rplba: Generate Random Choice Response Times using pLBA Model
In TasCL/cpda: Probability Density Approximation
Description
Usage
Arguments
Details
Value
Examples
Description
This function uses two-accumulator piecewise LBA model to generate random
choice RTs. There are 3 variants: rplba, rplba1, and
rplba2. Each of them has a corresponding R version,
rplbaR, rplbaR1, and rplbaR2, for the purpose of
speed testing. Because the difference of random number generators in C and
R, they do not generate exactly identical RTs. When generating large
enough observations, the distributions generated by R and C will match.
Usage
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rplba(n, pVec)
rplba1(n, pVec)
rplba2(n, pVec)
rplba3(n, pVec)
rplba4(n, pVec)
rplbaR1(n = 10, pVec = c(A = 1.51, b = 2.7, v1 = 3.32, v2 = 2.24, w1 = 1.51,
w2 = 3.69, sv = 1, rD = 0.31, swt = 0.5, t0 = 0.08))
rplbaR2(n = 10, pVec = c(A1 = 1.51, A2 = 1.51, b1 = 2.7, b2 = 2.7, v1 =
3.32, v2 = 2.24, w1 = 1.51, w2 = 3.69, sv1 = 1, sv2 = 1, sw1 = 1, sw2 = 1, rD
= 0.31, swt = 0.5, t0 = 0.08))
rplbaR3(n, pVec = c(A1 = 1.5, A2 = 1.5, B1 = 1.2, B2 = 1.2, C1 = 0.3, C2 =
0.3, v1 = 3.32, v2 = 2.24, w1 = 1.51, w2 = 3.69, sv1 = 1, sv2 = 1, sw1 = 1,
sw2 = 1, rD = 0.3, tD = 0.3, swt = 0.5, t0 = 0.08))
Arguments
n
number of observations. Must be an integer
pVec
a numeric vector storing pLBA model parameters. The sequence is
critical. See details for the sequence.
Details
The main function rplba implements a more flexible
version of pLBA random number generator than the other two. It uses the
following parameterisation (order matter):
-
A1 accumulator 1 start-point upper bound. A is
the upper bound of the interval [0, A], which is used by an uniform
distribution to generate a start-point. Average amount of
prior evidence (i.e., before accumulation process even begins) across trials
is A/2.
-
A2 accumulator 2 start-point upper bound.
-
B1 accumulator 1 traveling distance. Note this is not
a decision threshold!. LBA convention denotes decision threshold/caution as
b (lowercase) and traveling distance as B (uppercase). B=b-A is
the traveling distance, and b-A/2 is a measure of average
decision caution.
-
B2 accumulator 2 traveling distance.
-
C1 the amount of traveling distance change for
accumulator 1 at the stage 2.
-
C2 the amount of traveling distance change for
accumulator 2 at the stage 2.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv1 accumulator 1 drift rate standard deviation,
stage 1.
-
sv2 accumulator 2 drift rate standard deviation,
stage 1.
-
sw1 accumulator 1 drift rate standard deviation,
stage 2.
-
sw2 accumulator 2 drift rate standard deviation,
stage 2.
-
rD the delay duration while stage 1 drift rate switches
to stage 2 drift rate
-
tD the delay duration while stage 1 threshold switches
to stage 2 threshold
-
swt switch time, usually determined by experimental
design.
-
t0 non-decision time in second.
rplba1 uses the following parameterisation:
-
A a common start-point interval for both accumulators.
-
b a common response threshold for both accumulators.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv a common standard deviation for both accumulators
-
rD a delay period while drift rate switch to a
second stage process
-
swt switch time, usually determined by experimental
design
-
t0 non-decision time in second.
rplba2 uses the following parameterisation:
-
A1 start-point interval of the accumulator 1.
-
A2 start-point interval of the accumulator 2.
-
b1 accumulator 1 response threshold.
-
b2 accumulator 2 response threshold.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv1 the standard deviation of accumulator 1 drirt rate
during stage 1.
-
sv2 the standard deviation of accumulator 2 drirt rate
during stage 1.
-
sw1 the standard deviation of accumulator 1 drirt rate
during stage 2.
-
sw2 the standard deviation of accumulator 2 drirt rate
during stage 2.
-
rD a delay period while drift rate switch to a
second stage process
-
swt switch time, usually determined by experimental
design
-
t0 non-decision time in second.
Value
A n x 2 matrix with a first column storing choices and second
column storing response times.
Examples
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################
## Example 1 ##
################
pVec3.1 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.1,
tD=.1, swt=0.5, t0=0.08)
pVec3.2 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.1,
tD=.15, swt=0.5, t0=0.08)
pVec3.3 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.15,
tD=.1, swt=0.5, t0=0.08)
n <- 1e5
set.seed(123); system.time(dat5.1 <- cpda::rplbaR(n, pVec3.1))
set.seed(123); system.time(dat5.2 <- cpda::rplbaR(n, pVec3.2))
set.seed(123); system.time(dat5.3 <- cpda::rplbaR(n, pVec3.3))
set.seed(123); system.time(dat6.1 <- cpda::rplba( n, pVec3.1))
set.seed(123); system.time(dat6.2 <- cpda::rplba( n, pVec3.2))
set.seed(123); system.time(dat6.3 <- cpda::rplba( n, pVec3.3))
tmp5.1 <- data.frame(choice=factor(dat5.1[,1]), rt=dat5.1[,2])
tmp5.2 <- data.frame(choice=factor(dat5.2[,1]), rt=dat5.2[,2])
tmp5.3 <- data.frame(choice=factor(dat5.3[,1]), rt=dat5.3[,2])
tmp6.1 <- data.frame(choice=factor(dat6.1[,1]), rt=dat6.1[,2])
tmp6.2 <- data.frame(choice=factor(dat6.2[,1]), rt=dat6.2[,2])
tmp6.3 <- data.frame(choice=factor(dat6.3[,1]), rt=dat6.3[,2])
tmp5.1$fun <- "R"
tmp5.2$fun <- "R"
tmp5.3$fun <- "R"
tmp6.1$fun <- "C"
tmp6.2$fun <- "C"
tmp6.3$fun <- "C"
tmp5.1$vec <- "1"
tmp5.2$vec <- "2"
tmp5.3$vec <- "3"
tmp6.1$vec <- "1"
tmp6.2$vec <- "2"
tmp6.3$vec <- "3"
df <- rbind(tmp5.1, tmp5.2, tmp5.3, tmp6.1, tmp6.2, tmp6.3)
df$fun <- factor(df$fun)
## Show R and C functions produce almost identical distributions
## Not run:
## Set up a colour palette
cb <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2",
"#D55E00", "#CC79A7")
require(ggplot2)
ggplot(data=df, aes(x = rt, fill=fun, color=fun)) +
geom_density(alpha=0.2) +
facet_grid(vec~ choice) +
scale_fill_manual(values=cb)
## Or you can use lattice or base graphics
require(lattice)
histogram( ~rt | vec+choice+fun, data=df, breaks="fd", type="density",
xlab="Response Time (s)",
panel=function(x, ...) {
panel.histogram(x, ...)
panel.densityplot(x, darg=list(kernel="gaussian"),...)
})
## End(Not run)
par(mfrow=c(3,2))
hist(tmp5.1[tmp5.1$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.1[tmp6.1$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.1[tmp5.1$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.1[tmp6.1$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
#############
hist(tmp5.2[tmp5.2$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.2[tmp6.2$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.2[tmp5.2$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.2[tmp6.2$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
#############
hist(tmp5.3[tmp5.3$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.3[tmp6.3$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.3[tmp5.3$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.3[tmp6.3$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
par(mfrow=c(1,1))
################
## Example 2 ##
################
pVec1 <- c(A=1.51, b=2.7, v1=3.32, v2=2.24, w1=1.51, w2=3.69,
sv=1, rD=0.31, swt=0.5, t0=0.08)
pVec2 <- c(A1=1.51, A2=1.51, b1=2.7, b2=2.7, v1=3.32, v2=2.24,
w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.31,
swt=0.5, t0=0.08)
system.time(dat1 <- cpda::rplba1( n, pVec1))
system.time(dat2 <- cpda::rplba2( n, pVec2))
system.time(dat3 <- cpda::rplbaR1(n, pVec1))
system.time(dat4 <- cpda::rplbaR2(n, pVec2))
tmp1 <- data.frame(choice=factor(dat1[,1]), rt=dat1[,2])
tmp2 <- data.frame(choice=factor(dat2[,1]), rt=dat2[,2])
tmp3 <- data.frame(choice=factor(dat3[,1]), rt=dat3[,2])
tmp4 <- data.frame(choice=factor(dat4[,1]), rt=dat4[,2])
tmp1$fun <- "rplba1"
tmp2$fun <- "rplba2"
tmp3$fun <- "rplba1-R"
tmp4$fun <- "rplba2-R"
tmp0 <- rbind(tmp1, tmp2, tmp3, tmp4)
tmp0$fun <- factor(tmp0$fun)
## Not run:
require(ggplot2)
ggplot(data = tmp0, aes(x = rt, fill=fun, color=fun)) +
geom_density(alpha=0.2) +
facet_grid(.~ choice) +
scale_fill_manual(values=cb)
## End(Not run)
TasCL/cpda documentation built on May 3, 2019, 11:48 p.m.
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Description Usage Arguments Details Value Examples
Description
This function uses two-accumulator piecewise LBA model to generate random
choice RTs. There are 3 variants: rplba, rplba1, and
rplba2. Each of them has a corresponding R version,
rplbaR, rplbaR1, and rplbaR2, for the purpose of
speed testing. Because the difference of random number generators in C and
R, they do not generate exactly identical RTs. When generating large
enough observations, the distributions generated by R and C will match.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | rplba(n, pVec)
rplba1(n, pVec)
rplba2(n, pVec)
rplba3(n, pVec)
rplba4(n, pVec)
rplbaR1(n = 10, pVec = c(A = 1.51, b = 2.7, v1 = 3.32, v2 = 2.24, w1 = 1.51,
w2 = 3.69, sv = 1, rD = 0.31, swt = 0.5, t0 = 0.08))
rplbaR2(n = 10, pVec = c(A1 = 1.51, A2 = 1.51, b1 = 2.7, b2 = 2.7, v1 =
3.32, v2 = 2.24, w1 = 1.51, w2 = 3.69, sv1 = 1, sv2 = 1, sw1 = 1, sw2 = 1, rD
= 0.31, swt = 0.5, t0 = 0.08))
rplbaR3(n, pVec = c(A1 = 1.5, A2 = 1.5, B1 = 1.2, B2 = 1.2, C1 = 0.3, C2 =
0.3, v1 = 3.32, v2 = 2.24, w1 = 1.51, w2 = 3.69, sv1 = 1, sv2 = 1, sw1 = 1,
sw2 = 1, rD = 0.3, tD = 0.3, swt = 0.5, t0 = 0.08))
|
Arguments
n |
number of observations. Must be an integer |
pVec |
a numeric vector storing pLBA model parameters. The sequence is critical. See details for the sequence. |
Details
The main function rplba implements a more flexible
version of pLBA random number generator than the other two. It uses the
following parameterisation (order matter):
-
A1 accumulator 1 start-point upper bound.
Ais the upper bound of the interval[0, A], which is used by an uniform distribution to generate a start-point. Average amount of prior evidence (i.e., before accumulation process even begins) across trials isA/2. -
A2 accumulator 2 start-point upper bound.
-
B1 accumulator 1 traveling distance. Note this is not a decision threshold!. LBA convention denotes decision threshold/caution as b (lowercase) and traveling distance as B (uppercase).
B=b-Ais the traveling distance, andb-A/2is a measure of average decision caution. -
B2 accumulator 2 traveling distance.
-
C1 the amount of traveling distance change for accumulator 1 at the stage 2.
-
C2 the amount of traveling distance change for accumulator 2 at the stage 2.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv1 accumulator 1 drift rate standard deviation, stage 1.
-
sv2 accumulator 2 drift rate standard deviation, stage 1.
-
sw1 accumulator 1 drift rate standard deviation, stage 2.
-
sw2 accumulator 2 drift rate standard deviation, stage 2.
-
rD the delay duration while stage 1 drift rate switches to stage 2 drift rate
-
tD the delay duration while stage 1 threshold switches to stage 2 threshold
-
swt switch time, usually determined by experimental design.
-
t0 non-decision time in second.
rplba1 uses the following parameterisation:
-
A a common start-point interval for both accumulators.
-
b a common response threshold for both accumulators.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv a common standard deviation for both accumulators
-
rD a delay period while drift rate switch to a second stage process
-
swt switch time, usually determined by experimental design
-
t0 non-decision time in second.
rplba2 uses the following parameterisation:
-
A1 start-point interval of the accumulator 1.
-
A2 start-point interval of the accumulator 2.
-
b1 accumulator 1 response threshold.
-
b2 accumulator 2 response threshold.
-
v1 accumulator 1 drift rate, stage 1
-
v2 accumulator 2 drift rate, stage 1
-
w1 accumulator 1 drift rate, stage 2
-
w2 accumulator 2 drift rate, stage 2
-
sv1 the standard deviation of accumulator 1 drirt rate during stage 1.
-
sv2 the standard deviation of accumulator 2 drirt rate during stage 1.
-
sw1 the standard deviation of accumulator 1 drirt rate during stage 2.
-
sw2 the standard deviation of accumulator 2 drirt rate during stage 2.
-
rD a delay period while drift rate switch to a second stage process
-
swt switch time, usually determined by experimental design
-
t0 non-decision time in second.
Value
A n x 2 matrix with a first column storing choices and second
column storing response times.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | ################
## Example 1 ##
################
pVec3.1 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.1,
tD=.1, swt=0.5, t0=0.08)
pVec3.2 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.1,
tD=.15, swt=0.5, t0=0.08)
pVec3.3 <- c(A1=1.51, A2=1.51, B1=1.2, B2=1.2, C1=.3, C2=.3, v1=3.32,
v2=2.24, w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.15,
tD=.1, swt=0.5, t0=0.08)
n <- 1e5
set.seed(123); system.time(dat5.1 <- cpda::rplbaR(n, pVec3.1))
set.seed(123); system.time(dat5.2 <- cpda::rplbaR(n, pVec3.2))
set.seed(123); system.time(dat5.3 <- cpda::rplbaR(n, pVec3.3))
set.seed(123); system.time(dat6.1 <- cpda::rplba( n, pVec3.1))
set.seed(123); system.time(dat6.2 <- cpda::rplba( n, pVec3.2))
set.seed(123); system.time(dat6.3 <- cpda::rplba( n, pVec3.3))
tmp5.1 <- data.frame(choice=factor(dat5.1[,1]), rt=dat5.1[,2])
tmp5.2 <- data.frame(choice=factor(dat5.2[,1]), rt=dat5.2[,2])
tmp5.3 <- data.frame(choice=factor(dat5.3[,1]), rt=dat5.3[,2])
tmp6.1 <- data.frame(choice=factor(dat6.1[,1]), rt=dat6.1[,2])
tmp6.2 <- data.frame(choice=factor(dat6.2[,1]), rt=dat6.2[,2])
tmp6.3 <- data.frame(choice=factor(dat6.3[,1]), rt=dat6.3[,2])
tmp5.1$fun <- "R"
tmp5.2$fun <- "R"
tmp5.3$fun <- "R"
tmp6.1$fun <- "C"
tmp6.2$fun <- "C"
tmp6.3$fun <- "C"
tmp5.1$vec <- "1"
tmp5.2$vec <- "2"
tmp5.3$vec <- "3"
tmp6.1$vec <- "1"
tmp6.2$vec <- "2"
tmp6.3$vec <- "3"
df <- rbind(tmp5.1, tmp5.2, tmp5.3, tmp6.1, tmp6.2, tmp6.3)
df$fun <- factor(df$fun)
## Show R and C functions produce almost identical distributions
## Not run:
## Set up a colour palette
cb <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2",
"#D55E00", "#CC79A7")
require(ggplot2)
ggplot(data=df, aes(x = rt, fill=fun, color=fun)) +
geom_density(alpha=0.2) +
facet_grid(vec~ choice) +
scale_fill_manual(values=cb)
## Or you can use lattice or base graphics
require(lattice)
histogram( ~rt | vec+choice+fun, data=df, breaks="fd", type="density",
xlab="Response Time (s)",
panel=function(x, ...) {
panel.histogram(x, ...)
panel.densityplot(x, darg=list(kernel="gaussian"),...)
})
## End(Not run)
par(mfrow=c(3,2))
hist(tmp5.1[tmp5.1$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.1[tmp6.1$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.1[tmp5.1$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.1[tmp6.1$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
#############
hist(tmp5.2[tmp5.2$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.2[tmp6.2$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.2[tmp5.2$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.2[tmp6.2$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
#############
hist(tmp5.3[tmp5.3$choice==1,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 1")
lines(density(tmp6.3[tmp6.3$choice==1,"rt"]), col="red", lty="dashed", lwd=1.5)
hist(tmp5.3[tmp5.3$choice==2,"rt"], breaks="fd", col="gray", freq=FALSE,
xlab="RT (s)", main="pLBA-Choice 2")
lines(density(tmp6.3[tmp6.3$choice==2,"rt"]), col="red", lty="dashed", lwd=1.5)
par(mfrow=c(1,1))
################
## Example 2 ##
################
pVec1 <- c(A=1.51, b=2.7, v1=3.32, v2=2.24, w1=1.51, w2=3.69,
sv=1, rD=0.31, swt=0.5, t0=0.08)
pVec2 <- c(A1=1.51, A2=1.51, b1=2.7, b2=2.7, v1=3.32, v2=2.24,
w1=1.51, w2=3.69, sv1=1, sv2=1, sw1=1, sw2=1, rD=0.31,
swt=0.5, t0=0.08)
system.time(dat1 <- cpda::rplba1( n, pVec1))
system.time(dat2 <- cpda::rplba2( n, pVec2))
system.time(dat3 <- cpda::rplbaR1(n, pVec1))
system.time(dat4 <- cpda::rplbaR2(n, pVec2))
tmp1 <- data.frame(choice=factor(dat1[,1]), rt=dat1[,2])
tmp2 <- data.frame(choice=factor(dat2[,1]), rt=dat2[,2])
tmp3 <- data.frame(choice=factor(dat3[,1]), rt=dat3[,2])
tmp4 <- data.frame(choice=factor(dat4[,1]), rt=dat4[,2])
tmp1$fun <- "rplba1"
tmp2$fun <- "rplba2"
tmp3$fun <- "rplba1-R"
tmp4$fun <- "rplba2-R"
tmp0 <- rbind(tmp1, tmp2, tmp3, tmp4)
tmp0$fun <- factor(tmp0$fun)
## Not run:
require(ggplot2)
ggplot(data = tmp0, aes(x = rt, fill=fun, color=fun)) +
geom_density(alpha=0.2) +
facet_grid(.~ choice) +
scale_fill_manual(values=cb)
## End(Not run)
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