can be used to provide meaningful visual representation of the relationship between two variables in a simple bivariate model.

To start I will construct a theoretical data set that consists of ten thousand x and y pairs of observations. One method that can be used to accomplish this is to use the R rnorm() function to generate a set of random integers with a specified mean and standard deviation. I will use this function to generate both the x and y variable.

Before starting this tutorial make sure that R is running and that the datasets, LSD, and stats packages have been installed. Use the following code to generate the x and y values such that the mean of x= 10 with a standard deviation of 7, and the mean of y=7 with a standard deviation of 3:

###### ############################################## ## make sure package LSD is loaded ## library(LSD) x <- rnorm(50000, mean=10, sd=15)   # # generates x values #stores results in variable x y <- rnorm(50000, mean=7, sd=3)    ## generates y values #stores results in variable y ####################################################

Now the scatterplot can be created using the code:

###### ############################################## ## plot randomly generated x and y values ## plot(x,y, main=”Scatterplot of 50,000 points”) ####################################################

As can be seen the resulting plot is mostly a mass of black with relatively few individual x and y points shown other than the outliers.  We can do a quick histogram on the x values and the y values to check the normality of the resulting distribution. This shown in the code below:
####################################################
## show histogram of x and y distribution
####################################################
hist(x)   ## histogram for x mean=10; sd=15; n=50,000
##
hist(y)   ## histogram for y mean=7; sd=3; n-50,000
####################################################

The histogram shows a normal distribution for both variables. As is expected, in the x vs. y scatterplot the center mass of points is located at the x = 10; y=7 coordinate of the graph as this coordinate contains the mean of each distribution. A more meaningful scatterplot of the dataset can be generated using a the R functions smoothScatter() and heatscatter(). The smoothScatter() function is located in the graphics package and the heatscatter() function is located in the LSD package.

The smoothScatter() function creates a smoothed color density representation of a scatterplot. This allows for a better visual representation of the density of individual values for the x and y pairs. To use the smoothScatter() function with the large dataset created above use the following code:

###### ############################################## ## use smoothScatter function to visualize the scatterplot of #50,000 x ## and y values ## the x and y values should still be in the workspace as #created  above with the rnorm() function ## smoothScatter(x, y, main = “Smoothed Color Density Representation of 50,000 (x,y) Coordinates”) ## ####################################################

The resulting plot shows several bands of density surrounding the coordinates x=10, y=7 which are the means of the two distributions rather than an indistinguishable mass of dark points.

Similar results can be obtained using the heatscatter() function. This function produces a similar visual based on densities that are represented as color bands. As indicated above, the LSD package should be installed and loaded to access the heatscatter() function. The resulting code is:

###### ############################################## ## produce a heatscatter plot of x and y ## library(LSD) heatscatter(x,y, main=”Heat Color Density Representation of 50,000 (x, y) Coordinates”) ## function heatscatter() with #n=50,000 ####################################################

In comparing this plot with the smoothScatter() plot one can more clearly see the distinctive density bands surrounding the coordinates x=10, y=7. You may also notice depending on the computer you are using that there is a noticeably longer processing time required to produce the heatscatter() plot.

This tutorial has hopefully provided some useful information relative to visual displays of large data sets. In the next segment I will discuss how these techniques can be used on a live database containing millions of cases.

# R for Beginners: Some Simple Code to Produce Informative Graphs, Part One

A Tutorial by D. M. Wiig

The R programming language has a multitude of packages that can be used to display various types of graph. For a new user looking to display data in a meaningful way graphing functions can look very intimidating. When using a statistics package such as SPSS, Stata, Minitab or even some of the R Gui’s such R Commander sophisticated graphs can be produced but with a limited range of options. When using the R command line to produce graphics output the user has virtually 100 percent control over every aspect of the graphics output.

For new R users there are some basic commands that can be used that are easy to understand and offer a large degree of control over customisation of the graphical output. In part one of this tutorial I will discuss some R scripts that can be used to show typical output from a basic correlation and regression analysis.

For the first example I will use one of the datasets from the R MASS dataset package. The dataset is ‘UScrime´ which contains data on certain factors and their relationship to violent crime. In the first example I will produce a simple scatter plot using the variables ‘GDP’ as the independent variable and ´crimerate´ the dependent variable which is represented by the letter ‘y’ in the dataset.

Before starting on this project install and load the R package ‘MASS.’ Other needed packages are loaded when R is started. The scatter plot is produced using the following code:

####################################################
### make sure that the MASS package is installed
###################################################
library(MASS)   ## load MASS
attach(UScrime)   ## use the UScrime dataset
## plot the two dimensional scatterplot and add appropriate #labels
#
plot(GDP, y,
main=”Basic Scatterplot of Crime Rate vs. GDP”,
xlab=”GDP”,
ylab=”Crime Rate”)
#
####################################################

The above code produces a two-dimensional plot of GDP vs. Crimerate. A regression line can be added to the graph produced by including the following code:

####################################################
## add a regression line to the scatter plot by using simple bivariate #linear model
## lm generates the coefficients for the regression model.extract
## col sets color; lwd sets line width; lty sets line type
#
abline(lm(y ~ GDP), col=”red”, lwd=2, lty=1)
#
####################################################

As is often the case in behavioral research we want to evaluate models that involve more than two variables. For multivariate models scatter plots can be generated using a 3 dimensional version of the R plot() function. For the above model we can add a third variable ‘Ineq’ from the dataset which is a measure the distribution of wealth in the population. Since we are now working with a multivariate linear model of the form ‘y = b1(x1) + b2(x2) + a’ we can use the R function scatterplot3d() to generate a 3 dimensional representation of the variables.

Once again we use the MASS package and the dataset  ‘UScrime’ for the graph data. The code is seen below:

####################################################
## create a 3d graph using the variables y, GDP, and Ineq
####################################################
#
library(scatterplot3d)   ##load scatterplot3d function
require(MASS)
attach(UScrime)   ## use data from UScrime dataset
scatterplot3d(y,GDP, Ineq,
main=”Basic 3D Scatterplot”) ## graph 3 variables, y
#
###################################################

The following graph is produced:

The above code will generate a basic 3d plot using default values. We can add straight lines from the plane of the graph to each of the data points by setting the graph type option as ‘type=”h”, as seen in the code below:

###### ##############################################

require(MASS)
library(scatterplot3d)
attach(UScrime)
model <- scatterplot3d(GDP, Ineq, y,
type=”h”, ## add vertical lines from plane with this option
main=”3D Scatterplot with Vertical Lines”)
####################################################

This results in the graph:

There are numerous options that can be used to go beyond the basic 3d plot. Refer to CRAN documentation to see these. A final addition to the 3d plot as discussed here is the code needed to generate the regression plane of our linear regression model using the y (crimerate), GDP, and Ineq variables. This is accomplished using the plane3d() option that will draw a plane through the data points of the existing plot. The code to do this is shown below:

###### ##############################################require(MASS)library(scatterplot3d)attach(UScrime)model <- scatterplot3d(GDP, Ineq, y, type=”h”,   ## add vertical line from plane to data points with this #option main=”3D Scatterplot with Vertical Lines”)## now calculate and add the linear regression datamodel1 <- lm(y ~ GDP + Ineq)   #model\$plane3d(model1)   ## link the 3d scatterplot in ‘model’ to the ‘plane3d’ option with ‘model1’ regression information # ####################################################

The resulting graph is:

To draw a regression plane through the data points only change the ‘type’ option to ‘type=”p” to show the data points without vertical lines to the plane. There are also many other options that can be used. See the CRAN documentation to review them.

I have hopefully shown that relatively simple R code can be used to generate some informative and useful graphs. Once you start to become aware of how to use the multitude of options for these functions you can have virtually total control of the visual presentation of data. I will discuss some additional simple graphs in the next tutorial that I post.

# R For Beginners: Some Simple R Code to do Common Statistical Procedures, Part Two

An R tutorial by D. M. Wiig

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# R For Beginners: Basic R Code for Common Statistical Procedures Part I

An R tutorial by D. M. Wiig

This section gives examples of code to perform some of the most common elementary statistical procedures. All code segments assume that the package ‘car’ has been loaded and the file ‘Freedman’ has been loaded as the active dataset. Use the menu from the R console to load the ’car’ dataset or use the following command line to access the CRAN site list and packages:

install.packages()

Once the ’car’ package has been downloaded and installed use the following command to make it the active library.

require(car)

Load the ‘Freedman’ data file from the dataset ‘car’

data(Freedman, package="car")

List basic descriptives of the variables:

summary(Freedman)

Perform a correlation between two variables using Pearson, Kendall or Spearman’s correlation:

cor(filename[,c("var1","var2")], use="complete.obs", method="pearson")

cor(filename[,c("var1","var2")], use="complete.obs", method="spearman")

cor(filename[,c("var1","var2")], use="complete.obs", method="kendall")

Example:

cor(Freedman[,c("crime","density")], use="complete.obs", method="pearson")

cor(Freedman[,c("crime","density")], use="complete.obs", method="kendall")

cor(Freedman[,c("crime","density")], use="complete.obs", method="spearman")

In the next post I will discuss basic code to produce multiple correlations and linear regression analysis.  See other tutorials on this blog for more R code examples for basic statistical analysis.

# R Video Tutorial: Basic R Code to Load a Data File and Produce a Histogram

R For Beginners:  Some Simple R Code to Load a Data File and Produce a Histogram

A tutorial by D. M. Wiig

I have found that a good method for learning how to write R code is to examine complete code segments written to perform specific tasks and to modify these procedures to fit your specific needs. Trying to master R code in the abstract by reading a book or manual can be informative but is more often confusing.  Observing what various code segments do by observing the results allows you to learn with hands-on additions and modifications as needed for your purposes.

In this document I have included a short video tutorial that discusses  loading a dataset from the R library, examining the contents of the dataset and selecting one of the variables to examine using a basic histogram.  I have included an annotated code chunk of the procedures discussed in the video.

The video appears below with the code segment following.

Here is the annotated code used in the video:

# R For Beginners: Installing the JGR GUI On a Linux Platform

A Tutorial by D. M. Wiig

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Watch for more tutorials discussing  R statistics on a Linux platform.

# R for Beginners: Using R Commander for Basic t Tests and One Way ANOVA

R for Beginners:  Using R Commander for Basic t Tests and One Way ANOVA

A tutorial by D. M. Wiig

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I hope that you found this tutorial informative.  Stop back by to check for new installments.  I have many currently in the writing stage.

# R for Beginners: Using R Commander, Graphing and Correlation

A tutorial by Douglas M. Wiig

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# R for Beginners: Installing and Using the R Commander GUI, Part One

A tutorial by D.M. Wiig

This tutorial is posted as an embedded Word document.  To view the document full screen click on the button in the lower right corner of the window. Please note that you must be online for the full page Word document display to work.