Mixed models in R using the lme4 package Part 2: Lattice...
Transcript of Mixed models in R using the lme4 package Part 2: Lattice...
![Page 1: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/1.jpg)
Presenting data xyplot densityplot dotplot
Mixed models in R using the lme4 packagePart 2: Lattice graphics
Douglas Bates
University of Wisconsin - Madisonand R Development Core Team
University of LausanneJuly 1, 2009
![Page 2: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/2.jpg)
Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
![Page 3: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/3.jpg)
Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
![Page 4: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/4.jpg)
Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
![Page 5: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/5.jpg)
Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
![Page 6: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/6.jpg)
Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
![Page 7: Mixed models in R using the lme4 package Part 2: Lattice ...lme4.r-forge.r-project.org/slides/2009-07-01-Lausanne/2LatticeD.pdf · 7/1/2009 · There are several styles of graphics](https://reader030.fdocuments.us/reader030/viewer/2022041014/5ec53c8a27207d51475aa40d/html5/thumbnails/7.jpg)
Presenting data xyplot densityplot dotplot
Exploring and presenting data
• When possible, use graphical presentations of data. Timespend creating informative graphical displays is well invested.
• Ron Snee, a friend who spent his career as a statisticalconsultant for DuPont, once said, “Whenever I am writing areport, the most important conclusion I want to communicateis always presented as a graphic and shown early in the report.On the other hand, if there is a conclusion I feel obligated toinclude but would prefer people not notice, I include it as atable.”
• One of the strengths of R is its graphics capabilities.
• There are several styles of graphics in R. The style inDeepayan Sarkar’s lattice package is well-suited to the type ofdata we will be discussing.
• Deepayan’s book, Lattice: Multivariate Data Visualizationwith R (Springer, 2008) provides in-depth documentation andexplanations of lattice graphics.
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Presenting data xyplot densityplot dotplot
The formula/data method of specifying graphics
• The first two arguments to lattice graphics functions areusually formula and data.
• This specification is used in model-fitting functions (lm, aov,lmer, ...) and in other functions such as xtabs.
• The formula incorporates a tilde, (∼), character. A one-sidedformula specifies the value on the x-axis. A two-sided formulaspecifies the x and y axes.
• The second argument, data, is usually the name of a dataframe.
• Many optional arguments are available. Ones that we will usefrequently allow for labeling axes (xlab, ylab), and controllingthe type of information, type.
• The lattice package is not attached by default. You mustenter library(lattice) before you can use lattice functions.
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Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
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Presenting data xyplot densityplot dotplot
A simple scatterplot in lattice
> xyplot(optden ~ carb, Formaldehyde)
carb
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Presenting data xyplot densityplot dotplot
Scatterplots in lattice
• A scatter plot is the most versatile plot in applied statistics. Itis simply a plot of a numeric response, y, versus a numericcovariate, x.
• The lattice function xyplot produces scatter plots. I typicallyspecify type = c("g","p") requesting a background grid inaddition to the plotted points.
• The type argument takes a selection from
”p” points”g” background grid”l” lines
”b” both points and lines”r” reference (or “regression”) straight line
”smooth” scatter-plot smoother lines
• In evaluating a scatterplot the aspect ratio (ratio of verticalsize to horizontal size) can be important. In particular,differences in slopes are most apparent near 45o.
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General principles of lattice graphics
• The formula is of the form ∼x or y∼x or y∼x | f where x isthe variable on the x axis (usually continuous), y is thevariable on the y axis and f is a factor that determines thepanels.
• Titles can be added with xlab, ylab, main and sub. Titles canbe character strings or, more generally, expressions that allowfor special characters, subscripts, superscripts, etc. Seehelp(plotmath) for details.
• The groups argument, if used, specifies different point stylesand different line styles for each level of the group. If lines arecalculated, each group has separate lines.
• If groups is used, we usually also use auto.key to add a keyrelating the line or point styles to the groups.
• The layout specifies the number of columns and rows ofpanels.
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An enhanced scatterplot of the Formaldehyde data
Amount of carbohydrate (ml)
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Saving plots
• I recommend using the facilities in the R application to saveplots and transcripts.
• To save a plot, ensure that the graphics window is active anduse the menu item File→Save To Clipboard→Windows
Metafile. (On a Mac, save as PDF.) Then switch to a wordprocessor and paste the figure.
• Adjust the aspect ratio of the graphics window to suit thepasted version of the plot before you copy the graphic.
• Those who want more control (and less cutting and pasting)could consider the Sweave system or the odfWeave package.
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Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
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Presenting data xyplot densityplot dotplot
Histograms and density plots• A histogram is a type of bar plot created from dividing
numeric data into adjacent bins (typically having equal width).• The purpose of a histogram is to show the distribution or
density of the observations. It is almost never a good way ofdoing this.
• A densityplot is a better way of showing the density or, evenbetter, comparing the densities of observations associatedwith different groups. Also, densityplots for different groupscan be overlaid.
• If you have only a few observations you may want to use acomparative box-and-whisker plot (bwplot) or a comparativedotplot instead. Density plots based on a small number ofobservations tend to be rather “lumpy”.
• If the data are bounded, perhaps because the data must bepositive, a density plot can blur the boundary. However, thismay indicate that the data are more meaningfully representedon another scale.
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Presenting data xyplot densityplot dotplot
Histogram of the InsectSprays data> histogram(~count, InsectSprays)
count
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Presenting data xyplot densityplot dotplot
Density plot of the InsectSprays data> densityplot(~count, InsectSprays)
count
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Presenting data xyplot densityplot dotplot
Density plot of the square root of the count> densityplot(~sqrt(count), InsectSprays, xlab = "Square root of count")
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Presenting data xyplot densityplot dotplot
Density plot of the square root with fancy label> densityplot(~sqrt(count), InsectSprays, xlab = expression(sqrt("count")))
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Presenting data xyplot densityplot dotplot
Comparative density plot of square root> densityplot(~sqrt(count), InsectSprays, groups = spray,+ auto.key = list(columns = 6))
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A B C D E F
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Presenting data xyplot densityplot dotplot
Comparative density plot, separate panels> densityplot(~sqrt(count) | spray, InsectSprays, layout = c(1,+ 6))
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Presenting data xyplot densityplot dotplot
Comparative density plot, separate panels, strip at left> densityplot(~sqrt(count) | spray, InsectSprays, layout = c(1,+ 6), strip = FALSE, strip.left = TRUE)
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Presenting data xyplot densityplot dotplot
Comparative density plot, separate panels, reordered> densityplot(~sqrt(count) | reorder(spray, count), InsectSprays)
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Presenting data xyplot densityplot dotplot
Outline
Presenting data
Scatter plots
Histograms and density plots
Box-and-whisker plots and dotplots
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Presenting data xyplot densityplot dotplot
Box-and-whisker plot and dotplot
• A box-and-whisker plot gives a rough summary (based on thefive-number summary - min, 1st quartile, median, 3rd quartile,max) of the distribution.
• A dotplot consists of points on a number line. For a largenumber of data values we jitter the y values to avoidoverplotting. By default a density plot also shows a dotplot.
• Box-and-whisker plots or dotplots are often used forcomparison of groups.
• It is widely believed that a comparative boxplot should havethe response on the vertical axis. Most of the time it is moreeffective to put the response on the horizontal axis.
• If the default ordering of the groups is arbitrary reorder themaccording to the level of the response (mean response, bydefault).
• Reordering makes it easier to see if the variability increaseswith the level of the response.
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Presenting data xyplot densityplot dotplot
Vertical comparative box-and-whisker plot> bwplot(sqrt(count) ~ spray, InsectSprays)
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Presenting data xyplot densityplot dotplot
Horizontal comparative box-and-whisker plot> bwplot(spray ~ sqrt(count), InsectSprays)
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Presenting data xyplot densityplot dotplot
Reordered horizontal comparative box-and-whisker plot> bwplot(reorder(spray, count) ~ sqrt(count), InsectSprays)
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Presenting data xyplot densityplot dotplot
Compressed horizontal comparative box-and-whisker plot> bwplot(reorder(spray, count) ~ sqrt(count), InsectSprays,+ aspect = 0.2)
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• You can extract much more information from this, compressedplot than from the original vertical box-and-whisker plot.
• In Edward Tufte’s phrase, this plot has a greater“information/ink ratio”.
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Presenting data xyplot densityplot dotplot
Comparative dotplots
• When the number of observations per group is small, abox-and-whisker plot can obscure the structure of the data,rather than illuminating it.
• By default, the density plot provides a dotplot on the “rug”.
• A comparative dotplot displays all of the data. The principlesdescribed for a comparative boxplot (factor on vertical axis,reorder levels if no natural order, choose an appropriate scale)apply here too.
• By default, the character in the dotplot is filled. I often useoptional arguments pch = 21 and jitter.y = TRUE to avoidoverplotting.
• Setting type = c("p","a") provides a line joining the groupaverages.
• Interaction plots can be produced as a comparative dotplotwith groups
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Presenting data xyplot densityplot dotplot
Comparative dotplot of InsectSprays
> dotplot(reorder(spray, count) ~ sqrt(count), InsectSprays,+ type = c("p", "a"), pch = 21, jitter.y = TRUE)
count
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Presenting data xyplot densityplot dotplot
Summary
• In order of importance the graphic displays I consider arescatter plots, density plots, box-and-whisker plots, dot plotsand histograms.
• Pay careful attention to layout and axis labels. Include unitsin the axis labels, if known.
• For mixed models we always have at least one unorderedcategorical covariate and often have a numeric response.Comparative dot plots and box-and-whisker plots will beimportant data presentation techniques for us.
• Plots of a continuous response by levels of a categoricalvariable work best with the category on the vertical axis.Consider reordering the levels of the category if they do nothave a natural order.