This is the R Code :

# Sections # # 0. Setup # 1. Entering data and making a matrix with # row and column labels # 2. Lattice dot plot arguments and panel layouts # 2.1 Side comments on plot aspect ratio # # 3. Different panel layouts # 4. Graph and Table convention for the y-axis. # 5. Putting similar rows together # and showing the dot to dot path # # 6. Simplifying plot appearance # by sorting panels # 7. ggplot and using factors to control # row name order and panel order # 7.1 Creating data.frame from a matrix # and include factors # 7.2 Creat an indexed dat.frame that # stacked values from the race columns # 7.3 Putting the race levels in the desired # order from Section # # 8. Creating twe perceptual groups in eacn # panel # 8.1 Order the dataframe rows # 8.2 Add a factor to create 2 groups of 3 # using cut # 8.3 Make the perceptually grouped dot plot # 8.4 Create 3 groups of size 2 using cut

#==================================================

# 0. Setup

library(lattice) library(tidyverse) source('hw.R')

# 1. Entering data and making a matrix with # row and column labels # # The basic data structure 6 x 4 table. # # The row and column labels are: # Family type: # Married with father working, Married with both working, # Divorced mother, Never-married mother, # Race and ethnicity: White, Black, Hispanic, and Asian

# For simplicity we use the label family for family type # and the lablerace for race and ethnicity.

# 1.1 Entering the data in a matrix

# There are many options such as entering # the data using Excel and reading the file in # R. # # For very small data sets direct entry into # R is convenient. The entry and storage # of data a structure such as a matrix can be # done in different ways. # Below, for each race, we enter the family percents # Then we bind race vectors together # as columns in a matrix. Finally we # add the row and column labels.

# Entering data as four vectors. White <- c(22, 50, 8, 2, 13, 6) Black <- c(5, 24, 13, 24, 20, 15) Hispanic <- c(21, 33, 9, 7, 20, 9) Asian <- c(24, 53, 4, 1, 12, 5)

# cbind() binds vectors together as # columns in a matrix. mat <- cbind(white, black, hispanic, asian) mat

# Defining vectors of simplified labels type <- c( "Married, Father Working", "Married, Both Working", "Divorced Mother","Never-married Mother", "Other", "Grandparents") race <- c("White","Black","Hispanic","Asian")

# Labeling matrix rows and column colnames(mat) <- race rownames(mat) <- type mat

# We can transpose a matrix using t() # We can rearrange rows and column using the # [,] notation and subscript vectors.

t(mat)

mat[6:1,] # reverses the rows mat[,4:1] # reverses the columns mat[6:1,4:1] # reverses both

# 2. Lattice dot plot arguments and panel layouts # # The lattice package dotplot function has several # arguments. Some apply to bar plots # and other panel graphics. # # In the example below, the first argument # is our matrix, mat. (The first argument # can be a data.frame.) # # We save the plot as an object # in oneColumn for latter plotting.

oneColumn = dotplot(mat, groups = FALSE, layout = c(1, 4), aspect = .7, origin = 0,type = c("p","h"), main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list(x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } ) oneColumn

# Above, the layout argument, layout=c(1,4), # specifies producing one column with # four rows of panels. # # The argument, aspect=.7, sets the ratio of # the panel width to height as .7. # # The type=c("p","h") argument # specifies plotting points and # horizontal lines. # The origin=0 argument starts # the horizontal line at zero.

# We skip over the other arguments and # focus on the panel layouts. If you # have already looked at the arguments # and, for example,and have guessed that # the grid lines will be white, you are # right.

#-----------------------------------------

# 2.1 Side comments on plot aspect ratios # # The aspect ratio of time series plots # can be particularly important. We # more easily perceive differences in slopes # when they are close to # plus or minus 45 degrees than when they # are nearly vertical or horizontal. # By eye or algorithm we can set a plot aspect # ratio so more of the ascending and descending # line segments are close to the preferred angles. # # Side note; Common television screen aspect ratios are # 4/3 and 16/9.

#=========================================

# 3. Different panel layouts

# In the dot plot produced above, # we see there are four sets of row # labels, one for each panel, and # one set of grid line labels.

# What if we choose a two columns and two # rows of layout for the panels?

dotplot(mat, groups = FALSE, layout = c(2,2),aspect = .7, origin = 0,type = c("p","h"), main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list( x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0, v = -1, col = "white", lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } )

# Now we see two sets of row labels and # two sets of grid line labels.

# Another reasonable layout is # one row layout with four columns of panels.

dotplot(mat,groups = FALSE, layout = c(4,1), aspect = .7, origin = 0,type = c("p","h"), main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list(x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } )

# Now we see one set of row labels and # four sets of grid line labels. # We return to this layout in a later section.

# First we illustrate sorting and showing reference # values in the one column layout.

#=================================================

# 4. Graph and table conventions for the y-axis

# Run the two lines below and look again at # the matrix, mat, on the Console # and at the 1 column panel layout

mat oneColumn # Saved above

# It may be a surprise to see Married, Father working # as the bottom row label and White as the bottom # panel. # # These examples illustrate the conflict between # the table reading convention, where the top row is 1, # and the graph y-axis convention, where the # bottom row is 1. # # Lattice uses the graph convention by default. # # With matrices we can easily reverse row order # and the column order using subscripts. # This will produce the table convention version # for both row labels and panels.

mat mat[6:1,4:1] # reverse both orders

dotplot(mat[6:1,4:1],groups = FALSE, layout = c(1,4),aspect = .7, origin = 0,type = c("p","h"), main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list(x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } )

# Now we see the table convention. However, # the given type order and race order # does not put similar rows close # together and similar panels close together.

#========================================= # # 5. Putting similar rows together # and showing the dot to dot path

# Look at matrix in the R console.

mat

# Consider each family type row as a case # with four values, one for each race. # When sorting cases with # multivariate values in the same units # (here percents) we can often compute a # summary statistic for each case and use # the vector of summary statistics to sort # the cases. # # Below we use rowMeans () to compute # the mean of each row.

typeMeans <- rowMeans(mat) typeMeans

# Note that divorced-mother and never-married # mother have tied values. We might want to use # additional criteria to break ties.

# Below we use order() to obtain subscripts # to put the rows in a decreasing (the default) # or increasing sort order. We # also make a larger matrix with typeMeans # as new column to show that the reordering # works.

typeOrd <- order(typeMeans) cbind(mat,typeMeans)[typeOrd,]

# We use the typeOrd vector below # We also use # type = c("p","l") to plot points # and lines that connect the points.

dotplot(mat[typeOrd,4:1],groups = FALSE, layout = c(1,4),aspect = .7, type = c("p","l"), main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list(x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } )

# Now we explicity see the shapes produced # by lines connecting the dots. No imagining # is required. So what patterns do we notice? # # For starters we see that the shapes in the # White and Asian panels are very # similar. The panels should be juxtaposed

#-------------------------------------

# 5.1 Side comment: Eye traversal

# I suggest that a row labeled # dot plot's complexity of appearance # is an increasing function of the total # length of line segments connecting # the dots

# Since our eyes jump around a lot, our exact eye # traversal path will be a lot longer than # the dot to dot length even though we try # to look from dot to dot. # # A testable conjecture is that the presence of # lines will reduce the eye traversal length. In # any case, putting similar things close together # tends to simplify appearance, so we will # sort family type rows.

#----------------------------------------

# 5.2 Side comment other row sorting crieria

# William Cleveland suggested using the # median for sorting rows (or columns) # when there are outliers. # # Data analytics contexts may motive # using other summary statistic functions such as # the min(), max() or standard deviation, sd().

# ==========================================

# 6. Simplifying plot appearance # by sorting panels

# We have already noticed that the # White and Asian patterns are strikingly # similar! To simplify appearance we could # switch the positions of the Asian and # Black panels. However there are merits # to using a computational method for the # task of reordering races.

# The sorting description below transposes # data matrix to provide a discussion # in terms of sorting rows as we did above. # Now we are thinking of races as cases and # family types as variables.

raceRow <- t(mat)

# If we ignore available information about # the data and proceed (as above) # to sort rows based on the mean of each row # the row means at least provide a clue # that using row means is a bad choice. The # four means are almost the same!

rowMeans(raceRow) rowSums(raceRow)

# As documented in the study, family type # counts for each race were converted to # rounded percents. Hence the sum of # family type percents for the 4 races # should all be 100 and the means should # all be 100/6. The slight discrepancies # are due rounding, a computational artifact.

# There are two multivariate approaches # to sorting rows that will work. # These are based on principal components and # classical multidimensional scaling. # # A later lecture addresses principal components, # and the prcomp() function. We just use the # results here.

raceRowL <- prcomp(raceRow)

# RaceRowL is list structure with several # items. The component with x has the # principal components. We access this # using the $ syntax

racePc <- raceRowL$x

# racePc is matrix. # The first column in the 1st # principal component

firstPc <- racePc[,1] firstPc

raceOrd <- order(firstPc) raceRow[raceOrd,]

# In the rownames we see the order is # Asian, White, Hispanic, and Black.

# We can reverse the order based on # what we want to appear or discuss first. # When principal component values are multiplied # by -1 that are still have all the properties of # principal components. If we use different # software the signs may be reversed and still # be valid.

# We now create a matrix with sorted rows and # columns to use futher below. The ordering is # chosen so the plot will follow the table # convention.

matSorted <- mat[typeOrd,rev(raceOrd)] matSorted

dotplot(matSorted,groups = FALSE, layout = c(1,4),aspect = .7, origin = 0,type = c("p","l"), # changed "h", "l" main = "Who is Raising the Children?", xlab = "Race Rounded Percents May Not Total 100", scales = list(x = list(tck = 0, alternating = FALSE)), panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) panel.dotplot(col = rgb(0,.5,1),cex = 1.1,...) } )

# The key fact used here is that the # first principal component is the linear # combination of variables that provides # greatest variability. Flipping the points # about zero doesn't change the variance.

#-------------------------------------- # # 6.1 Side comment on classical multidimensional scaling # # You can skip this section. It is just # for the curious and not likely to be discuss # later in class.

# The multidimensional scaling approach # treats the race cases as a 4 points in # 6 dimensions. The first step # computes the Euclidean distance # matrix for the 4 choose 2 = 6 pairs # of race points

EucDis <- dist(raceRow) round(EucDis)

# The Console shows # The smallest distance, 6, is between # Asian and White. # The largest distance, 44, is between # Asian and Black.

# Given such distance matrix, classical (metric) # multidimensional scaling creates new points, # (here 4 points) in a lower dimension the we # specify (here 1). The distance matrix for the # created points in a particular dimension # minimizes sum of squared differences # between created distance matrix and the # original distance matrix.

# When we have many variables, we # use creatr points in2d or 3d # to produce 2D or 3D scatterplots. # # Here we have 6 variables and just want to plot # points on a line so they will have a sort order. # Below the two arguments for the cmdscale() function # are EucDis, the distance matrix computed above # and k=1 which means create 1D points.

racePoints <- cmdscale(EucDis,k = 1) racePoints

# Up to multipling by -1, these are the same # values as the first principal component values # obtained above.

# We can see the one dimensional # distances between race points # are only an approximation to # the distance matrix.

round(dist(racePoints),1) round(EucDis,1)

# Now, have heard a couple of lectures, # you might think. He should show the # differences. Okay.

round(dist(racePoints),1) round(EucDis,1)

# 7. Family type bar plot panels # and adding value by including the # panel race mean reference line

typePanelSorted <- t(matSorted) typePanelSorted typeRaceMeans = colMeans(typePanelSorted)

# When the panels are family types we can # make bar plots and include the average # of the race percents as a reference mean # for each panel.

barchart(typePanelSorted,groups = FALSE, layout = c(1,6),xlim = c(0,55), main = "Who is Raising the Children?", xlab = "Percent", scales = list(x = list(tck = 0, alternating = FALSE)), typeRaceMeans = typeRaceMeans, panel = function(...){ panel.fill(rgb(.9,.9,.9)) panel.grid(h = 0,v = -1,col = "white",lwd = 2) i <- panel.number() panel.abline(v = typeRaceMeans[i],col = "red",lwd = 3) panel.barchart(col = rgb(0,.5,1),cex = .95,...) } )

# This may help communicate the basis # for panel order. # # For panel layouts such a two rows and to # columns, controlling the layout order # and matching means to the correct # seem a bit complicated. # # Showing the means opens the door to showing # the deviations from means as bars or lines # draw from the red mean line. This can save # (or increase resolution)when none of the # original bar are close to zero. # # The deviation can also be represented # the negative and positive deviations # from a zero line, when the focus is # not longer on the means.

#================================================== # # 7. ggplot and using factors to control # row name order and panel order

# With the lattice package, # we could reorder matrix rows and columns. # This let us avoid the explicit # modification of factor levels to control # row name and the panel order. # # With ggplot2 we need a data.frame or tibbles with # factors whose level control the row plotting order # that the panel layout order.

#----------------------------------------- # # 7.1 Creating a data.frame from a matrix # and including factors

# We first created a data.frame from # a sorted matrix above, then include the # row.names as factors and finally use the # gather function in the tidyr package # to make it an indexed data.frame

famRace <- as.data.frame(matSorted) # make a data.frame famRace

types = row.names(famRace) famRace$Types = factor(types,levels = types)

#----------------------------------------------- # # 7.2 Make an indexed dataframe that stacks # the race column values

famRaceType <- gather(famRace, ke = Race, value = Percent,Asian:Black, factor_key = TRUE) famRaceType

# factor_key = TRUE kepts # the level order specified # rather than sorting in alphabet # order.

#-------------------------------------------- # # 7.3 famRaceType used raceLevels from # section 5 so is ready to use.

ggplot(famRaceType, aes(x = Percent,y = Types)) + geom_point(fill = "blue", shape = 21, size = 2.8) + labs(x = "Percent",y = "", title = "Who's Raising the Children?") + facet_grid(.~Race) + hw

#================================================ # # 8. Create two perceptual groups in each panel # # We will use geom_path lines to connect # the top three dots and to connect the # bottom three dots. # # geom_path connects the dot in a group using the # row order in the dataframe. # We need put the rows in the desired family # type order.

# 8.1 Order the data.frame rows so # so family factor numeric value varies within # each race factor numeric values

ord <- order(as.numeric(famRaceType$Race), as.numeric(famRaceType$Types))

famSorted <- famRaceType[ord,] famSorted

# 8.2 Use family type numbers 1:6 # and cut() to create # 2 groups of 3 family types

# Family types with numbers # 1:3 will be in the (0, 3.5] group # 4:6 will be in the (3.5, 6] group

famSorted <- mutate(famSorted, G2 = cut(as.numeric(Types), breaks = c(0, 3.5, 6)) )

famSorted

# Above we can see the structure # group of three in the G2 column

# The factor patterns may be easier to see # when converted to integers.

cbind(as.numeric(famSorted$Race), as.numeric(famSorted$Types), as.numeric(famSorted$G2))

# 8.3 Use paths to link the # dots in each perceptual group

ggplot(famSorted,aes(x = Percent,y = Types,group = G2))+ geom_path(color = "blue",size = 1) + geom_point(shape = 21,fill = "blue", color = "black", size = 2.7) + geom_point(shape = 21,fill = "white",color = 'white',size = 1) + labs(x = "Percent",y = "", title="Who's Raising the Children?") + facet_grid(.~Race) + hw

R code question:

# 8.4 Change the cut breaks in Section 8.2 # to produce 3 perceptual groups of size 2. # Rerun the needed parts of the 8.2 and # 8.3 script to produce the plot.