Continuous Variables
Two Variables
A typical scatterplot visualizes the relationship of two continuous
variables, here Years worked at a company, and annual
Salary. Following is the function call to Plot()
for the default visualization.
Because d is the default name of the data frame that
contains the variables for analysis, the data parameter
that names the input data frame need not be specified. That is, no need
to specify data=d, though this parameter can be explicitly
included in the function call if desired.
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, fill="skyblue") # interior fill color of points
## Plot(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
Enhance the default scatterplot with parameter enhance.
The visualization includes the mean of each variable indicated by the
respective line through the scatterplot, the 95% confidence ellipse,
labeled outliers, least-squares regression line with 95% confidence
interval, and the corresponding regression line with the outliers
removed.
Plot(Years, Salary, enhance=TRUE)
## [Ellipse with Murdoch and Chow's function ellipse from their ellipse package]
##
## >>> Suggestions
## Plot(Years, Salary, color="red") # exterior edge color of points
## Plot(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
## >>> Outlier analysis with Mahalanobis Distance
##
## MD ID
## ----- -----
## 8.14 Correll, Trevon
## 7.84 Capelle, Adam
##
## 5.63 Korhalkar, Jessica
## 5.58 James, Leslie
## 3.75 Hoang, Binh
## ... ...
A variety of fit lines can be plotted. The available values:
"loess" for general non-linear fit, "lm" for
linear least squares, "null" for the null (flat line)
model, "exp" for the exponential growth and decay,
"quad" for the quadratic model, and power for
the general power beyond 2. Setting fit to
TRUE plots the "loess" line. With the value of
power, specify the value of the root with parameter
fit_power.
Here, plot the general non-linear fit. For emphasis set
plot_errors to TRUE to plot the residuals from
the line. The sum of the squared errors is displayed to facilitate the
comparison of different models.
Plot(Years, Salary, fit="loess", plot_errors=TRUE)
##
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, color="red") # exterior edge color of points
## Plot(Years, Salary, MD_cut=6) # label Mahalanobis dist > 6 as outliers
##
## Fit: Mean Squared Error, MSE = 100,834,065
##
Next, plot the exponential fit and show the residuals from the
exponential curve. These data are approximately linear so the
exponential curve does not vary far from a straight line. The function
displays the corresponding sum of squared errors to assist in comparing
various models to each other.
Plot(Years, Salary, fit="exp", plot_errors=TRUE)
##
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, color="red") # exterior edge color of points
## Plot(Years, Salary, MD_cut=6) # label Mahalanobis dist > 6 as outliers
##
## Regression of linearized data by transforming the data values with log()
## Need back transformation exp() of regression model to compute predicted values
##
## Line: b0 = 10.777 b1 = 0.041 Fit: MSE = 128,210,353 Rsq = 0.722
##
The parameter transforms the y variable to the specified
power from the default of 1 before doing the regression
analysis. The availability of this parameter provides for a wide range
of modifications to the underlying functional form of the fit curve.
Three Variables
Map a continuous variable, such as Pre, to the plotted
points with the size parameter, a bubble plot.
Plot(Years, Salary, size=Pre)
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, fill="skyblue") # interior fill color of points
## Plot(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(Years, Salary, out_cut=.10) # label top 10% from center as outliers
## Plot(x=Years, y=Salary, size=Pre, radius=0.18) # larger bubbles
##
## >>> Pearson's product-moment correlation
##
## Years: Time of Company Employment
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 36
## Sample Correlation of Years and Salary: r = 0.852
##
## Hypothesis Test of 0 Correlation: t = 9.501, df = 34, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.727 to 0.923
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## radius: 0.12 size of largest bubble
## power: 0.50 relative bubble sizes
Indicate multiple variables to plot along either axis with a vector
defined according to the base R function c(). Plot the
linear model for each variable according to the fit
parameter set to "lm". By default, when multiple lines are
plotted on the same panel, the confidence interval is turned off by
internally setting the parameter fit_se set to
0. Explicitly override this parameter value as needed.
Plot(c(Pre, Post), Salary, fit="lm", fit_se=0)
##
## >>> Suggestions
## Plot(c(Pre, Post), Salary, enhance=TRUE) # many options
## Plot(c(Pre, Post), Salary, fill="skyblue") # interior fill color of points
## Plot(c(Pre, Post), Salary, MD_cut=6) # label Mahalanobis dist > 6 as outliers
##
##
## Variable: Pre with Salary
##
## >>> Pearson's product-moment correlation
##
## Pre: Test score on legal issues before instruction
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 37
## Sample Correlation of Pre and Salary: r = -0.007
##
## Hypothesis Test of 0 Correlation: t = -0.043, df = 35, p-value = 0.966
## 95% Confidence Interval for Correlation: -0.330 to 0.318
##
##
## Variable: Post with Salary
##
## >>> Pearson's product-moment correlation
##
## Post: Test score on legal issues after instruction
## Salary: Annual Salary (USD)
##
## Number of paired values with neither missing, n = 37
## Sample Correlation of Post and Salary: r = -0.070
##
## Hypothesis Test of 0 Correlation: t = -0.416, df = 35, p-value = 0.680
## 95% Confidence Interval for Correlation: -0.385 to 0.260
Scatterplot Matrix
Multiple variables for the first parameter value, x, and
no values for y, plot as a scatterplot matrix. Pass a
single vector, such as defined by c(). Request the
non-linear fit line and corresponding confidence interval by specifying
TRUE or loess for the fit
parameter. Request a linear fit line with the value of
"lm".
Plot(c(Salary, Years, Pre, Post), fit="lm")
Smoothed and Binned Scatterplots
Smoothing and binning are two procedures for visualizing a
relationship with many data values.
To obtain a larger data set, in this example generate random data
with base R rnorm(), then plot. Plot() first
checks the presence of the specified variables in the global environment
(workspace). If not there, then from a data frame, of which the default
value is d. Here, randomly generate values from normal
populations for x and y in the workspace.
set.seed(13)
x=rnorm(4000)
y= 8*x + rnorm(4000,1, 30)
Plot(x, y)
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
## >>> Suggestions
## Plot(x, y, enhance=TRUE) # many options
## Plot(x, y, color="red") # exterior edge color of points
## Plot(x, y, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(x, y, out_cut=.10) # label top 10% from center as outliers
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
With large data sets, even for continuous variables there can be much
over-plotting of points. One strategy to address this issue smooths the
scatterplot by turning on the smooth parameter. The
individual points superimposed on the smoothed plot are potential
outliers. The default number of plotted outliers is 100. Turn off the
plotting of outliers completely by setting parameter
smooth_points to 0. Show the linear trend with
fit set to "lm".
Plot(x, y, smooth=TRUE, fit="lm")
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## >>> Suggestions
## Plot(x, y, enhance=TRUE) # many options
## Plot(x, y, fill="skyblue") # interior fill color of points
## Plot(x, y, MD_cut=6) # label Mahalanobis dist > 6 as outliers
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
##
## Line: b0 = 1.030687568 b1 = 7.919636637 Fit: MSE = 917.031808 Rsq = 0.063
##
Another strategy for alleviating over-plotting makes the fill color
mostly transparent with the trans parameter, or turn off
completely by setting fill to "off". The
closer the value of trans is to 1, the more transparent is
the fill.
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
## >>> Suggestions
## Plot(x, y, enhance=TRUE) # many options
## Plot(x, y, color="red") # exterior edge color of points
## Plot(x, y, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(x, y, MD_cut=6) # label Mahalanobis dist > 6 as outliers
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 4000
## Sample Correlation of x and y: r = 0.251
##
## Hypothesis Test of 0 Correlation: t = 16.397, df = 3998, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.222 to 0.280
Another way to visualize a relationship when there are many data
points is to bin the x-axis. Specify the number of bins with
parameter n_bins. Plot() then computes the mean of
y for each bin and connects the means by line segments. This
procedure plots the conditional means by default without any assumption
of form such as linearity. Specify the stat parameter for
median to compute the median of y for each bin. The
standard Plot() parameters fill,
color, size and segments also
apply.
## >>> Note: x is not in a data frame (table)
## >>> Note: y is not in a data frame (table)
##
## Table: Summary Stats
##
## x y
## ------- ------- ---------
## n 4000 4000
## n.miss 0 0
## min -3.239 -104.740
## max 3.589 112.460
## mean -0.003 1.006
##
##
## Table: mean of y for levels of x
##
## bin n midpt mean
## --- ---------------- ----- ------- --------
## 1 [-3.246,-1.873] 116 -2.560 -16.734
## 2 (-1.873,-0.508] 1090 -1.191 -5.699
## 3 (-0.508,0.858] 2001 0.175 0.848
## 4 (0.858,2.223] 743 1.541 12.374
## 5 (2.223,3.596] 50 2.909 25.696
One Variable
The default plot for a single continuous variable includes not only
the scatterplot, but also the superimposed violin plot and box plot,
with outliers identified. Call this plot the VBS plot.
## [Violin/Box/Scatterplot graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## --- Salary ---
## Present: 37
## Missing: 0
## Total : 37
##
## Mean : 73795.557
## Stnd Dev : 21799.533
## IQR : 31012.560
## Skew : 0.190 [medcouple, -1 to 1]
##
## Minimum : 46124.970
## Lower Whisker: 46124.970
## 1st Quartile : 56772.950
## Median : 69547.600
## 3rd Quartile : 87785.510
## Upper Whisker: 122563.380
## Maximum : 134419.230
##
##
## (Box plot) Outliers: 1
##
## Small Large
## ----- -----
## Correll, Trevon 134419.23
##
## Number of duplicated values: 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.61 size of plotted points
## out_size: 0.82 size of plotted outlier points
## jitter_y: 0.45 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
Control the choice of the three superimposed plots – violin, box, and
scatter – with the vbs_plot parameter. The default setting
is "vbs" for all three plots. Here, for example, obtain
just the box plot. Or, use the alias BoxPlot() in place of
Plot().
Plot(Salary, vbs_plot="b")
## [Violin/Box/Scatterplot graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## --- Salary ---
## Present: 37
## Missing: 0
## Total : 37
##
## Mean : 73795.557
## Stnd Dev : 21799.533
## IQR : 31012.560
## Skew : 0.190 [medcouple, -1 to 1]
##
## Minimum : 46124.970
## Lower Whisker: 46124.970
## 1st Quartile : 56772.950
## Median : 69547.600
## 3rd Quartile : 87785.510
## Upper Whisker: 122563.380
## Maximum : 134419.230
##
##
## (Box plot) Outliers: 1
##
## Small Large
## ----- -----
## Correll, Trevon 134419.23
##
## Number of duplicated values: 0
Cleveland Dot Plot
Create a Cleveland dot plot when one of the variables has unique (ID)
values. In this example, for a single variable, row names are on the
y-axis. The default plots sorts by the value plotted with the default
value of parameter sort_yx of "+" for an
ascending plot. Set to "-" for a descending plot and
"0" for no sorting.
## >>> Suggestions
## Plot(Salary, y=row_names, sort_yx=FALSE, segments_y=FALSE)
##
##
## --- Salary ---
##
## n miss mean sd min mdn max
## 37 0 73795.6 21799.5 46125.0 69547.6 134419.2
##
##
## (Box plot) Outliers: 1
##
## Small Large
## ----- -----
## 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
The standard scatterplot version of a Cleveland dot plot follows,
with no sorting and no line segments.
Plot(Salary, row_names, sort_yx="0", segments_y=FALSE)
## >>> Suggestions
##
##
## --- Salary ---
##
## n miss mean sd min mdn max
## 37 0 73795.6 21799.5 46125.0 69547.6 134419.2
##
##
## (Box plot) Outliers: 1
##
## Small Large
## ----- -----
## 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
This Cleveland dot plot has two x-variables, indicated as a standard
R vector with the c() function. In this situation, the two
points on each row are connected with a line segment. By default the
rows are sorted by distance between the successive points.
Plot(c(Pre, Post), row_names)
## >>> Suggestions
## Plot(c(Pre, Post), y=row_names, sort_yx=FALSE, segments_y=FALSE)
##
##
## --- Pre ---
##
## n miss mean sd min mdn max
## 37 0 78.8 12.0 59.0 80.0 100.0
##
##
## --- Post ---
##
## n miss mean sd min mdn max
## 37 0 81.0 11.6 59.0 84.0 100.0
##
## No (Box plot) outliers
##
## n diff Row
## ---------------------------
## 1 -4.0 Gvakharia, Kimberly
## 2 -4.0 Downs, Deborah
## 3 -3.0 Anderson, David
## 4 -3.0 Correll, Trevon
## 5 -3.0 Kralik, Laura
## 6 -3.0 Jones, Alissa
## 7 -2.0 Capelle, Adam
## 8 -2.0 Stanley, Emma
## 9 -2.0 Adib, Hassan
## 10 -2.0 Skrotzki, Sara
## 27 5.0 Bellingar, Samantha
## 28 6.0 LaRoe, Maria
## 29 7.0 Cassinelli, Anastis
## 30 7.0 Hamide, Bita
## 31 7.0 Sheppard, Cory
## 32 8.0 Campagna, Justin
## 33 10.0 Ritchie, Darnell
## 34 12.0 Anastasiou, Crystal
## 35 12.0 Wu, James
## 36 13.0 Korhalkar, Jessica
## 37 13.0 Cooper, Lindsay
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #4398D0 #B28B2A filled color of the points
## color: #4398D0 #B28B2A edge color of the points
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
Categorical and Continuous Variables
A mixture of categorical and continuous variables can be plotted a
variety of ways, as illustrated below.
Two Continuous, One Categorical
Plot a scatterplot of two continuous variables for each level of a
categorical variable on the same panel with the by
parameter. Here, plot Years and Salary each for the
two levels of Gender in the data. Colors and geometric plot
shapes can distinguish between the plots. For all variables except an
ordered factor, the default plots according to the default qualitative
color palette, "hues", with the geometric shape of a
point.
Plot(Years, Salary, by=Gender)
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, fill="skyblue") # interior fill color of points
## Plot(Years, Salary, fit="lm", fit_se=c(.90,.99)) # fit line, stnd errors
## Plot(Years, Salary, out_cut=.10) # label top 10% from center as outliers
Change the plot colors with the fill (interior) and
color (exterior or edge) parameters. Because there are two
levels of the by variable, specify two fill colors and two
edge colors each with an R vector defined by the c()
function. Also, include the regression line for each group with the
fit parameter and increase the size of the plotted points
with the size parameter.
Plot(Years, Salary, by=Gender, size=2, fit="lm",
fill=c("olivedrab3", "gold1"),
color=c("darkgreen", "gold4")
)
##
## >>> Suggestions
## Plot(Years, Salary, enhance=TRUE) # many options
## Plot(Years, Salary, out_cut=.10) # label top 10% from center as outliers
##
## Gender: M Line: b0 = 30842.335 b1 = 4047.307 Fit: MSE = 107,647,877 Rsq = 0.819
##
## Gender: W Line: b0 = 47109.787 b1 = 2882.272 Fit: MSE = 144,700,625 Rsq = 0.598
##
Change the plotted shapes with the shape parameter. The
default value is "circle" with both an exterior color and
filled interior, specified with "color" and
"fill". Other possible values, with fillable interiors, are
"circle", "square", "diamond",
"triup" (triangle up), and "tridown" (triangle
down). Other possible values include all uppercase and lowercase
letters, all digits, and most punctuation characters. The numbers 0
through 25 defined by the R points() function also apply.
If plotting levels according to by, then list one shape for
each level to be plotted.
A Trellis (facet) plot creates a separate panel for the plot of each
level of the categorical variable. Generate Trellis plots with the
by1 parameter. In this example, plot the best-fit linear
model for the data in each panel according to the fit
parameter. By default, the 95% confidence interval for each line is also
displayed.
Plot(Years, Salary, by1=Gender, fit="lm")
## [Trellis graphics from Deepayan Sarkar's lattice package]
##
## Regression analysis of linearized data
## Need back transformation of regression model to compute predicted values
##
## Gender 1 Line: b0 = 30842.335 b1 = 4047.307 Fit: MSE = 107,647,877 Rsq = 0.819
##
## Gender 2 Line: b0 = 47109.787 b1 = 2882.272 Fit: MSE = 144,700,625 Rsq = 0.598
Turn off the confidence interval by setting the parameter
fit_se to 0 for the value of the confidence level.
One Continuous, One Categorical
A categorical variable plotted with a continuous variable results in
a traditional scatterplot though, of course, the scatter is confined to
the straight lines that represent the levels of the categorical
variable, its values.
The first two parameters of Plot() are x
and y. In this example, the categorical variable,
Dept, listed second, specifies the y variable, as
in y=Dept. There is no distinction in this function call for
two continues variables or one continuous and one categorical. The
Plot() function evaluates each variable for continuity and
responds appropriately.
## >>> Suggestions
## Plot(Salary, Dept, means=FALSE) # do not plot means
## Plot(Salary, Dept, stat="mean") # only plot means
## ANOVA(Salary ~ Dept) # inferential analysis
##
## Salary: Annual Salary (USD)
## - by levels of -
## : Department Employed
##
## n miss mean sd min mdn max
## ACCT 5 0 61792.8 12774.6 46125.0 69547.6 72502.5
## ADMN 6 0 81277.1 27585.2 53788.3 71058.6 122563.4
## FINC 4 0 69010.7 17852.5 57139.9 61937.6 95027.6
## MKTG 6 0 70257.1 19869.8 51036.8 61659.0 99062.7
## SALE 15 0 78830.1 23476.8 49189.0 77714.9 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
To avoid point overlap, if there is at least one duplicated value of
continuous y for any level of categorical x,
by default some horizontal jitter for each plotted point is added, which
was not needed in this example. Manually adjust the jitter with either
parameter jitter_x or, if x is continuous and
y categorical, the jitter_y parameter. In
addition, if the categorical variable is an R factor or a
variable of type character, by default the mean of the
continuous variable is displayed at each level of the categorical
variable, as well in the text output. If the categorical variable is
numeric, better to convert the variable to a factor to have just the
categories on the axis and not a continuous scale. For example,
d$Gender <- factor(d$Gender).
Another helpful technique for large data sets is to add some fill
transparency with the trans parameter, with values such as
0.8 and 0.9. The combination of jitter and transparency allows for
plotting many thousands of points.
An alternative display of the distribution of a continuous variable
and a categorical variable is a superimposed violin, box, and scatter
plot, a VBS plot. To plot the points in different colors according to
the level of the categorical variable, invoke the by
parameter. Here, plot Salary across the levels of
Gender on the same panel.
## [Violin/Box/Scatterplot graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender
##
## n miss mean sd min mdn max
## M 18 0 81147.458 23128.436 49188.960 79792.950 134419.230
## W 19 0 66830.598 18438.456 46124.970 61356.690 122563.380
##
## Max Dupli-
## Level cations Values
## ------------------------------
## M 0
## W 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.56 size of plotted points
## out_size: 0.80 size of plotted outlier points
## jitter_y: 0.54 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
Or, create a Trellis plot that consists of a VBS plot on a separate
panel for each level of the categorical variable. Accomplish the Trellis
plot with the by1 parameter. Here, plot Salary
across the levels of Dept. Again, specify one, two, or, by
default, all three superimposed plots: violin, box, and scatter. In this
example, the categorical variable, Gender specifies the
by1 variable.
## [Trellis graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender: Man or Woman
##
## n miss mean sd min mdn max
## M 18 0 81147.458 23128.436 49188.960 79792.950 134419.230
## W 19 0 66830.598 18438.456 46124.970 61356.690 122563.380
##
## Max Dupli-
## Level cations Values
## ------------------------------
## M 0
## W 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.56 size of plotted points
## out_size: 0.80 size of plotted outlier points
## jitter_y: 0.54 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
The default coloring of the boxes for variables other than an ordered
factor follows the default qualitative palette, "hues". For
an ordered factor, the fill color follows the default sequential palette
of the corresponding theme, such as "blues". Customize
colors with the box_fill parameter.
Just show the box plots according to the vbs_plot
parameter, which has a default setting of vbs for the
superimposed violin, box, and scatter plots. Set vbs_plot
to "b". Or, use the alias BoxPlot(). Change
the fill color of each box with the box_fill parameter. In
addition to the traditional median for a box plot, show the mean as well
as with the vbs_mean parameter. If specifying just one fill
color, then all boxes are filled with that color.
Or, drop the box plot and only plot the violins and the scatter
plots. Without the boxes, the violins take on the default colors.
Specify a value of "vs" for the vbs_plot
parameter. If only plotting the violins, then can also use the alias
ViolinPlot(). Change the fill color of the violins with
parameter violin_fill.
Plot(Salary, by1=Gender, vbs_plot="vs")
## [Trellis graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender: Man or Woman
##
## n miss mean sd min mdn max
## M 18 0 81147.458 23128.436 49188.960 79792.950 134419.230
## W 19 0 66830.598 18438.456 46124.970 61356.690 122563.380
##
## Max Dupli-
## Level cations Values
## ------------------------------
## M 0
## W 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.56 size of plotted points
## out_size: 0.80 size of plotted outlier points
## jitter_y: 0.54 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
The following plot uses the alias BoxPlot() to generate
a Trellis plot of boxplots only across the levels of
Gender.
BoxPlot(Salary, by1=Gender, vbs_mean=TRUE, box_fill="lightgoldenrod")
## [Trellis graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender: Man or Woman
##
## n miss mean sd min mdn max
## M 18 0 81147.458 23128.436 49188.960 79792.950 134419.230
## W 19 0 66830.598 18438.456 46124.970 61356.690 122563.380
##
## Max Dupli-
## Level cations Values
## ------------------------------
## M 0
## W 0
Show the different distributions of the continuous variable across
the levels of the categorical variable with a scatterplot. Here, show
the distribution of Salary for Males and Females across the
various departments.
Plot(Salary, Dept, by=Gender)
## >>> Suggestions
## Plot(Salary, Dept, by=Gender, means=FALSE) # do not plot means
## Plot(Salary, Dept, by=Gender, stat="mean") # only plot means
## ANOVA(Salary ~ Dept) # inferential analysis
##
## Salary: Annual Salary (USD)
## - by levels of -
## : Department Employed
##
## n miss mean sd min mdn max
## ACCT 5 0 61792.8 12774.6 46125.0 69547.6 72502.5
## ADMN 6 0 81277.1 27585.2 53788.3 71058.6 122563.4
## FINC 4 0 69010.7 17852.5 57139.9 61937.6 95027.6
## MKTG 6 0 70257.1 19869.8 51036.8 61659.0 99062.7
## SALE 15 0 78830.1 23476.8 49189.0 77714.9 134419.2
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #4398D0 #B28B2A filled color of the points
## color: #4398D0 #B28B2A edge color of the points
## size: 0.80 size of plotted points
## jitter_y: 0.00 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
One Continuous, Two Categorical
To do a Trellis plot with two categorical variables, invoke the
by2 parameter in addition to the by1
parameter. By default, the box fill colors are unique for each level of
the by1 variable, and then the colors cycle through all the
values of the by2 variable. With so many panels to plot,
explicitly set them in a single column by setting parameter
n_col to 1. The corresponding row parameter is
n_row.
Plot(Salary, by1=Gender, by2=Dept, n_col=1)
## [Trellis graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender: Man or Woman
##
## n miss mean sd min mdn max
## M 18 0 81147.458 23128.436 49188.960 79792.950 134419.230
## W 19 0 66830.598 18438.456 46124.970 61356.690 122563.380
##
## Max Dupli-
## Level cations Values
## ------------------------------
## M 0
## W 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.56 size of plotted points
## out_size: 0.80 size of plotted outlier points
## jitter_y: 0.54 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
To specify custom colors with the box_fill parameter,
specify the number of colors according to the number of levels of the
by1 variable. The colors for by1 then cycle
over the by2 values.
Alternatively, invoke the by parameter and the
by1 parameter. The values of the by variable
plot as separate panels, the Trellis part, and the by
variable plot for each panel.
Plot(Salary, by1=Dept, by=Gender, n_col=1)
## [Trellis graphics from Deepayan Sarkar's lattice package]
## >>> Suggestions
## Plot(Salary, out_cut=2, fences=TRUE, vbs_mean=TRUE) # Label two outliers ...
## Plot(Salary, box_adj=TRUE) # Adjust boxplot whiskers for asymmetry
## ttest(Salary ~ Gender) # Add the data parameter if not the d data frame
## ANOVA(Salary ~ Dept) # Add the data parameter if not the d data frame
## Salary: Annual Salary (USD)
## - by levels of -
## Gender: Department Employed
##
## n miss mean sd min mdn max
## ACCT 5 0 61792.776 12774.606 46124.970 69547.600 72502.500
## ADMN 6 0 81277.117 27585.151 53788.260 71058.595 122563.380
## FINC 4 0 69010.675 17852.498 57139.900 61937.625 95027.550
## MKTG 6 0 70257.128 19869.812 51036.850 61658.990 99062.660
## SALE 15 0 78830.065 23476.839 49188.960 77714.850 134419.230
##
## Max Dupli-
## Level cations Values
## ------------------------------
## ACCT 0
## ADMN 0
## FINC 0
## MKTG 0
## SALE 0
##
## Parameter values (can be manually set)
## -------------------------------------------------------
## size: 0.52 size of plotted points
## out_size: 0.79 size of plotted outlier points
## jitter_y: 0.50 random vertical movement of points
## jitter_x: 0.00 random horizontal movement of points
## bw: 9529.04 set bandwidth higher for smoother edges
Two Continuous, Three Categorical
Plot() can display the relationships for up to five
variables. The two primary variables, x and y, that
form the basis of the scatter plot, are continuous. Usually these two
variables are listed first in the function call and so do not need their
parameter names specified. Indicate two categorical variables that form
the Trellis panels with parameters by1 and
by2. Call these two variables the Trellis variables, which
define a Trellis panel for each combination of their values. Finally,
there can be a categorical grouping variable, the by
variable, which plots different groups within each Trellis panel.
To illustrate, first, the data. Use the Cars93 data set that is
installed with lessR, which describes characteristics
of 1993 cars.
##
## >>> Suggestions
## Details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Make character 93 0 32 Acura Acura ... Volvo Volvo
## 2 Type character 93 0 6 Small Midsize ... Compact Midsize
## 3 MinPrice double 93 0 79 12.9 29.2 25.9 ... 22.9 21.8 24.8
## 4 MidPrice double 93 0 81 15.9 33.9 29.1 ... 23.3 22.7 26.7
## 5 MaxPrice double 93 0 79 18.8 38.7 32.3 ... 23.7 23.5 28.5
## 6 MPGcity integer 93 0 21 25 18 20 ... 18 21 20
## 7 MPGhiway integer 93 0 22 31 25 26 ... 25 28 28
## 8 Airbags integer 93 0 3 0 2 1 ... 0 1 2
## 9 DriveTrain integer 93 0 3 1 1 1 ... 1 0 1
## 10 Cylinders integer 92 1 5 4 6 6 ... 6 4 5
## 11 Engine double 93 0 26 1.8 3.2 2.8 ... 2.8 2.3 2.4
## 12 HP integer 93 0 57 140 200 172 ... 178 114 168
## 13 RPM integer 93 0 24 6300 5500 5500 ... 5800 5400 6200
## 14 RevMile integer 93 0 78 2890 2335 2280 ... 2385 2215 2310
## 15 Manual integer 93 0 2 1 1 1 ... 1 1 1
## 16 FuelCap double 93 0 38 13.2 18 16.9 ... 18.5 15.8 19.3
## 17 PassCap integer 93 0 6 5 5 5 ... 4 5 5
## 18 Length integer 93 0 51 177 195 180 ... 159 190 184
## 19 Wheelbase integer 93 0 27 102 115 102 ... 97 104 105
## 20 Width integer 93 0 16 68 71 67 ... 66 67 69
## 21 Uturn integer 93 0 14 37 38 37 ... 36 37 38
## 22 RearSeat double 91 2 24 26.5 30 28 ... 26 29.5 30
## 23 LugCap integer 82 11 16 11 15 14 ... 15 14 15
## 24 Weight integer 93 0 81 2705 3560 3375 ... 2810 2985 3245
## 25 Source integer 93 0 2 0 0 0 ... 0 0 0
## ------------------------------------------------------------------------------------------
The categorical variables are integer coded 0 and 1, so recode to R
factors to obtain more descriptive labels.
d$Transmission <- factor(d$Manual, levels=0:1, labels=c("Auto", "Manual"))
d$Source <- factor(d$Source, levels=0:1, labels=c("Foreign", "Domestic"))
Plot MPGcity according to Weight. Specify the number of Cylinders and
Manual transmission or not as Trellis conditioning variables to form the
Trellis plot. Specify the Source of the vehicle, Foreign or Domestic as
a grouping variable to plot with separate colors on each panel.
Plot(Weight, MPGcity, by1=Cylinders, by2=Transmission, by=Source, n_col=1)
## [Trellis graphics from Deepayan Sarkar's lattice package]
From the visualization the patterns emerge. As Weight increases city
MPG decreases. Domestic cars tend to weigh more. Foreign cars tend to
have fewer cylinders, which also leads to better fuel mileage.
Categorical Variables
To avoid over-plotting, the plot of two categorical variables results
in a bubble plot of their joint frequencies.
d <- Read("Employee", quiet=TRUE)
## >>> Suggestions
## Plot(Dept, Gender, size_cut=FALSE)
## Plot(Dept, Gender, trans=.8, bg="off", grid="off")
## SummaryStats(Dept, Gender) # or ss
##
## Dept: Department Employed
## - by levels of -
## Gender: Man or Woman
##
## Joint and Marginal Frequencies
## ------------------------------
##
## Dept
## Gender ACCT ADMN FINC MKTG SALE Sum
## M 2 2 3 1 10 18
## W 3 4 1 5 5 18
## Sum 5 6 4 6 15 36
##
## Cramer's V: 0.415
##
## Chi-square Test: Chisq = 6.200, df = 4, p-value = 0.185
## >>> Low cell expected frequencies, chi-squared approximation may not be accurate
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## radius: 0.22 size of largest bubble
## power: 0.50 relative bubble sizes
The parameter radius scales the size of the bubbles
according to the size of the largest displayed bubble in inches. The
power parameter sets the relative size of the bubbles. The
default power value of 0.5 scales the bubbles so that the
area of each bubble is the value of the corresponding sizing variable. A
value of 1 scales so the radius of each bubble is the value of the
sizing variable, increasing the discrepancy of size between the
variables.
In this example, increase the absolute size of the bubbles as well as
the relative discrepancy in their sizes. If the bubbles become too
large, so that the largest bubbles become truncated, increase the
spacing of the respective axes with the pad_x and/or
pad_y parameters.
Plot(Dept, Gender, radius=.6, power=0.8, pad_x=0.05, pad_y=0.05)
## >>> Suggestions
## Plot(Dept, Gender, radius=0.6, power=0.8, pad_x=0.05, pad_y=0.05, size_cut=FALSE)
## Plot(Dept, Gender, radius=0.6, power=0.8, pad_x=0.05, pad_y=0.05, trans=.8, bg="off", grid="off")
## SummaryStats(Dept, Gender) # or ss
##
## Dept: Department Employed
## - by levels of -
## Gender: Man or Woman
##
## Joint and Marginal Frequencies
## ------------------------------
##
## Dept
## Gender ACCT ADMN FINC MKTG SALE Sum
## M 2 2 3 1 10 18
## W 3 4 1 5 5 18
## Sum 5 6 4 6 15 36
##
## Cramer's V: 0.415
##
## Chi-square Test: Chisq = 6.200, df = 4, p-value = 0.185
## >>> Low cell expected frequencies, chi-squared approximation may not be accurate
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## radius: 0.60 size of largest bubble
## power: 0.80 relative bubble sizes
Alternatively, plot two categorical variables with a Trellis (facet)
chart by invoking the by1 parameter. If the first listed
variable in the function call, the x parameter, is
categorical, the result is a dot chart for each level of the
by1 variable.
## [Trellis graphics from Deepayan Sarkar's lattice package]
Plotting a single categorical variable yields the corresponding
bubble plot of frequencies.
## >>> Suggestions
## Plot(Dept, color_low="lemonchiffon2", color_hi="maroon3")
## Plot(Dept, values="count") # scatter plot of counts
##
## --- Dept: Department Employed ---
##
## ACCT ADMN FINC MKTG SALE Total
## Frequencies: 5 6 4 6 15 36
## Proportions: 0.139 0.167 0.111 0.167 0.417 1.000
##
## Chi-squared test of null hypothesis of equal probabilities
## Chisq = 10.944, df = 4, p-value = 0.027
##
## Some Parameter values (can be manually set)
## -------------------------------------------------------
## fill: #324E5C filled color of the points
## color: #324E5C edge color of the points
## radius: 0.22 size of largest bubble
## power: 0.50 relative bubble sizes