CODEWITHSUNDEEP
rgraphicsgraphplotggplot2
Remi.b
Remi.b

Reputation: 18239

Displaying estimates, confidence intervals and true parameters

Below is the kind of data I have. Please don't pay attention to how the data are created, neither on whether the numbers seem realistic in whatever context. The question is only about graphics.

set.seed(12)
TrueParameter = rep(c(10,15,18), each=8)
Estimate = rep(c(rnorm(8, 10, 1), rnorm(8, 15, 0.5), rnorm(8, 18, 2)))
LowBound95 = Estimate - abs(rnorm(24, 0, 5))
HighBound95 = Estimate + abs(rnorm(24, 0, 5))
LowBound99 = LowBound95 - abs(rnorm(24, 0, 5))
HighBound99 = HighBound95 + abs(rnorm(24, 0, 5))
dt = data.frame(TrueParameter = TrueParameter, Estimate = Estimate, LowBound95 = LowBound95, HighBound95 = HighBound95, LowBound99 = LowBound99, HighBound99 = HighBound99)

TrueParameter  Estimate LowBound95 HighBound95 LowBound99 HighBound99
1             10  8.519432  3.3932082   12.176699  1.2461752    14.43811
2             10 11.577169 10.2402453   14.040165  9.3276472    17.51385
3             10  9.043256  8.0477272    9.256680  7.5311749    10.45175
4             10  9.079995  8.4243818    9.643348  5.2551908    14.67984
5             10  8.002358  7.2733584   10.286494  0.9180895    19.92009
6             10  9.727704  7.9173804   19.829378  5.9976284    20.08653
7             10  9.684651  6.3147455   14.939102  3.7309665    23.94172
8             10  9.371745 -0.9884341   13.045005 -1.8782768    15.80229
9             15 14.946768 12.2416248   17.643017 12.2203346    18.17831
10            15 15.214007  9.8615466   21.785371  3.4912489    25.73099
11            15 14.611140 12.7488565   15.861334 11.7383049    17.08261
12            15 14.353059 11.9273521   15.924082  6.1050227    17.84498
13            15 14.610217 13.2362959   16.642950 13.1193988    22.48913
14            15 15.005976 12.6084131   19.978079  8.1226293    27.56944
15            15 14.923792 10.9332653   19.202634 10.0496430    19.56754
16            15 14.648268  9.6260119   15.633912  4.0574665    18.27229
17            18 20.377758 19.8528371   24.549384 17.1433928    27.17201
18            18 18.681025 12.9010601   22.914975  8.0840684    26.64948
19            18 19.013936 16.1232632   28.784463 14.2410212    34.69653
20            18 17.413390  9.4352614   28.159690  4.5118924    34.93323
21            18 18.447283 16.9047645   23.302884 12.4169675    24.36431
22            18 22.014403 19.7670733   27.739711 19.1207606    28.18712
23            18 20.023958 15.1386918   22.650961  9.9701769    23.93612
24            18 17.395082 16.4450922   18.646682 14.7336458    24.66812

The first column is the known true parameter of the data. The second column is the estimate of this true parameter and the columns three and four represent the 95% confidence interval for this estimate while the columns 5 and 6 represent the 99% confidence interval.

My question is both a question of programming and a question of design (I hope it doesn't make this post too off-topic then); How can I best display those data?

I was thinking about having all true parameters the ones below the others (whether or not they happen to take the same value). The true parameters would then be represented by a vertical line. The two confidence intervals would be drawn as horizontal lines (in two colours) with a black dot for the estimate. We could then easily see what fraction of the confidence intervals overlap the true parameter. But I welcome someone to come up with a different design! Here is a similar to display this kind of data. The differences are that the parameter is not a constant in my case and that I'd like to be able to display several confidence intervals.

enter image description here

I usually use ggplot2 but I welcome answers based on any R functions and package. There might actually exist packages that would be very convenient for this kind of plot.

Upvotes: 2

Views: 885

Answers (1)

jbaums
jbaums

Reputation: 27398

I know you asked for convenient functions and/or packages, but anyway... here's how I usually do this in base R.

I often plot multiple confidence intervals with by varying lwd.

For example:

plot(dt$Estimate, pch=20, ylim=range(pretty(c(dt$LowBound99, dt$HighBound99))),
     xlab='', ylab='', las=1, cex.axis=0.8, cex=1.5, xaxt='n')
segments(seq_len(nrow(dt)), dt$LowBound99, y1=dt$HighBound99, lend=1)
segments(seq_len(nrow(dt)), dt$LowBound95, y1=dt$HighBound95, lwd=4, lend=1)

I think it's useful to use lend=1 for segments so that the ends of intervals are clearly defined.

enter image description here

You can then overlay true parameter values as points:

points(dt$TrueParameter, pch=21, bg='white')

enter image description here

Or plot them as horizontal segments beneath the other elements:

plot(dt$Estimate, pch=20, ylim=range(pretty(c(dt$LowBound99, dt$HighBound99))),
     xlab='', ylab='', las=1, xaxt='n',
     panel.first=plot(dt$TrueParameter ~ factor(seq_len(nrow(dt))), add=TRUE,
                      xlab='', ylab='', axes=FALSE, border='gray70', medlwd=4))

segments(seq_len(nrow(dt)), dt$LowBound99, y1=dt$HighBound99, lend=1)
segments(seq_len(nrow(dt)), dt$LowBound95, y1=dt$HighBound95, lwd=4, lend=1)

enter image description here

Above, we take advantage of the horizontal median indicators of boxplots, which are deployed by default when x is factor and y is numeric. (Since there is only one true value per x, the rest of the box is not drawn.) We could use points with pch='-' or maybe pch=-0x2013L here, but they are a little poorly centred around the plotting coordinate.

Upvotes: 2

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