sim_birds: Simulated social learning data
In rmcelreath/wythamewa: Parus major social learning analysis
Description
Usage
Arguments
Details
Author(s)
Examples
Description
Flexible simulation of social and individual learning in foraging groups.
Usage
1
Arguments
N
Number of individuals
N_solve
Number of time steps
s
Vector of social learning weight values
gamma
Vector of updating rate values
conf
Vector of conformity strength values
pay
Vector of payoff bias weight values
d1
Payoff to first behavioral option, or vector of payoffs
d2
Payoff to second option, or vector of payoffs
A0
Initial attraction values
Details
This function simulates groups of birds learning under the assumed statistical model. It produces data suitable to feed directly into the statistical model, for purpose of validating the analysis code. It can also be used to explore a variety of learning dynamics.
Author(s)
Richard McElreath
Examples
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#####################################
# examples of model behavior
# this code reproduces Figure 5.
dhi_set <- rep(c(2.5,1),each=30)
dlo_set <- rep(c(1,2.5),each=30)
# if conformity too strong, population cannot track high payoff
set.seed(100)
sim_dat <- sim_birds( 10 , 60 , s=0.5 , gamma=0.6 , conf=10 , pay=0 ,
d1=dhi_set , d2=dlo_set )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Too much conformity" )
# moderate conformity, population can track high payoff
set.seed(101)
sim_dat <- sim_birds( 10 , 60 , s=0.4 , gamma=0.6 , conf=5 , pay=0 ,
dhi=rep(c(2.5,1),each=30) , dlo=rep(c(1,2.5),each=30) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Enough conformity" )
# Too little conformity, slower tracking
set.seed(101)
sim_dat <- sim_birds( 10 , 60 , s=0.4 , gamma=0.6 , conf=1 , pay=0 ,
dhi=rep(c(2.5,1),each=30) , dlo=rep(c(1,2.5),each=30) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Too little conformity" )
# now sample from actual posterior and simulate
# need posterior samples in object "post"
# see ?ewa_fit to produce it
data(WythamUnequal)
dat <- WythamUnequal
N_birds <- dat$N_birds
ks <- apply(post$ks,2,mean)
kg <- apply(post$kg,2,mean)
kl <- apply(post$kl,2,mean)
kp <- apply(post$kp,2,mean)
N <- 10
idx <- sample( 1:N_birds , size=N )
N_solve <- 60
sim_dat <- sim_birds( N , N_solve , s=ks[idx] , gamma=kg[idx] , conf=kl[idx] , pay=kp[idx] ,
d1=rep(c(2.5,1),each=N_solve/2) , d2=rep(c(1,2.5),each=N_solve/2) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=N_solve/2 + 0.5 , lty=2 , col="red" )
mtext("Individuals sampled from posterior distribution")
###########################
# fake data for validating model fitting code
N <- 20
N_solve <- 400
s <- logistic(rnorm(N))
pay <- logistic(rnorm(N,-0.5,0.1))
conf <- 1.5 + runif(N,0,0.1)
sim_dat <- sim_birds(N=N,N_solve=N_solve,s=s,pay=pay,conf=conf,gamma=s/2)
x <- sim_dat
# put data into format that Stan code assumes
nrows <- N*N_solve
bird_id <- rep( 1:N , each=N_solve )
solve_hi <- as.vector(x)
turn <- rep( 1:N_solve , times=N )
s_prop <- sapply( 1:nrows , function(i) {
if (turn[i]>1) {
return( (sum(x[turn[i],]) - x[turn[i],bird_id[i]])/(N-1) )
} else {
return(-1)
}
} )
A_init <- rep( 4 , times=N )
# fit model
# prep data to pass to Stan
datx <- list(
N = nrows,
N_birds = N,
bird = bird_id,
solve_hi = solve_hi,
s_prop = s_prop,
age = rep(0,nrows),
A_init = A_init
)
# define full model
lms <- list(
"mu[1] + a_bird[bird[i],1] + b_age[1]*age[i]",
"mu[2] + a_bird[bird[i],2] + b_age[2]*age[i]",
"mu[3] + a_bird[bird[i],3] + b_age[3]*age[i]",
"mu[4] + a_bird[bird[i],4] + b_age[4]*age[i]"
)
links <- c("logit", "logit", "log", "logit", "")
prior <- "
mu ~ normal(0,1);
diff_hi ~ cauchy(0,1);
b_age ~ normal(0,1);
to_vector(z_bird) ~ normal(0,1);
L_Rho_bird ~ lkj_corr_cholesky(3);
sigma_bird ~ exponential(2);"
mod1 <- ewa_def( model=lms , prior=prior , link=links , data=datx )
# run the model
m <- ewa_fit( mod1 , warmup=500 , iter=1000 , chains=3 , cores=3 ,
control=list( adapt_delta=0.99 , max_treedepth=12 ) )
# check convergence
precis( m , pars=c("mu","b_age","sigma_bird") , depth=2 )
# process and plot
post <- extract.samples(m)
ks <- apply(post$ks,2,mean)
kg <- apply(post$kg,2,mean)
kl <- apply(post$kl,2,mean)
kp <- apply(post$kp,2,mean)
ks_sd <- apply(post$ks,2,sd)
kg_sd <- apply(post$kg,2,sd)
kl_sd <- apply(post$kl,2,sd)
kp_sd <- apply(post$kp,2,sd)
# validation plots
the_col <- rangi2
blank(ex=1.66)
par(mfrow=c(2,2))
plot( s , ks , xlab="social learning weight (true)" , ylab="social learning weight (estimated)" , col=rangi2 , xlim=c(0,1) , ylim=c(0,1) )
for ( i in 1:length(ks) ) lines( c(s[i],s[i]) , ks[i]+c(1,-1)*ks_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
plot( s/2 , kg , xlab="updating rate (true)" , ylab="updating rate (estimated)" , col=rangi2 )
for ( i in 1:length(kg) ) lines( c(s[i]/2,s[i]/2) , kg[i]+c(1,-1)*kg_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
if ( length(conf)==1 ) conf <- rep(conf,length(kl)) + runif(length(kl),-0.1,0.1)
plot( conf , kl , xlab="conformity strength (true)" , ylab="conformity strength (estimated)" , col=rangi2 , xlim=c(1,3) , ylim=c(1,5) )
for ( i in 1:length(kl) ) lines( c(conf[i],conf[i]) , kl[i]+c(1,-1)*kl_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
if ( length(pay)==1 ) pay <- rep(pay,length(kp)) + runif(length(kp),-0.1,0.1)
plot( pay , kp , xlab="payoff bias weight (true)" , ylab="payoff bias weight (estimated)" , col=rangi2 )
for ( i in 1:length(kp) ) lines( c(pay[i],pay[i]) , kp[i]+c(1,-1)*kp_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
rmcelreath/wythamewa documentation built on May 14, 2019, 2:56 p.m.
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Description Usage Arguments Details Author(s) Examples
Description
Flexible simulation of social and individual learning in foraging groups.
Usage
1 |
Arguments
N |
Number of individuals |
N_solve |
Number of time steps |
s |
Vector of social learning weight values |
gamma |
Vector of updating rate values |
conf |
Vector of conformity strength values |
pay |
Vector of payoff bias weight values |
d1 |
Payoff to first behavioral option, or vector of payoffs |
d2 |
Payoff to second option, or vector of payoffs |
A0 |
Initial attraction values |
Details
This function simulates groups of birds learning under the assumed statistical model. It produces data suitable to feed directly into the statistical model, for purpose of validating the analysis code. It can also be used to explore a variety of learning dynamics.
Author(s)
Richard McElreath
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 | #####################################
# examples of model behavior
# this code reproduces Figure 5.
dhi_set <- rep(c(2.5,1),each=30)
dlo_set <- rep(c(1,2.5),each=30)
# if conformity too strong, population cannot track high payoff
set.seed(100)
sim_dat <- sim_birds( 10 , 60 , s=0.5 , gamma=0.6 , conf=10 , pay=0 ,
d1=dhi_set , d2=dlo_set )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Too much conformity" )
# moderate conformity, population can track high payoff
set.seed(101)
sim_dat <- sim_birds( 10 , 60 , s=0.4 , gamma=0.6 , conf=5 , pay=0 ,
dhi=rep(c(2.5,1),each=30) , dlo=rep(c(1,2.5),each=30) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Enough conformity" )
# Too little conformity, slower tracking
set.seed(101)
sim_dat <- sim_birds( 10 , 60 , s=0.4 , gamma=0.6 , conf=1 , pay=0 ,
dhi=rep(c(2.5,1),each=30) , dlo=rep(c(1,2.5),each=30) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=30.5,lty=2)
mtext( "Too little conformity" )
# now sample from actual posterior and simulate
# need posterior samples in object "post"
# see ?ewa_fit to produce it
data(WythamUnequal)
dat <- WythamUnequal
N_birds <- dat$N_birds
ks <- apply(post$ks,2,mean)
kg <- apply(post$kg,2,mean)
kl <- apply(post$kl,2,mean)
kp <- apply(post$kp,2,mean)
N <- 10
idx <- sample( 1:N_birds , size=N )
N_solve <- 60
sim_dat <- sim_birds( N , N_solve , s=ks[idx] , gamma=kg[idx] , conf=kl[idx] , pay=kp[idx] ,
d1=rep(c(2.5,1),each=N_solve/2) , d2=rep(c(1,2.5),each=N_solve/2) )
plot( NULL , xlim=c(1,nrow(sim_dat)) , ylim=c(0,ncol(sim_dat)+1) , xlab="turn" , ylab="bird" , yaxt="n" )
axis( 2 , at=1:ncol(sim_dat) , labels=1:ncol(sim_dat) )
for ( i in 1:ncol(sim_dat) )
points( 1:nrow(sim_dat) , rep(i,nrow(sim_dat)) , pch=ifelse(sim_dat[,i]==1,16,1) )
abline(v=N_solve/2 + 0.5 , lty=2 , col="red" )
mtext("Individuals sampled from posterior distribution")
###########################
# fake data for validating model fitting code
N <- 20
N_solve <- 400
s <- logistic(rnorm(N))
pay <- logistic(rnorm(N,-0.5,0.1))
conf <- 1.5 + runif(N,0,0.1)
sim_dat <- sim_birds(N=N,N_solve=N_solve,s=s,pay=pay,conf=conf,gamma=s/2)
x <- sim_dat
# put data into format that Stan code assumes
nrows <- N*N_solve
bird_id <- rep( 1:N , each=N_solve )
solve_hi <- as.vector(x)
turn <- rep( 1:N_solve , times=N )
s_prop <- sapply( 1:nrows , function(i) {
if (turn[i]>1) {
return( (sum(x[turn[i],]) - x[turn[i],bird_id[i]])/(N-1) )
} else {
return(-1)
}
} )
A_init <- rep( 4 , times=N )
# fit model
# prep data to pass to Stan
datx <- list(
N = nrows,
N_birds = N,
bird = bird_id,
solve_hi = solve_hi,
s_prop = s_prop,
age = rep(0,nrows),
A_init = A_init
)
# define full model
lms <- list(
"mu[1] + a_bird[bird[i],1] + b_age[1]*age[i]",
"mu[2] + a_bird[bird[i],2] + b_age[2]*age[i]",
"mu[3] + a_bird[bird[i],3] + b_age[3]*age[i]",
"mu[4] + a_bird[bird[i],4] + b_age[4]*age[i]"
)
links <- c("logit", "logit", "log", "logit", "")
prior <- "
mu ~ normal(0,1);
diff_hi ~ cauchy(0,1);
b_age ~ normal(0,1);
to_vector(z_bird) ~ normal(0,1);
L_Rho_bird ~ lkj_corr_cholesky(3);
sigma_bird ~ exponential(2);"
mod1 <- ewa_def( model=lms , prior=prior , link=links , data=datx )
# run the model
m <- ewa_fit( mod1 , warmup=500 , iter=1000 , chains=3 , cores=3 ,
control=list( adapt_delta=0.99 , max_treedepth=12 ) )
# check convergence
precis( m , pars=c("mu","b_age","sigma_bird") , depth=2 )
# process and plot
post <- extract.samples(m)
ks <- apply(post$ks,2,mean)
kg <- apply(post$kg,2,mean)
kl <- apply(post$kl,2,mean)
kp <- apply(post$kp,2,mean)
ks_sd <- apply(post$ks,2,sd)
kg_sd <- apply(post$kg,2,sd)
kl_sd <- apply(post$kl,2,sd)
kp_sd <- apply(post$kp,2,sd)
# validation plots
the_col <- rangi2
blank(ex=1.66)
par(mfrow=c(2,2))
plot( s , ks , xlab="social learning weight (true)" , ylab="social learning weight (estimated)" , col=rangi2 , xlim=c(0,1) , ylim=c(0,1) )
for ( i in 1:length(ks) ) lines( c(s[i],s[i]) , ks[i]+c(1,-1)*ks_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
plot( s/2 , kg , xlab="updating rate (true)" , ylab="updating rate (estimated)" , col=rangi2 )
for ( i in 1:length(kg) ) lines( c(s[i]/2,s[i]/2) , kg[i]+c(1,-1)*kg_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
if ( length(conf)==1 ) conf <- rep(conf,length(kl)) + runif(length(kl),-0.1,0.1)
plot( conf , kl , xlab="conformity strength (true)" , ylab="conformity strength (estimated)" , col=rangi2 , xlim=c(1,3) , ylim=c(1,5) )
for ( i in 1:length(kl) ) lines( c(conf[i],conf[i]) , kl[i]+c(1,-1)*kl_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
if ( length(pay)==1 ) pay <- rep(pay,length(kp)) + runif(length(kp),-0.1,0.1)
plot( pay , kp , xlab="payoff bias weight (true)" , ylab="payoff bias weight (estimated)" , col=rangi2 )
for ( i in 1:length(kp) ) lines( c(pay[i],pay[i]) , kp[i]+c(1,-1)*kp_sd[i] , col=rangi2 )
abline(a=0,b=1,lty=2)
|
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