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Trellis Graphics User`s Manual

1. yield Figure 9 1 80 CHAPTER 9 MULTIPANEL CONDITIONING 9 4 Columns Rows and Pages A multipanel conditioning display is a three way rectangular array laid out into columns rows and pages In figure 9 1 there are two columns six rows and one page The numbers of columns rows and pages are selected by an algorithm that attempts of fill up as much of the graphics region as possible subject to certain constraints As we will see in section 9 6 there is an argument layout that allows you to choose the numbers 9 5 Packet Order and Panel Order In the above formula the conditioning variable year appeared first and site appeared second This gives an explicit ordering to the conditioning variables Each of these variables is a factor with levels gt levels barleySyear 1 1932 1931 gt levels barleySsite 1 Grand Rapids Duluth University Farm 4 Morris Crookston Waseca The levels of each factor are ordered by their order of appearance in the levels attribute As we will discuss shortly we can control the order by making the factor an ordered one A packet is information sent to a panel for display For figure 9 1 each packet includes the values of variety and yield for a particular combination of year and site Packets are ordered by the orderings of the conditioning variables and their levels the levels of the first conditioning variable vary the fastest the levels of the second condition
2. Compact tario tao opi Pr ge e log mileage means base 2 Figure 7 5 48 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 7 barchart Overall dot plots are a more effective display method than bar charts avoiding some of the perceptual problems of bar charts Still there are circumstances where bar charts are harmless Figure 7 6 is a bar chart of the mileage means without logs barchart names mileage means aspect 1 mileage means 7 7 BARCHART 49 Van Sporty Small Medium Large Compact 20 22 24 26 28 30 mileage means Figure 7 6 50 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 8 piechart Pie charts have severe perceptual problems Experiments in graphical perception have shown that compared with dot plots they convey information far less reliably But if you want to display some data and perceiving the information is not so important then a pie chart is fine Figure 7 7 is a pie chart of the mileage means piechart names mileage means mileage means 7 8 PIECHART Large Kyods 51 Figure 7 7 52 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 9 qqmath Normal probability plots or normal q q plots are the single most powerful tool for determining if the distribution of a set of measurements is well approximated by the normal distribution Figure 7 8 is a normal probability plot of the mileages for small cars qqmath Mileage data
3. The factor Type is on the left of the formula because it goes on the vertical axis and the numeric vector Mileage is on the right because it goes on the horizontal axis You cannot reverse the arguments to reverse the axes 7 3 BWPLOT M Van e Sporty nn z e Small u Medium e Large DE e cai Compact awd 20 25 30 Mileage Figure 7 2 42 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 4 stripplot A strip plot sometimes called a one dimensional scatterplot is similar to a box plot in general layout but the individual data points are shown instead of the box plot summary Figure 7 3 is a stripplot stripplot Type jitter TRUE aspect 1 Mileage data fuel frame Setting jitter TRUE causes some random noise to be added vertically to the points to alleviate the overlap of the plotting symbols When jitter FALSE the default the points for each level lie ona horizontal line 7 4 STRIPPLOT 43 Van 6 Sporty Small Medium Large o Compact ow OD 00 DO O 20 25 Mileage 30 35 Figure 7 3 44 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 5 q90 The quantile quantile plot or q q plot is an extremely powerful tool for comparing the distributions of two sets of data The idea is quite simple quantiles of one data set are graphed against corresponding quantil
4. fuel frame subset Type Small That is the ordered data are graphed against quantiles of the standard normal distribution Note that the formula for qamath is used in a way unlike any of the previous examples Only one data object appears in the formula to the right of the because this graphical method utilizes only one data object aqmath can also make probability plots for other distributions It has an argument distribution whose input is any function that computes quantiles The default is qnorm If we used qqmath Mileage data fuel frame subset Type Small aspect 1 distribution qexp the result would be an exponential probability plot Note that the name of the function appears as the default label on the horizontal scale of the plot 7 9 QQMATH 53 36 m 34 o 32 o Mileage 30 m 28 o n 26 o o qnorm Figure 7 8 54 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 10 histogram A histogram can be useful for showing the distribution of a single set of data but two or more histograms are typically not nearly as powerful as a box plot or q q plot for comparing data distributions Figure 7 9 is a histogram of mileage histogram Mileage data fuel frame aspect 1 nint 10 The argument nint determines the number of intervals The histogram algorithm chooses the intervals to make the bar widths be simple numbers while trying to make
5. 3 102 CHAPTER 10 SCALES AND LABELS 10 3 xlim ylim In Trellis the upper value of the scale line for a numeric variable is the maximum of the data to be plotted plus 4 of the range of the data Similarly the lower value of the scale line for a numeric variable is the minimum of the data to be plotted minus 4 of the range of the data The 4 helps prevent the data values from running into the edge of the plot We can alter the extremes of the horizontal scale line by the argument xlim a vector of two values The first value replaces the minimum of the data in the above procedure and the second value replaces the maximum Similarly we can alter the vertical scale by ylim In figures 10 1 to 10 3 NOx is graphed along the vertical scale The limits of this variable are gt range gas NOx 1 0 537 5 344 In figure 10 4 the values 0 and 6 have been included in the vertical scale xyplot NOx E data gas aspect 1 2 ylim e 0 6 10 3 XLIM YLIM 103 Oo NOx W 0 7 0 8 0 9 1 0 1 1 1 2 Figure 10 4 104 CHAPTER 10 SCALES AND LABELS 10 4 scales The argument scales affects tick marks and tick mark labels In figure 10 4 there are seven tick marks and tick mark labels along the vertical scale and six along the horizontal In figure 10 5 scales is used to reduce the number of ticks and increase the size of the tick labels xyplot NOx E data gas aspect 1 2 ylim 29
6. 5 The variables are weight displacement of the engine fuel consumption in miles per gallon fuel consumption in gallons per mile and a classification into type of vehicle The first four variables are numeric The fifth variable is a factor gt table fuel frame Type Compact Large Medium Small Sporty Van 15 3 13 13 9 7 38 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 2 xyplot We have already seen xyplot in action in many of our previous examples This function is a basic graphical method graphing one set of numerical values on a vertical scale against another set of numerical values on a horizontal scale Figure 7 1 is a scatterplot of mileage against weight xyplot Mileage aspect 1 Weight data fuel frame The variable on the left of the goes on the vertical or y axis and the variable on the right goes on the horizontal or x axis 7 2 XYPLOT 39 o 35 o m o o 0g O o o 30 o O o O 0 O 00 00 oo o o 25 o o o o co o 000 o 6 6 o 00 o o 00 o o o 20 ooo o di o oo o oo o 2000 2500 3000 3500 Weight Figure 7 1 40 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 3 bwplot The box and whisker plot or box plot is a very clever invention of John Tukey that is widely used for comparing the distributions of several data sets Figure 7 2 is a box plot of mileage classified by vehicle type bwplot Type aspect 1 Mileage data fuel frame
7. GIVEN E lt equal count ethanol E number 9 overlap 1 4 There are two inputs to the algorithm the number of intervals and a target fraction of points to be shared by each pair of successive intervals In figure 9 5 the inputs are 9 and 1 4 The algorithm picks interval endpoints that are values of the data the left endpoint of the lowest interval is the minimum of the data and the right endpoint of the highest interval is the maximum of the data The endpoints are chosen to make the counts of points in the intervals as nearly equal as possible and the fractions of points shared by successive intervals as close to the target fraction as possible 9 13 EQUAL COUNT NOx 91 8 10 12 14 16 18 8 10 12 14 16 18 l l l l l l l l l l l l Ji l l l GIVEN El GIVEN E E GIVENE MI GIVEN E E 4 4 e El O 4 3 5 o O O g e O O b o o I o Od De Q O O O o O O o 4 O O 8 or 1 po o P 8 o O 9 O l l l l DD GIVEN E EM GIVEN E FGIVEN E GIVEN E GENE 4 O o ob Bo 8 9 p o O o p O O o 4 b E O O gt gt ne S b 4 o O e O O 8 o o o o 8 oo le a o 4 k L O DO o O T T T T T TT T T TT T T T T T T T TM T T T T T 8 10 12 14 16 18 8 10 12 14 16 18 8 10 12 14 16 18 Figure 9 5 92 CHAPTER 9 MULTIPANEL CONDITIONING The command that produced figure 9 5 is xyplot NOx C GIVEN E data ethanol aspect 2 5 The aspect ratio was chosen to be 2 5 to approximately b
8. ZEE MoS eda e RR id iii EE EE a Be TR ee iii r zm ees ECO EE RENEE arm pom dee CREA ERE EEE va OP mmm pe pe CE Pee Manchuria a Manchuria sM Z RZ ERZE iii RZE EE WD oro EE EPE A A Fk o 5 mn EE ne cieca sota RR ___ wr MOBIL ES Bo noca EEE A E E ce ee No 462 E No 462 ooo E NE A _ rs A antes m mem nn PORN MTA STE mms s e O PR g vi mm laid e manam BE SR e REA e a a enge APE e EE ERIYNE PRE EEE OE LIO RE Svansota E Svansota i 188 a pria ed m e een ge lie a een a e nn O PA ____ __ ye CEE Tonale lil ee ee eee i m m ZZO WEZ EEE EEE a a EEE e e e AE e ee ee Se 0 PRE SIAE PESI III A ZIE T T T T T T I I I 20 30 40 50 60 Figure 9 2 84 Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids CHAPTER 9 MULTIPANEL CONDITIONING 20 30 40 50 60 i i Es i E i Trebi 2 19 EECC ee M ERA en a Wo R eli SA ee E a ma mne EEE e e A ONE fas ge i nn rr e re e e E O NN A ROIO CSO ee virata RN RA RECE zamena A DEE Wisin ponam de eci ae E me m A A E TERES e aed REIT E EE PINCO SATO RE R er m ice ee No 457 een No 457 2 19
9. and the second is vertical both in the plane of the screen The third component is perpendicular to the screen The surface is rotated about these axes in the order given in the list Here is how it worked for figure 7 15 The surface began with datax as the horizontal screen axis datay as the vertical and dataz as the perpendicular The origin was at the lower left in the back First the surface was rotated 45 about the perpendicular screen axis where a positive rotation is counterclockwise Then there was a 60 rotation about the horizontal screen axis where a negative rotation brings the picture at the top of the screen away from the viewer and the bottom toward the viewer Finally there was no rotation about the vertical screen axis had there been one with a positive number of degrees then the left side of the picture would have moved toward the viewer and the right away If drape T acolor encoding is added to the surface using the same encoding method of the level plot 7 17 WIREFRAME dataz 8 R o SE 57 LLP ses gt datay 67 datax Figure 7 15 68 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 18 cloud A static 3 D plot of a scatter of points is typically not effective because the depth cues are insufficient to give a strong 3 D effect Still on rare occasions such a plot can be useful sometimes as a presentation or teaching tool Figure 7 16 is a 3 D scatterplot of the
10. control is direct and easy to exert 1 4 Trellis and the Core S PLUS Graphics The core S PLUS graphics is a collection of low level drawing functions and graphics parameter settings The low level functions draw graphical elements For example points draws plotting symbols and lines draws lines The parameter settings govern the details of how graphical elements are rendered For example pch sets the plotting symbol to a plus sign Trellis Graphics employs the core graphics in two ways First Trellis has been implemented using the core graphics Second when you write a panel function to tailor the display to your data you use features of the core graphics typically these are very simple features considerably simpler than the Trellis implementation which used just about every feature of the core 8 CHAPTER 1 ABOUT TRELLIS GRAPHICS 1 5 Trellis vs the Old S PLUS High Level Graphics Since the very beginning of S PLUS there has been a collection of high level graphics functions that are used to display graphs Examples are plot qqnorm and persp These routines like Trellis Graphics are also implemented using the core graphics Trellis Graphics provides more functionality than the old high level capabilities there are many new ways to display data such as multipanel conditioning It has also greatly improved some of the old display methods For example wireframe does a better job of 3 D rendering tha
11. first three variables in the data frame fuel frame cloud Mileage Weight Disp data fuel frame screen list z 30 x 60 y 0 xlab W ylab D zlab M The behavior of the argument screen is the same as that for wireframe We have used three additional arguments to specify scale labels such labeling will be discussed in chapter 10 7 18 CLOUD 69 Figure 7 16 70 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 19 The Display Functions and Their Formulas The following listing of the general display functions and their formulas is instructive because it shows certain conventions and consistencies in the formula mechanism Graph One Numerical Variable Against Another xyplot numerici numeric2 Compare the Sample Distributions of Two or More Sets of Data bwplot factor numeric stripplot factor numeric ag factor numeric Graph Measurements with Labels dotplot character numeric barchart character numeric piechart character numeric Graph the Sample Distribution of One Set of Data qqmath numeric histogram numeric densityplot numeric Graph Multivariate Data splom data frame parallel data frame 7 19 THE DISPLAY FUNCTIONS AND THEIR FORMULAS 71 Graph a Function of Two Variables Evaluated on a Grid contourplot numerici numeric2 numeric3 levelplot numericl numeric2 numeric3 wireframe numerici numeric2 numeric3
12. layout 9 10 A Data Set ethanol The data frame ethanol contains three variables from an industrial experiment with 88 runs 9 10 A DATA SET ETHANOL 87 gt names ethanol 1 NOx nan gn gt dim ethanol 1 88 3 The concentrations of oxides of nitrogen NOx in the exhaust of an engine were measured for different settings of compression ratio C and equivalence ratio E These measurements were part of the same experiment that produced the measurements in the data frame gas introduced in section 5 1 88 CHAPTER 9 MULTIPANEL CONDITIONING 9 11 Conditioning On Discrete Values of a Numeric Variable For the barley data the explanatory variables are factors so it is natural to condition on the levels of each factor This is not the case for the ethanol data both explanatory variables C and E are numeric Suppose for the ethanol data that we want to graph NOx against E given C The variable C has five unique values in other words the variable while numeric is discrete gt table ethanol C TaB 9 12 15 18 22 17 14 19 16 It makes sense then to condition on the unique values of C Figure 9 4 does this xyplot NOx E Es data ethanol aspect 1 2 When a numeric variable is used as a conditioning variable in the argument formula then conditioning is automatically carried out on the sorted unique values In other words the levels of the variable in such a case are the unique values The order of the
13. levels is from smallest to largest For C the first level is 7 5 the second is 9 and so forth Thus the first packet includes values of NOx and E for C 7 5 the second packet includes the values for C 9 and so forth As before the packets fill the panels according to the packet order and the panel order In figure 9 4 the values of C which are indicated by the thin darkened bars in the strip labels increase from bottom to top 9 11 CONDITIONING ON DISCRETE VALUES OF A NUMERIC VARIABLE 89 NOx Figure 9 4 90 CHAPTER 9 MULTIPANEL CONDITIONING 9 12 Conditioning On Intervals of a Numeric Variable For the ethanol data we graphed NOx against E given C in figure 9 4 We would like to see NOx against C given E as well But E varies in a nearly continuous way there are 83 unique values out of total of 88 values Clearly we cannot condition on single values Instead we condition on intervals This is done in figure 9 5 On each panel NOx is graphed against C for E in an interval The intervals which are portrayed by the darkened bars in the strip are ordered from low to high so as we go left to right and bottom to top through the panels the intervals go from low to high The intervals overlap In the next section we will see how they were created and the expression that produced the graph 9 13 equal count The nine intervals in figure 9 5 were produced by the equal count algorithm
14. the number of intervals as close to nint as possible 7 10 HISTOGRAM 55 20 15 Percent of Total 20 25 30 35 Mileage Figure 7 9 56 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 11 densityplot Like histograms density plots can be of help in understanding the distribution of a single set of data but box plots and q q plots typically give more incisive comparisons of distributions Figure 7 10 is a density plot of mileage densityplot Mileage data fuel frame aspect 1 2 width 5 The argument width controls the width of the smoothing window in the same units as the data mpg here as the width increases the smoothness increases 7 11 DENSITYPLOT 57 0 0 0 6 USO OO GO Oooo 6 6 0000 O E 18 20 26 30 35 40 Mileage Figure 7 10 58 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 12 splom The scatterplot matrix is an exceedingly powerful tool for displaying measurements of three or more variables Figure 7 11 is a scatterplot matrix of the variables in fuel frame splom fuel frame Note that the factor Type has been converted to a numeric variable and plotted just like the other variables which are numeric The six levels of Type simply take the values 1 to 6 in this conversion 7 12 SPLOM 59 Sporty Van 3 00 w oo a 00 Cf van E 00m o DOD do 0000 o 00000 OO sporty Do amo GMO Co 009 aso Comm oo pon
15. year site data barley The name of the factor for example site does not appear because seeing the names of the levels is typically enough to convey the name of the factor Thus the text comes from the names given to variables and factor levels in the data sets that are plotted If we want to change the text we can change the names For example if we want to change the long label University Farm to U Farm then we can change the names of the levels of the factor site gt levels barleySsite 1 Grand Rapids Duluth University Farm 4 Morris Crookston Waseca gt levels barleySsite 3 lt U Farm 10 6 THE TEXT IN STRIP LABELS Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota 109 yield Figure 10 7 110 CHAPTER 10 SCALES AN
16. 18 Figure 12 4 126 CHAPTER 12 PANEL FUNCTIONS 12 6 subscripts For a multipanel display another component of the packet sent to each panel is the subscripts that subset each formula variable to provide the variable values to the packet Knowing these subscripts is helpful for getting the values of other variables that might be needed for rendering on the panel In such a case the panel function takes a new argument subscripts that contains the subscripts In figure 12 5 the observation numbers have been added to the graph of NOx against E given C xyplot NOx E C data ethanol groups row names ethanol aspect 1 2 panel function x y subscripts groups text x y groups subscripts cex 75 See trellis args for more information about subscripts 12 6 SUBSCRIPTS NOx e 581 41 53 88 43 14 m 2 87 E c I 55 19 74 zi 34 7518 i 72 1376 33 ue 111 67 sk 4 2 9 17 i 12 85 510 I c 480 20 6 71 46 36 47 69 8 le 845 7907 E 648 50 E 51 a 40 5 15 si 60 78 T T T T 0 6 0 8 1 0 1 2 E 127 Figure 12 5 128 CHAPTER 12 PANEL FUNCTIONS 12 7 The Common Core S PLUS Graphics Features The common core graphics functions used in writing panel functions are points lines text segments polygon You can use the S PLUS online help to see what they do The common core parameters used in writing panel functions are c
17. 2 FORMULA gas NOx 25 0 7 0 8 0 9 1 0 1 1 1 2 gas E Figure 5 1 26 CHAPTER 5 GIVING DATA TO GENERAL DISPLAY FUNCTIONS The use of formula here is the same as that in the S PLUS statistical modeling functions such as 1m and aov To the left or right of the you can use any S PLUS expression For example if you had wanted to graph the log base 2 of gas NOx you would have used the formula log gas NOx base 2 gas E The argument formula is a special one in Trellis Graphics It is always the first argument of a general display functions such as xyplot We can omit typing formula provided the formula is the first argument Thus the expression xyplot gas NOx gas C also produces figure 5 1 formula is the only argument that should be given by position all others must be given by name Certain single symbol operators that perform functions in S PLUS have a new meaning in the formula language e g and although Trellis as we will see uses only and If you want to use any of these operators for their general meaning in any formula expression for example if you want to use as multiplication you must put the expression inside the identity function 1 unless it is already given as an argument to a function Here is an example log 2 gas NOx base 2 I 2 gas E We use I on the right of the formula to protect against the in 2 gas E but not on the left because 2 g
18. 6 scales list cex 2 tick number 4 The argument scales is a list The list component cex affects the size The list component t ick number affects the number but it is just a suggestion an algorithm goes off and tries to find tick values that are pretty while trying to come as close as possible to the specified number We can also specify the tick marks and labels separately for each scale The specification scales listic x 2 x List Eick n mber 4 y list tick number 10 changes cex on both scales but tick number has been set to 4 for the horizontal or x scale and has been set to 10 for the vertical or y scale Thus the rule is this specifications for the horizontal scale appear in scales as a component x that is itself a list specifications for the vertical scale appear in scales as a component y that is a list and specifications for both scales appear as remaining components of scales There is an exception to the behavior of scales The two 3 D general display functions wireframe and cloud currently do not accept changes to each scale separately in other words components x y and z cannot be used Also the general display functions splom and piechart have no tick marks and labels so scales does not apply at all 10 4 SCALES 105 NOx 0 8 1 0 1 2 Figure 10 5 106 CHAPTER 10 SCALES AND LABELS 10 5 aspect The aspect ratio the height of a panel da
19. D LABELS 10 7 par strip text strip key The size font and color of the text in the strip labels can by changed by the argument par strip text a list whose components are the parameters cex for size font for the font and col for the color For example we can make huge strip labels by par strip text list cex 2 The argument st rip allows very delicate control of what is put in the strip labels One usage that might be of interest in some cases is strip F which removes the strip labels altogether The argument key adds a key or legend to a graph See trellis args and key for details Chapter 11 Devices 11 1 Three Kick Methods You can send Trellis graphs to a printer directly or to a file for later printing But when you issue a command to do this the sending does not happen immediately You need to give the system a kick There are three ways to kick 1 send another graph 2 turn off the device with the command dev off 3 end your S PLUS session with q 11 2 trellis device The function trellis device specifies a device and enables Trellis Graphics to tailor rendering details such as color symbols and line types to the specified device We saw in section 3 2 that it can be used to specify screen devices As we will see it can be used to specify devices for sending directly to a printer or for sending to a file for later printing 112 CHAPTER 11 DEVICES 11 3 Sending to a Printer o
20. E Figure 12 3 124 CHAPTER 12 PANEL FUNCTIONS 12 5 Special Panel Functions Even if you write your own panel function you might want to use the default panel function as part of it This is often true when you want to augment a standard Trellis panel Also Trellis Graphics provides some special purpose panel functions One of them is panel loess It adds smooth curves to scatterplots Figure 12 4 adds smooth curves to a multipanel display of the ethanol data GIVEN E lt equal count ethanol E number 9 overlap 1 4 xyplot NOx C GIVEN E data ethanol aspect 2 5 panel function x y panel xyplot x y panel loess x y span 1 The default panel function panel xyplot draws the points of the scatterplot on each panel The special panel function panel loess computes and draws the smooth curves the argument span the smoothing parameter has been specified 12 5 SPECIAL PANEL FUNCTIONS 125 8 10 12 14 16 18 8 10 12 14 16 18 l l l l l l l l l l l Ji l l l l l GIVEN El GIVEN E E GIVENE MI GIVEN E E 4 4 e 8 O 4 3 Bo O O le O O b o b J g r 2 Bg o O e e o O O o 4 eo o ot po o pls U 6 x lt O l l i s DD GIVEN E E GIVEN E FGIVEN E GIVEN E GENE ad o O or e D 9 O O O 34 b B O p g gt b a b 24 e H Q do o O 8 O A T T T T T TT T T TT T T T T TT T T T TT T T T T T 8 10 12 14 16 18 8 10 12 14 16 18 8 10 12 14 16
21. Graph Three Numerical Variables cloud numerici numeric2 numeric3 72 CHAPTER 7 GENERAL DISPLAY FUNCTIONS Chapter 8 Arranging Several Graphs On One Page print Several graphs made separately by Trellis display functions can be displayed on a single page There is one restriction None of the individual graphs may be a multipanel conditioning display with more than one page 74 CHAPTER 8 ARRANGING SEVERAL GRAPHS ON ONE PAGE PRINT Figure 8 1 shows two graphs arranged on one page attach fuel frame box plot lt bwplot Type scatter plot lt xyplot Mileage detach print box plot position 010 0 1 4 more T print scatter plot position gt c 0 35 1 1 Mileage Weight The argument position specifies the position of each graph on the page using a page coordinate system in which the lower left corner of the page is 0 0 and the upper right corner is 1 1 The graph rectangle is the portion of the page allocated to a graph position takes a vector of four numbers the first two numbers are the coordinates of the lower left corner of the graph rectangle and the second two numbers are the coordinates of the upper right corner Notice that in the above example the graph rectangles overlap somewhat Here is the reason The description of a graph by the software contains margins empty space around the edges of the graph But in arranging graphs on a page we might well want to ov
22. No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Barley Yield bushels acre Figure 1 1 4 CHAPTER 1 ABOUT TRELLIS GRAPHICS 1 2 Seeing the Sunspot Cycles The top panel of figure 1 2 graphs the yearly sunspot numbers from 1849 to 1924 The aspect ratio the height of the data region of the graph divided by the width is 1 0 An aspect ratio of 1 0 is what you might expect to see as a default in cases where aspect ratio has not been considered But the graph fails to reveal an important property of the cycles In the bottom panel the data are graphed again but this time the aspect ratio has been chosen by an algorithm in Trellis Graphics called banking to 45 Now the property is revealed The sunspot cycles typically rise more rapidly than they fall this behavior is pronounced for the cycles with high peaks is less pronounced for those with medium peaks and disappears for those cycles with the lowest peaks In the top panel the aspect ratio of 1 0 prevents an accurate visual decoding of the slop
23. O o x O Z 3 o 2 o o 0 7 0 8 0 9 1 0 1 1 Figure 5 2 30 CHAPTER 5 GIVING DATA TO GENERAL DISPLAY FUNCTIONS 5 5 as data frame array as data frame ts make groups This chapter began our description of the standardization in specifying data for the general display functions Because of this standardization it is sometimes convenient to have the data placed on a data frame with subsets of the data delineated by the levels of a factor Data do not always start out in this form but three functions can help get them there as data frame array converts arrays to data frames as data frame ts converts time series and make groups converts a collection of vectors Use as data frame array as data frame ts and make groups to see how they work Chapter 6 Aspect Ratio The aspect ratio of a graph the height of a panel data region divided by its width is so important that we are going to introduce it early to have it available for ensuing displays See chapter 1 for an example where choosing the aspect ratio to carry out banking to 45 shows information in the data that cannot be seen if the graph is square that is has an aspect ratio of 1 32 CHAPTER 6 ASPECT RATIO One advance of Trellis Graphics is the direct control of the aspect ratio The argument is aspect You can set the ratio to a specific value In figure 6 1 the aspect ratio has been set to 3 4 xyplot NOx E data gas aspec
24. SSING ARGUMENTS TO A DEFAULT PANEL FUNCTION 119 de E 5 e n de BE de 4 E 4 E x o 3 A 2 i n 1 7 0 7 0 8 0 9 1 0 1 1 1 2 Figure 12 1 120 CHAPTER 12 PANEL FUNCTIONS 12 3 Writing A Panel Function panel If you write your own panel function you pass it on to the general display function using the argument panel For example if you have your own panel function mypanel you specify panel mypanel A panel function is always a function of at least two arguments the first two are named x and y Suppose for the gas data that you want to use xyplot to graph NOx against E and use a as the plotting symbol for all observations except that for which NOx is a maximum in which case you want to use M You cannot use the arguments of the panel function xyplot to do this so you must write your own First let us write the panel function panel special lt function x y biggest lt y max y points x biggest y biggest pch points x biggest y biggest pch M The function points is a core graphics function It graphs individual points on a graph Its first argument x contains the coordinates of the points along the horizontal scale and its second argument y contains the coordinates of the points along the vertical scale The third argument pch gives the symbol used to display the points Figure 12 2 shows the result of g
25. Trellis Graphics User s Manual Richard A Becker and William S Cleveland AT amp T Bell Laboratories Murray Hill NJ 07974 December 21 1995 Copyright 1995 AT amp T Bell Laboratories All Rights Reserved Chapter 1 About Trellis Graphics Making graphs is very basic to data analysis Whether you use the leading edge of statistical methods or whether you want to quickly see the main features of your data graphs are a must They are the single most powerful class of tools for analyzing data Trellis Graphics is a new system for making graphs written using the core S PLUS graphics functions Trellis has many exciting features some of them quite glitzy but the true measure of a visualization system is how much it enables you to learn from your data So in this chapter we will begin with two sets of data then discuss features and finally tell you who developed Trellis 2 CHAPTER 1 ABOUT TRELLIS GRAPHICS 1 1 Discovering the Missed Happening at Morris Figure 1 1 is a Trellis display of data from an agricultural field trial to study the crop barley At six sites in Minnesota ten varieties of barley were grown in each of two years The data are the yields for all combinations of site variety and year so there are 6 x 10 x 2 120 observations In figure 1 1 each panel displays the 20 yields at a single site The barley experiment was run in the 1930s The data first appeared in a 1934 report published by the experimente
26. aboratories 10 CHAPTER 2 ABOUT THIS USER S MANUAL 2 2 What You Need to Know About the Rest of S PLUS to Use Trellis You can employ Trellis Graphics to do quite useful things with just a minimum of knowledge of the rest of S PLUS All you need to get started is a knowledge of the material in chapters 1 5 7 and 10 11 of A Gentle Introduction to S PLUS one of the manuals available from StatSci 2 3 Other Reading About Trellis Color and black and white versions of this Manual are available on the Web from Statistics Research at AT amp T Bell Labs http netlib att com netlib att stat info trellis html Another document A Tour of Trellis Graphics by Rick Becker Bill Cleveland Ming Shyu and Stephen Kaluzny is more narrative and less of a reference guide and it presents usages not presented here This document is also available at the above Web site But even more fundamentally this User s Manual does not show you examples of the use of Trellis to analyze data complete with problem description data description analysis and conclusions Data analysis is discussed in The Visual Design and Control of Trellis Display by Rick Becker Bill Cleveland and Ming Shyu This document is also available at the above Web site Even more examples can be found in the book Visualizing Data by Bill Cleveland It was written at a time when Trellis Graphics was in its infancy so not all of today s capabilities are discussed but the
27. ank the underlying pattern of the points to 45 Notice that the automatic layout algorithm chose five columns and two rows 9 14 Shingles shingle The result of equal count is an object of class shingle The class is named shingle because of the overlap like shingles on a roof First a shingle contains the numerical values of the variable and can be treated as an ordinary numeric variable gt range GIVEN E 1 0 535 1 232 gt range ethanol E 1 0 535 1 232 Second a shingle has the intervals attached as an attribute There is a plot method a special Trellis function that displays the intervals Figure 9 6 shows the intervals of GIVEN E plot GIVEN E 9 14 SHINGLES SHINGLE 95 Panel al 0 6 0 8 1 0 1 2 GIVEN E Figure 9 6 94 CHAPTER 9 MULTIPANEL CONDITIONING You can use the function levels to extract the intervals from the shingle gt levels GIVEN E min max 0 535 0 686 0 655 0 761 0 733 0 811 0 808 0 899 0 892 1 002 0 990 1 045 1 042 1 125 1 115 1 189 1 175 1 232 A shingle can be specified directly by the function shingle Use shingle to see how it works 9 15 skip between page prepanel The multipanel conditioning of Trellis Graphics has four more arguments that assist in the control of the layout visual design labeling and scaling skip allows a panel position to be skipped when packets are sent to the panels for drawing betwee
28. arden trelliswork and hence the name Trellis Graphics Banking to 45 Selecting the aspect ratio or shape of a graph to maximize the accuracy of our visual decoding of information was an outstanding problem of statistical graphics for decades The solution a breakthrough in data display has been implemented in Trellis Graphics Banking to 45 chooses the aspect ratio to center the absolute values of the slopes of selected line segments on 45 Perceptual experiments have shown that this maximizes the accuracy of our visual decoding of the relative values of the slopes 1 4 TRELLIS AND THE CORE S PLUS GRAPHICS 7 Automation Trellis Graphics employs automation methods that save you time by automatically selecting rendering aspects for example multipanel layout line types plotting symbols colors and character sizes to achieve effective visual perception of the structure of data These automation methods are tuned to the graphics device you are using Tailoring Trellis to Your Data Still even though our automation methods work well you will want to alter displays You can alter what goes in the data region of your graph by altering a panel function a simple procedure that describes what the panel display method should be And you can alter panel functions to produce completely new types of displays tailored to the needs of your data You have very delicate control over labels and scales if you need it Yet this
29. as NOx sits inside a function 5 3 data One annoyance in the use of the above formulas is that we had to continually refer to the data frame gas This is not necessary if we attach gas to the search list of databases We can draw figure 5 1 by 5 3 DATA 27 attach gas xyplot NOx E Another possibility is to use the argument data xyplot NOx E data gas In this case the variables of gas are available for use in formula just during the execution of xyplot The effect is the same as attach gas xyplot NOx E detach gas The use of data has another benefit In the call to xyplot we see explicitly that the data frame gas is being used this can be helpful for understanding at some future point how the graph was produced 28 CHAPTER 5 GIVING DATA TO GENERAL DISPLAY FUNCTIONS 5 4 subset Suppose you want to redo figure 5 1 and omit the observations for which E is 1 1 or greater You could do this by xyplot NOx E lt 1 1 E E lt 1 1 data gas But it is a nuisance to repeat the logical subsetting E lt 1 1 And the nuisance would be much greater if there were many variables in the formula instead of just two It is typically easier to use the argument subset instead xyplot NOx E data gas subset E lt 1 1 The result is shown in figure 5 2 The argument subset can take any expression that subsets vectors 5 4 SUBSET 29 o o o O o 5 o o o 4 7
30. ave been ordered from bottom to top by the site medians Grand Rapids has the smallest median and Waseca has the largest Finally the year panels are ordered from left to right by the year medians 1932 has the smaller median and 1931 has the larger This median ordering is achieved by making the data set for each explanatory variable an ordered factor where the levels are ordered by the medians For example suppose variety started out as a factor without the median ordering We get the ordered factor through the following barley variety lt ordered barley variety levels names sort variety medians 86 CHAPTER 9 MULTIPANEL CONDITIONING 9 8 Controlling the Pages of a Multipage Display If a multipage display is sent to a screen device the default behavior is for the pages to be drawn in succession in other words a page is overwritten by the drawing of its successor This gives you little time to look at any but the last page You can control the page flow by par ask TRUE S PLUS queries you before each page is drawn hit return to go to the next page 9 9 Summary How to Lay Out a Multipanel Display To lay out a multipanel display in a certain way you specify the following e An ordering of the conditioning variables by the order you enter them in the argument formula e An ordering of the levels of each factor possibly by creating an ordered factor e The number of columns rows and pages through the argument
31. data region is given to a panel function that is an argument of the general display function The other arguments of the general display function manage the superstructure of the graph scales labels boxes around the data region and keys The panel function manages the symbols lines and so forth that encode the data in the data region Panel functions are discussed in chapter 12 4 4 Core S PLUS Graphics Trellis Graphics is implemented in the core S PLUS graphics Also when you write a panel function you use functions and graphics parameters from the core Core S PLUS graphics is discussed in chapter 12 4 5 Devices and Settings You need an output device to see a graph The specification of a screen device was introduced in chapter 3 Of course you also want to send graphs to printers and to files Trellis Graphics allows you to do this in many ways Sending graphs to files and printers is discussed in chapter 11 4 6 DATA STRUCTURES 21 Trellis Graphics has many settings for graph rendering details plotting symbols colors line types and so forth that are automatically chosen depending on the device you select Chapter 12 mentions the settings functions 4 6 Data Structures The general display functions take in data in certain ways The Trellis library contains several functions that change data structures of certain types to a data frame which makes it easier to pass the data on to the display functions C
32. e is much fine detail for example many peaks and valleys Figure 7 14 is a level plot of the gauss surface levelplot dataz datax datay data gauss aspect 1 cuts 6 The values of the surface are encoded by color or gray scale For devices with full color the scale goes from pure magenta to white and then to pure cyan If the device does not have full color a gray scale is used For a levelplot the range of the function values is divided into intervals and each interval is assigned a color A rectangle centered on each grid point is given the color of the interval containing the value of the function at the grid point In figure 7 14 there are six intervals The argument cuts specifies the number of intervals 65 7 16 LEVELPLOT 0 6 0 4 datay 0 2 1 5 0 0 0 5 1 0 datax Figure 7 14 66 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 17 wireframe Wireframe displays can be quite useful for displaying f x y when we have no need to study conditional dependence which is revealed far better by multipanel conditioning Figure 7 15 is a 3 D wireframe plot of the gauss surface wireframe dataz datax datay data gauss drape F screen list z 45 x 60 y 0 The arrows point in the direction of increasing values of the variables The argument screen is a list The three components of the list x y and z refer to screen axes The first component is horizontal
33. ellis device postscript sets up a screen and a hardcopy device Only one device is current and that one receives your graphics commands For our example postscript is current since it was set up last You can change the current device gt dev set which 2 motif 2 Now mot if is current You can show the current device gt dev cur motif 2 You can see the list of all active devices 11 5 MULTIPLE DEVICES DEV LIST DEV CUR DEV SET 115 gt dev list motif postscript 2 3 Finally as we have seen dev off turns off the current device and shows the new current device gt dev off postscript 3 On Windows you can use these functions but you can also use the Tools Graphics Device menu to list select and close graphics devices including Trellis devices You cannot open a Trellis device from this menu but you can manipulate it once it is open 116 CHAPTER 11 DEVICES Chapter 12 Panel Functions The data region of a single panel graph is the rectangular region where the data are plotted The data region of a multipanel graph is the collection of rectangular regions one per panel where the data go A panel function has the sole responsibility for drawing in the data region produced by a general display function The panel function is passed in through an argument of the general display function The other arguments of the general display function manage the superstructure of the graph
34. erlap margin space to use the page space as efficiently as possible Also to create visual harmony the right side of the box plot was bought in 05 units to make it line up with the right side of the scatterplot Arranging graphs on a page usually requires a few iterations using the eye as a judge of graph placement But it s fun 75 35 o E O D QO O 30 5 E O O S o 00 00 OG O we 25 7 o 6 5 E 00 o 000 o o o O 00 O Q6 o 8 o 20 000 0 ok O oo O GG a 2000 2500 3000 3500 Weight Van e Sporty ak wos mses areata eee O lesa rei Small o en Medium gt gt D Large i Compact gt e I Mileage Figure 8 1 76 CHAPTER 8 ARRANGING SEVERAL GRAPHS ON ONE PAGE PRINT Chapter 9 Multipanel Conditioning 9 1 A Data Set barley The data frame barley contains data from the barley experiment discussed in section 1 1 gt names barley 1 yield variety year site The first of these four variables is numeric and the remaining three are factors The experiment was run in the state of Minnesota in the 1930s At six sites ten varieties of barley were grown in each of two years The data collected for the experiment are the yields for all combinations of site variety and year so there are 6 x 10 x 2 120 observations 78 CHAPTER 9 MULTIPANEL CONDITIONING 9 2 About Multipanel Display Fi
35. es of the line segments connecting successive observations In the bottom panel banking allows a more accurate visual decoding of the slopes 1 2 SEEING THE SUNSPOT CYCLES 3 150 n 100 E 50 L h 0 E 1750 1800 1850 1900 Sunspot Number vs Year a AAA se PP E 0 m 1750 1800 1850 1900 Sunspot Number vs Year Figure 1 2 6 CHAPTER 1 ABOUT TRELLIS GRAPHICS 1 3 Trellis Features Trellis Graphics is a large leap forward in helping you to understand the structure of your data to understand the properties of models fitted to your data and to understand how well such models describe the structure of your data Here are a few of its many new features Multipanel Conditioning Figure 1 1 illustrates multipanel conditioning each panel of the figure shows the dependence of yield on variety conditional on year and site Multipanel conditioning is an exceptionally powerful visualization tool for studying the dependence of a response on two or more explanatory variables It is particularly effective for ferreting out interactions The panels are laid out into columns rows and pages Figure 1 1 has only one page but for large data sets conditioning can result in a large number of panels so more than one page is needed This layout of panels is reminiscent of a g
36. es of the other data set The variable fuel frame Type has five levels gt table fuel frameSType Compact Large Medium Small Sporty Van ES 3 13 13 9 7 Figure 7 4 is a q q plot comparing the quantiles of mileage for compact cars with the corresponding quantiles for small cars qq Type Mileage data fuel frame aspect 1 subset Type Compact Type Small The factor on the right side of the formula should have two levels Note that the default labels for the two scales are the names of the levels 75 QQQ 35 30 Small 25 4 30 35 Compact Figure 7 4 46 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 6 dotplot The dot plot which displays data with labels provides highly accurate visual decodings typically far more accurate than other methods for displaying labeled data Let us compute the mean mileage for each vehicle type gt mileage means lt tapply fuel frameSMileage fuel frameSType mean gt mileage means Compact Large Medium Small Sporty Van 24 13333 20 33333 21 76923 31 26 18 85714 Figure 7 5 is a dotplot of the log base 2 means dotplot names mileage means log mileage means base 2 aspect 1 cex 1 25 The argument cex is passed to the panel function to change the size of the dot of the dot plot in this case more on this in chapter 12 7 6 DOTPLOT 47 VNR SPONY A tee uo lt il i fe MediUM een poe Large prr O E
37. et gauss To further illustrate the general display routines we will compute a function of two variables over a grid datax lt rep seq 1 5 1 5 length 50 50 datay lt rep seq 1 5 1 5 length 50 rep 50 50 dataz lt exp datax 2 datay 2 datax datay gauss lt data frame datax datay dataz Thus dataz is the exponential of a quadratic function defined over a 50 by 50 grid in other words the surface is proportional to a normal density 7 15 contourplot Contour plots are helpful displays for studying a function f x y when we have no need to study the conditional dependence of f on x given y or of f ony given x Conditional dependence is revealed far better by multipanel conditioning Figure 7 13 is a contour plot of the gaussian surface contourplot dataz datax datay data gauss aspect 1 at seq 1 9 by 2 The argument at specifies the values as which the contours are to be computed and drawn If the argument is not specified reasonable default values are chosen 63 7 15 CONTOURPLOT 1 5 1 0 4 0 5 gt l OM ta 0 0 O 015 0 5 1 0 1 5 15 1 0 05 20 pal s o datax Figure 7 13 64 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 16 levelplot Level plots are also helpful displays for studying a function f x y They are no better than contour plots when the function is simple but often are better when ther
38. examples it does have are presented in great detail The book is available from the publisher Hobart Press at books hobart com 2 4 SOME IMPORTANT CONVENTIONS USED IN THIS MANUAL 11 2 4 Some Important Conventions Used in this Manual S PLUS commands and expressions names of S PLUS objects and the arguments of S PLUS functions appear in bold For example in this guide we will make use of a data frame gas which has two numeric variables NOx and E Later we will use the function xyplot and its argument formula to make a scatterplot of NOx against E xyplot formula gas NOx gasSE In the previous paragraph we used two other conventions The name of the function that makes the scatterplot is actually xyplot but we write it as xyplot to signal that this S PLUS object is a function Similarly the argument is formula but we write it as ormula to signal that we are making reference to an argument Some material is a bit detailed and could stand reading after you have a little experience with Trellis Graphics We have used smaller type for such material just as in this paragraph 12 CHAPTER 2 ABOUT THIS USER S MANUAL 2 5 Data Sets In this Manual a number of data sets are used as examples In addition Trellis Graphics contains functions that draw graphs to show how the system works these functions use data sets The data sets in these examples are contained in either the Trellis library or other S PLUS databases
39. file graph ps after the kick Similarly trellis device win printer printer type pcl f rmat printer file graph pel does the same for PCL Note that if you issue two commands to draw two separate graphs without changing the device in any way the first will overwrite the second You can also create a Windows metafile that can be inserted into documents trellis device win printer format placeable metafile file graph wmf On Windows the use of the above commands only alert Trellis Graphics what the device is so it can customize You still use Windows to actually select the device Also you can print hard copy by using the S PLUS File Print menu but this typically produces an undesirable graph because Trellis Graphics cannot customize the rendering to your hard copy device 11 4 Devices for this Manual The graphs for this Manual were produced on UNIX The device used for the black and white graphs was 114 CHAPTER 11 DEVICES trellis device postscript and the device used to produce the four color graphs at the beginning of the Manual was trellis device postscript color T 11 5 Multiple Devices dev list dev cur dev set S PLUS allows you to run multiple devices A common usage is to have a screen device and a hardcopy device the first for experimenting and the second for sending what you hope will be a finished product Suppose you are on UNIX Then trellis device motif tr
40. gure 9 1 uses multipanel conditioning to display the barley data Each panel displays the yields of the ten varieties for one year at one site variety is graphed along the vertical scale and yield is graphed along the horizontal scale For example the lower left panel displays values of variety and yield for Grand Rapids in 1932 The panel variables are yield and variety and the conditioning variables are year and site 9 3 formula Figure 9 1 was made by the following command dotplot variety yield year site data barley The is read as given Thus the formula is read as variety is graphed against yield given year and site Thus a simple use of formula creates a complex multipanel display 9 3 FORMULA Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota 79
41. hapter 5 mentions functions that restructure arrays time series and groups of vectors into data frames 22 CHAPTER 4 A ROADMAP OF TRELLIS GRAPHICS Chapter 5 Giving Data to General Display Functions For a graphics function to draw a graph it needs to know the data on which the drawing is based This chapter is about arguments to the Trellis drawing functions that allow you to specify the data 24 CHAPTER 5 GIVING DATA TO GENERAL DISPLAY FUNCTIONS 5 1 A Data Set gas The data frame gas contains two variables from an industrial experiment with 22 runs in which the concentrations of oxides of nitrogen NOx in the exhaust of an engine were measured for different settings of equivalence ratio E gt names gas 1 NOx ng gt dim gas 1 22 2 5 2 formula The function xyplot makes an x y plot a graph of two numerical variables the result might be scattered points curves or both xyplot has its own section in chapter 7 but for now we will use it to illustrate how to specify data Figure 5 1 is a scatterplot of gas NOx against gas E xyplot formula gas NOx gasSE The argument formula specifies the variables that are to be graphed In this case they are gas NOx and gas C For xyplot the variable to the left of the goes on the vertical axis and the variable to the right of the goes on the horizontal axis The formula gas NOx gas E is read as gas NOx is graphed against gas E 5
42. he horizontal or x scale and the label for the vertical or y scale are taken from the argument formula We can specify these scale labels as well as a main title at the top and a subtitle at the bottom This is illustrated in figure 10 2 xyplot NOx E data gas aspect xlab ylab main 1 2 Equivalence Ratio Oxides of Nitrogen Air Pollution sub Single Cylinder Engine 10 2 XLAB YLAB MAIN SUB Oxides of Nitrogen 99 Air Pollution O a a O O O O O o9 O O 0 7 0 8 0 9 1 0 1 1 1 2 Equivalence Ratio Single Cylinder Engine Figure 10 2 100 CHAPTER 10 SCALES AND LABELS Each of these four label arguments can also be a list One component of the list can be a new character string for the text of the label The other components specify the size font and color of the text The component cex specifies the size font a positive integer specifies the font and col a positive integer specifies the color Figure 10 3 changes the sizes of the title and subtitle xyplot NOx E data gas aspect 1 2 xlab Equivalence Ratio ylab Oxides of Nitrogen main List Air Pollution cex 2 sub list Single Cylinder Engine cex 1 25 10 2 XLAB YLAB MAIN SUB Oxides of Nitrogen 101 0 7 0 8 Air Pollution 0 9 1 0 Equivalence Ratio Single Cylinder Engine 1 1 1 2 Figure 10
43. ht inches 2 1 0 1 2 Soprano 2 ea Soprano 1 Unit Normal Quantile 17 Figure 3 1 18 CHAPTER 3 GETTING STARTED Chapter 4 A Roadmap of Trellis Graphics 4 1 General Display Functions The Trellis library has a collection of general display functions that draw different types of graphs For example xyplot makes x y plots dotplot makes dot plots and wireframe makes 3 D wireframe displays The functions are general because they have the full capability of Trellis Graphics including multipanel conditioning The general display functions are introduced in chapter 7 4 2 Common Arguments There are a set of common arguments that all general display functions employ The usage of some of these arguments varies but each has a common purpose across all functions Many of the general display functions also have arguments that are specific to the types of graphs that they draw The common arguments are discussed in chapters 5 6 9 10 and 12 20 CHAPTER 4 A ROADMAP OF TRELLIS GRAPHICS 4 3 Panel Functions Panel functions are a critical aspect of Trellis Graphics They make it easy to tailor displays to your data even when the displays are quite complicated ones with many panels The data region of a panel on a graph resulting from a general display function is a rectangle that just encloses the data The sole responsibility for drawing in a
44. ing variable vary the next fastest and so forth For figure 9 1 the order of the packets is 9 5 PACKET ORDER AND PANEL ORDER 81 1932 Grand Rapids 1931 Grand Rapids 1932 Duluth 1931 Duluth 1932 University Farm 1931 University Farm 1932 Morris 1931 Morris 1932 Crookston 1931 Crookston 1932 Waseca 1931 Waseca The panels of a multipanel display are also ordered The bottom left panel is panel one From there we move fastest through the columns next fastest through the rows and the slowest through the pages The panel ordering rule is like a graph not like a table the origin is at the lower left and as we move either from left to right or from bottom to top the panel order increases The following shows the panel order for figure 9 1 which has two columns six rows and one page 11 12 9 10 7 8 5 6 3 4 1 2 In Trellis Graphics packets are assigned to panels according to the packet order and the panel order Packet 1 goes in panel 1 packet 2 goes into panel 2 and so forth In figure 9 1 the two orderings result in the year variable changing along the columns and the site variable changing along the rows Note that as the levels for one of these factors increase the darkened bars in the strip label for the factor move from left to right 82 CHAPTER 9 MULTIPANEL CONDITIONING 9 6 layout Multipanel conditioning is a powerful tool for understanding how a response depends on two or more explanatory variables In s
45. istake you will find the Trellis graphs are not rendered nearly as well because the graphical parameters of the core S PLUS graphics will not be customized to the device as they are when you use trellis device 3 3 dev off You turn off a graphics device by the command dev off 3 4 TRELLIS OBJECTS 15 3 4 Trellis Objects Trellis display functions return objects of class trellis The expression xyplot formula gas NOx gasSE draws a graph on the graphics device The expression foo lt xyplot formula gas NOx gas E saves the graph in foo but does not draw it If you then type foo the graph is drawn 3 5 print trellis It is the print method for trellis objects that sends a graph to a device In the example of the previous section typing foo causes S PLUS to use print foo to display the graph The reason for mentioning this is that you must sometimes explicitly use print foo when the graph is made from a function or from a source file 16 CHAPTER 3 GETTING STARTED 3 6 Example Functions The example functions in the Trellis library draw displays to show you the Trellis capabilities and a bit about how Trellis works The names of the example functions all begin with example You can see a list of all of these functions using the online help trellis examples Figure 3 1 shows the result of executing one of these example functions example normal qq 3 6 EXAMPLE FUNCTIONS Heig
46. iving panel special to xyplot xyplot NOx E data gas aspect 1 2 panel panel special 12 3 WRITING A PANEL FUNCTION PANEL 121 M Bid Li gt _ A p n gt 9 3 4 le 24 1 0 7 0 8 0 9 1 0 1 1 1 2 E Figure 12 2 122 CHAPTER 12 PANEL FUNCTIONS The panel function for figure 12 2 also could have been defined as part of the xyplot command Xyplot NOx E data gas aspect 1 2 panel function x y biggest lt y max y points x biggest y biggest pch points x biggest ylbiggest pch M 12 4 A Panel Function for a Multipanel Display In most cases a panel function that is used for a single panel display can be used for a multipanel display as well In figure 12 3 the panel function panel special just used in figure 12 2 is used to show the maximum value of NOx on each panel of a multipanel display of the ethanol data xyplot NOx E C data ethanol aspect 1 2 panel panel special 12 4 A PANEL FUNCTION FOR A MULTIPANEL DISPLAY 123 c 44 M 34 L 24 gt 14 R p c I 4 3 J Es 4 di lt 4 Fi mue sj M 34 lt x i i 24 L 14 F I c 4 J le E 44 L 34 L 24 a L 14 T T T T 0 6 0 8 1 0 1 2
47. me ee SR RAI O EE A EPE mame mr e dc sia GG b a EEE DE iii SOR a a aoe mamasa e m O ea e st RP EA Od Za ra Glabron DT Glabron 2 19 pm e EE ee sen se ONE PE n e eee aa ind ena ista ZA PSR ZE Me Pee ENTER N rw R EAT I Mia Pea zZ 2 19 SERRE RE ri sil ee ee ee Mie eee ceeded RR SAR EE tiro pala E E EE PREZ ZZ RENO es ne EEE REE EEE EE O veo E L nani nossa nono nono Li T T T T T T T T 20 30 40 50 60 Figure 9 3 9 7 MAIN EFFECTS ORDERING 85 9 7 Main Effects Ordering For the barley data the explanatory variables are categorical The data set for each is a factor Since there are only two years the year variable is treated as a factor rather than a numeric vector For each factor consider the median yield for each level For example for variety the level medians are gt variety medians lt tapply barleySyield barleySvariety median gt variety medians Svansota No 462 Manchuria No 475 Velvet Peatland 28 55 30 45 30 96667 31 06667 32 15 32 38334 Glabron No 457 Wisconsin No 38 Trebi 32 4 33 96666 36 95 39 2 The barley displays in figures 9 1 to 9 3 use an important display method main effects ordering of levels This greatly enhances our ability to perceive effects Consider figure 9 1 On each panel the varieties are ordered from bottom to top by the variety medians Svansota has the smallest median and Trebi has the largest The site panels h
48. n persp Trellis Graphics also has a better mechanism for the details of rendering graphs aspect ratio plotting symbols colors line types panel layouts coordinated scales on different graphs and so forth The defaults work better and users can now make changes with much more effective and predictable results 1 6 Who The visualization methods of Trellis Graphics and the design and implementation of the S PLUS code resulted from several years of hard running by Rick Becker Bill Cleveland and Ming Shyu at AT amp T Bell Laboratories in Murray Hill N J At StatSci Stephen Kaluzny took the baton pass with great skill and integrated the system into S PLUS Chapter 2 About This User s Manual 2 1 What Does this Manual Cover This User s Manual provides an introduction to Trellis Graphics Version 2 0 This version first appeared in S PLUS releases in the fall of 1995 The Manual was meant to be read from the beginning to teach you how to use Trellis It was also meant to serve as a reference while you are using Trellis the Table of Contents should be helpful for locating sections that describe the feature in which you are interested Also the Manual was meant to be introductory To keep things simple some of the more detailed features are mentioned but not discussed You can use the online help to get the details The Manual was written by two of the Trellis Graphics developers Rick Becker and Bill Cleveland of AT amp T Bell L
49. n puts space between any two adjacent columns or any two adjacent rows page can add page numbers text or even graphics to each page of a multipage Trellis display prepanel can help achieve a desired aspect ratio or scale limits when the ratio or the limits depend on what is drawn by a panel function For more information use trellis args Chapter 10 Scales and Labels The general display functions presented in chapter 7 have arguments that specify the scales and labels of graphs These arguments are discussed in this chapter 10 1 Little Languages Three of the arguments scales key and strip are powerful arguments with many specifications scales controls the tick marks and their labels key allows a key or legend to be added to a graph and strip controls the strip labels Each of these arguments is complex enough to be regarded as a little language We will discuss them only briefly For more information use trellis args key and strip default 96 CHAPTER 10 SCALES AND LABELS 10 2 xlab ylab mains sub Figure 10 1 is a scatterplot of NOx against E for the gas data which were introduced in section 5 1 xyplot NOx E data gas aspect 1 2 10 2 XLAB YLAB MAIN SUB 97 o s Gia e O om BE o o 4 9 x o 5 3 3 2 o i a o 1 o e 0 7 0 8 0 9 1 0 1 1 1 2 Figure 10 1 98 CHAPTER 10 SCALES AND LABELS In figure 10 1 the label for t
50. ol lty pch lwd cex Use par for their definitions 12 8 Settings show settings trellis par get trellis par set It is sometimes useful in writing a panel function to make use of the device settings that govern the rendering There are three functions that work with the settings show settings shows graphically the values of the settings trellis par get lets you get the settings for use in panel functions trellis par set lets you change the settings See the online help for details
51. or are computed by commands given in the Manual Chapter 3 Getting Started 3 1 library In S PLUS the Trellis Graphics library is named trellis it contains functions objects that are used by the Trellis code data sets and example functions that draw displays to help you to see how Trellis Graphics works If you are on Windows the library is automatically attached If you are on UNIX running S PLUS Version 3 3 or earlier you need to attach the library gt library trellis 3 2 trellis device You need to have a graphics device on which to draw If you have not specified a device but you execute a function that draws a graph then a color screen device is automatically set up for you 14 CHAPTER 3 GETTING STARTED The two devices that come up automatically can also be specified directly with trellis device On Windows the command is trellis device win graph On UNIX the command is trellis device motif For some UNIX systems there is another screen device openlook You can send Trellis graphs to a printer Also you can set up multiple devices for example you might have two devices that are graphics windows on your screen and one device that is a printer Information is given about this in chapter 11 WARNING If you have used the old S PLUS graphics then you will know that you set up devices in a different way For example on Windows you set up the screen device by win graph If you do this by m
52. r a File On UNIX the command trellis device postscript onefile FALSE sets up a PostScript device for direct sending to the printer A graph goes to the printer when you kick the system Adding color TRUE to the argument list specifies color postscript On UNIX the command trellis device postscript onefile FALSE print it FALSE file greatgraph ps sets up a PostScript device for sending to the file greatgraph ps The file writing is completed after you kick Again adding color TRUE to the argument list specifies color postscript Note that if you issue two commands to draw two separate graphs without changing the device in any way the first will overwrite the second On Windows you can specify various types of printers The command trellis device win printer printer type postscript specifies a PostScript printer for direct sending A graph goes to the printer when you kick the system Adding color TRUE to the argument list specifies color postscript For PCL printers LaserJet compatible use trellis device win printer printer type pcl However while you can get color printing on PCL printers by changing arguments to Trellis functions there is not yet an argument color to customize PCL for color printing 11 4 DEVICES FOR THIS MANUAL 113 On Windows the command trellis device win printer printer type postscript Format printer file graph ps writes PostScript to the
53. rs Since then the data have been analyzed and re analyzed R A Fisher presented the data for five of the sites in his classic book The Design of Experiments Publication in the book made the data famous and many others subsequently analyzed the them usually to illustrate a new statistical method Then in the early 1990s the data were visualized by Trellis Graphics The result was a big surprise Through 60 years and many analyses an important happening in the data had gone undetected Figure 1 1 shows the happening which occurs at Morris For all other sites 1931 produced a significantly higher overall yield than 1932 The reverse is true at Morris But most importantly the amount by which 1932 exceeds 1931 at Morris is similar to the amounts by which 1931 exceeds 1932 at the other sites Either an extraordinary natural event such as disease or a local weather anomaly produced a strange coincidence or the years for Morris were inadvertently reversed More Trellis displays a statistical modeling of the data and some background checks on the experiment led to the conclusion that the data are in error But it was Trellis displays such as figure 1 1 that provided the Aha which led to the conclusion 1 1 DISCOVERING THE MISSED HAPPENING AT MORRIS 3 Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet No 475 Manchuria No 462 Svansota Trebi Wisconsin No 38 No 457 Glabron Peatland Velvet
54. scales labels boxes around the data region and keys The panel function manages the symbols lines and so forth that encode the data in the data region Every general display function has a default panel function In all examples given so far in this Manual the default panel function has been doing the drawing 118 CHAPTER 12 PANEL FUNCTIONS 12 1 How to Change the Rendering in the Data Region You can change what is drawn in the data region by one of two mechanisms First a default panel function has arguments You can change the rendering by using these arguments in fact you can give them to the general display function which will pass them along to the panel function Second you can write your own panel function 12 2 Passing Arguments to a Default Panel Function The name of the default panel function for a general display function is panel followed by the name of the general function For example the default panel function for xyplot is panel xyplot You can use S PLUS online help to see the arguments of a default panel function For example panel xyplot tells you about the panel function for xyplot You can give an argument to a panel function by giving it to the general display function the general display function passes it on to the panel function Figure 12 1 uses an argument pch of panel xyplot to specify a as the plotting symbol xyplot NOx E data gas aspect 1 2 DOM Ma 12 2 PA
55. t 3 4 NOx 33 0 7 0 8 0 9 1 0 1 1 1 2 Figure 6 1 34 CHAPTER 6 ASPECT RATIO Setting aspect xy banks line segments to 45 Here is how it works Suppose x and y are data points to be plotted Consider the line segments that connect successive points The aspect ratio is chosen so that the absolute values of the slopes of these segments is centered on 45 This done in figure 6 2 by the expression xyplot NOx E data gas aspect xy We have used the data themselves in this example to carry out banking just to illustrate how it works The resulting aspect ratio is about 0 4 Ordinarily though we should bank based on a smooth underlying pattern in the data that is we should bank based on the line segments of a fitted curve You can do that with Trellis Graphics as well NOx 35 1 2 Figure 6 2 36 CHAPTER 6 ASPECT RATIO Chapter 7 General Display Functions Each general display function draws a particular type of graph For example dotplot makes dot plots wireframe makes 3 D wireframe displays histogram makes histograms and xyplot makes x y plots This chapter describes a collection of general display functions 7 1 A Data Set fuel frame The data frame fuel frame contains five variables that measure characteristics of 60 automobile models gt names fuel frame 1 Weight Disp Mileage Fuel Type gt dim fuel frame 1 60
56. t OM W 00 GDGO O a0 0000 YDE medium o 6 o doo o OOO lt Large Aman am o o 00000 amo O 8 5 Compact CARE e O 00 do 55 E do A O o oo olo s Bh 8 oo al DO o o L 50 oo co 0000 O OD O os a oto g 8 o p45 o8 a Eo 0 Fuel w E g 2 GO O jn 3 5 8 E o z s pew e bic _ FF a o O Lan O Co E G gt do Bo 68 o o L 30 o mo Mileage 8 g 9 O O 25 O Ta 090 Bo o 0 o E o o o O g 20 4 m o 8 8 O do 9 2 E O OL 300 pama 300 O od O O o o 0 0 200 O O g al e Oo Ebo o o 008 99 o 8 lo 150 4 O 0 o O 8 bik a go gg 800 8 da A b Bo piso 8 o 99 z 8 TINO 5 3000 3500 ES o o eg o 8 L 3500 0000 o a O D Ra o o o p o 889 9 8 o L 3000 O i BE E Weight e o En 8 g 8 8 2500 4 Q O O 5 O ca 60 2000 O O O 2000 2500 O doo 8 Figure 7 11 60 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 13 parallel Parallel coordinates are an interesting method but it is unclear at the time of this writing whether they have the power to uncover structure that is not more readily apparent using other graphical methods Figure 7 12 is a parallel coordinates display of the variables in fuel frame parallel fuel frame 7 13 PARALLEL A Type gt _ ZY LS PRA NU y D gt Fuel i 4 4 fi Mileage IG Nr A n Disp FF GE Weight Max Figure 7 12 62 CHAPTER 7 GENERAL DISPLAY FUNCTIONS 7 14 A Data S
57. ta region divided by the width is controlled by aspect This argument was introduced in chapter 6 for 2 D displays The behavior of aspect for the two 3 D general display functions wireframe and cloud is somewhat different Since there are three axes we must specify two aspect ratios to specify the shape of the 3 D box around the data Suppose the formula and the aspect arguments are formula z x y aspect c 1 2 Then the ratio of the length of the y axis to the length of the x axis is 1 and the ratio of the length of the z axis to the length of the x axis is 2 10 6 The Text in Strip Labels The default text in the strip label for a numeric conditioning variable is the name of the variable This is illustrated in figure 10 6 which displays the ethanol data introduced in section 9 10 xyplot NOx E C data ethanol 10 6 THE TEXT IN STRIP LABELS NOx 107 C amp O O o O z o O 0 6 0 8 1 0 1 2 gt Lc G 4 O O O a u O gt 8 O o 2 o le O o GO 1 o o O o C I o 9 o o S 6 L O O O O E O 8 o O 8 O o O 00 O T T T T T 0 6 0 8 1 0 1 2 Figure 10 6 108 CHAPTER 10 SCALES AND LABELS The default text in the strip label of a factor conditioning variable is the name of the factor level for the panel This is illustrated in figure 10 7 which displays the barley data introduced in section 9 1 dotplot variety yield
58. uch an analysis it is typically important to make as many displays as necessary to have each explanatory variable appear at least once as a panel variable In figure 9 1 variety an explanatory variable appears as a panel variable We will make a new display with site as a panel variable The argument layout specifies the numbers of columns rows and pages dotplot site yield year variety data barley layout c 2 5 2 The result is shown in figure 9 2 the first page and in figure 9 3 the second page If we do not specify layout Trellis Graphics chooses the numbers of columns rows and pages by a layout algorithm The algorithm takes into account the aspect ratio the number of packets the number of conditioning variables and the number of levels of each conditioning variable It chooses the numbers to maximize the size of the graph within the graphics region 9 6 LAYOUT Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids Waseca Crookston Morris University Farm Duluth Grand Rapids 20 30 40 50 60 1 mu vet 2 19 EEE EE R o EEE ENE ne ens FN de o RZA EM A EN CSRO eae nea ee FEE En Age e ER e nae o

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