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CHAPTER14. CONDITIONINGANDPLOTTINGTHREEORMOREVARIABLES
143
xYplot(Cbind(y, Lower, Upper) ∼ month | factor(year),
method=’filled bands’, type=’l’, data=s)
# Figure 14.3
# Use method=’bands’ for ordinary unfilled bands
2
3
4
5
6
7
2
4
6
8
10
12
1997
2
4
6
8
10
12
1998
month
y
Figure 14.3:
Nonparametric bootstrap conﬁdence limits for each month, but depicted with ﬁlled
bands
·
Here is an example using double bands, to depict the following quantiles:
.1 .25 .5 .75 .9
. The
0.25
and
0.75
quantiles are drawn with line thickness 2,
and the central line with a thickness of 4. Note that summarize produces a
matrix for
y
when
type=’matrix’
is speciﬁed, and
Cbind(y)
trusts the ﬁrst
column to be the point estimate (here the median)
s ← summarize(y, llist(month,year), quantile, probs=c(.5,.1,.25,.75,.9),
type=’matrix’)
xYplot(Cbind(y) ∼ month | factor(year), data=s,
type=’l’, method=’bands’, lwd.bands=c(1,2,2,1), lwd=4)
# Figure 14.4
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CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
144
2
4
6
8
2
4
6
8
10
12
1997
2
4
6
8
10
12
1998
month
y
Figure 14.4:
Central line depicts the median, and bands depict the
0.1,0.25,0.75,0.9
quantiles of the
raw data
xYplot
with
method=’quantile’
or
method=functionname
·
method=’quantile’
:
xYplot
automatically groups the
x
variable into inter-
vals containing a target of
nx
observations
·
Default value of
nx
is the lesser of 40 and
1
4
×
stratum size (specify
nx=0
to
do no grouping; useful when
x
variable is discrete such as
month
)
·
Quantiles given by the
probs
argument; default is
probs=c(.5,.25,.75)
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CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
145
·
Within each
x
group computes three quantiles of
y
and plots these as three
lines
·
Mean
x
within each
x
group is taken as the
x
-coordinate
·
Useful empirical display for large datasets in which scatterdiagrams are too
busy to see patterns of central tendency and variability; good for residual
plots for showing symmetry and lack of trend in central tendency and vari-
ability
b
·
Can also specify a general function of a data vector that returns a matrix of
statistics for
method
;the statistic in the ﬁrst column should be the measure
of central tendency
·
Arguments can be passed to that function a list
methodArgs
·
Example: Group
x
into intervals containing 40 observations, plot the
0.5, 0.25,0.75
quantiles of
y
against mean
x
in interval
set.seed(1)
age ← rnorm(1000, 30, 10)
sbp ← 0.3*(age-30) + rnorm(1000, 120, 15)
xYplot(sbp ∼ age, method=’quantile’,
# Figure 14.5
xlim=c(5,60), ylim=c(100,140))
·
Instead of quantiles of raw data, show parametric conﬁdence bands, and
require 60 observations in a group
xYplot(sbp ∼ age, method=smean.cl.normal, # Figure 14.6
xlim=c(5,60), ylim=c(100,140), nx=60)
b
Specify
method=smean.sdl
±2×
S.D.
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CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
146
100
110
120
130
140
10
20
30
40
50
60
age
sbp
Figure 14.5:
0.25,0.5,0.75
quantiles of
sbp
vs. intervals of
age
containing 40 observations
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CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
147
100
110
120
130
140
10
20
30
40
50
60
age
sbp
Figure 14.6:
Mean and parametric 0.95 conﬁdence limits for means, for intervals of
age
containing
60 observations
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CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
148
Dotplot
·
“Multivariate response”packaged by
Cbind
appears as the
x
-variable after
the
·
Does not work well with superposition of
groups
·
Example: Display proportions and approximate 0.95 conﬁdence limits from
d ← expand.grid(continent=c(’USA’,’Europe’), year=1999:2001)
d\$proportion ← c(.2, .18, .19, .22, .23, .20)
d\$SE ← c(.02, .01, .02, .015, .021, .025)
d
continent year proportion
SE
1
USA 1999
0.20 0.020
2
Europe 1999
0.18 0.010
3
USA 2000
0.19 0.020
4
Europe 2000
0.22 0.015
5
USA 2001
0.23 0.021
6
Europe 2001
0.20 0.025
Dotplot(year ∼ Cbind(proportion, proportion-1.96*SE, proportion+1.96*SE) |
continent, data=d, ylab=’Year’) # Figure 14.7
·
To re-arrange the order of the vertical groups, use the
reorder.factor
func-
tion
AH11.4,4.6
·
First just reverse the order of years on the
y
-axis
yr ← factor(d\$year, 2001:1999)
Dotplot(yr ∼ Cbind(proportion, proportion-1.96*SE, proportion+1.96*SE) |
continent, data=d, ylab=’Year’)
·
Next, reorder years by the average proportion over the two continents
yr ← factor(d\$year)
# reorder.factor only accepts factors
CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
149
1999
2000
2001
0.16
0.20
0.24
USA
0.16
0.20
0.24
Europe
proportion
Month
Figure 14.7:
Dot plot showing proportions and approximate 0.95 conﬁdence limits for population
probabilities
CHAPTER 14. CONDITIONING AND PLOTTING THREE OR MORE VARIABLES
150
yr ← reorder.factor(yr, d\$proportion, mean)
levels(yr)
[1] "1999" "2000" "2001"
This happens to be in the original order so the dot plot will be the same as
Figure 14.7
·
To use more accurate Wilson conﬁdence intervals on raw data:
set.seed(3)
d ← expand.grid(continent=c(’USA’,’Europe’), year=1999:2001,
reps=1:100)
# Generate binary events from a population probability of 0.2
# of the event, same for all years and continents
d\$y ← ifelse(runif(6*100) <= .2, 1, 0)
rm(y)
# remove old y so as to not confuse the following
attach(d)
s ← summarize(y, llist(continent,year),
function(y) {
n ← sum(!is.na(y))
s ← sum(y, na.rm=T)
binconf(s, n)
}, type=’matrix’)
Dotplot(year ∼ Cbind(y) | continent,
data=s, ylab=’Year’)
# Same format of output as Figure 14.7
·
Example:
dfr
data frame and associated raw response variable
y
from
above
·
Display a 5-number (5-quantile) summary (2 intervals, dot=median)
s ← summarize(y, llist(month,year), quantile,
probs=c(.5,.05,.25,.75,.95), type=’matrix’)
Dotplot(month ∼ Cbind(y) | factor(year),
data=s, ylab=’Month’) # Figure 14.8
dev.off()