options(width = 200)
library(foreign)
acsY10nas <- read.spss("ACS_all_schools to 2013_merge_6.sav", use.value.labels = FALSE,
to.data.frame = TRUE)
library(car)
acsY10nas$SEXMAIN <- recode(acsY10nas$SEXMAIN, "1=0;2=1")
acsY10nas$znas8 <- scale(acsY10nas$nas8)
acsY10nas$zhope <- scale(acsY10nas$hpmean_10_2012)
acsY10nas$zswb <- scale(acsY10nas$swbmean_10_2012)
acsY10nas$nasT <- recode(acsY10nas$nas8, "0:4=0; 4.01:6=1")
acsY10nas$schoolMAIN <- as.factor(acsY10nas$schoolMAIN)
Girls <- subset(acsY10nas, acsY10nas$SEXMAIN == "1", select = c(1:3046))
Girls$zboys <- scale(Girls$n_boys)
Girls$zgirls <- scale(Girls$n_girls)
Boys <- subset(acsY10nas, acsY10nas$SEXMAIN == "0", select = c(1:3046))
Boys$zboys <- scale(Boys$n_boys)
Boys$zgirls <- scale(Boys$n_girls)
Boys$id <- c(as.factor(Boys$ID10))
Boys$znas8 <- as.numeric(Boys$znas8)
Boys$schoolMAIN <- as.factor(Boys$schoolMAIN)
Boys$zboys <- as.factor(Boys$zboys)
# subset data to get complete cases of boys class
Boys <- subset(Boys, complete.cases(Boys$zboys), select = c(1:3049))
library(car)
Boys$school <- recode(Boys$schoolMAIN, "1=1;36=2;8=3;5=4;2=5;3=6;11=7;20=8;6=9;10=10;7=11;22=12;28=13")
### Simple Poisson model of Q1_male predicted by znas8 (boys rating boys)
## ignoring school and class size in this model
Q1mBB.model <- function() {
for (i in 1:n) {
znas8[i] ~ dnorm(0, 0.01)
Q1_male[i] ~ dpois(lambda[i])
log(lambda[i]) <- mu + b.znas8 * znas8[i] + epsilon[i]
epsilon[i] ~ dnorm(0, tau.epsilon)
}
mu ~ dnorm(0, 1e-04)
tau.epsilon <- pow(sigma.epsilon, -2)
sigma.epsilon ~ dunif(0, 100)
b.znas8 ~ dnorm(0, 0.01)
tau.znas8 <- pow(sigma.znas8, -2)
sigma.znas8 ~ dunif(0, 100)
}
library(R2jags)
n <- length(Boys$id) # of Y10 survey respondents
Q1_male <- Boys$Q1_male
znas8 <- Boys$znas8
Q1mBB.data <- list("n", "Q1_male", "znas8")
Q1mBB.params <- c("mu", "b.znas8", "sigma.znas8", "sigma.epsilon")
Q1mBB.inits <- function() {
list(b.znas8 = c(0))
}
set.seed(999)
Q1mBB.fit <- jags(data = Q1mBB.data, inits = Q1mBB.inits, Q1mBB.params, model.file = Q1mBB.model,
n.chains = 4, n.iter = 1000, n.burnin = 100)
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph Size: 5093
##
## Initializing model
print(Q1mBB.fit)
## Inference for Bugs model at "/var/folders/mn/jsy0lvks0117hn0pl7ysl4380000gp/T//RtmpK6vUiv/model56233e891f8e.txt", fit using jags,
## 4 chains, each with 1000 iterations (first 100 discarded)
## n.sims = 3600 iterations saved
## mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
## b.znas8 0.062 0.020 0.025 0.048 0.062 0.075 0.101 1.006 490
## mu 0.669 0.030 0.609 0.649 0.670 0.689 0.727 1.012 240
## sigma.epsilon 0.428 0.036 0.353 0.406 0.428 0.452 0.497 1.036 110
## sigma.znas8 49.990 28.910 2.563 25.114 49.216 75.661 97.829 1.001 3600
## deviance 9478.144 43.826 9397.550 9449.318 9476.623 9505.190 9570.271 1.016 220
##
## For each parameter, n.eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
##
## DIC info (using the rule, pD = var(deviance)/2)
## pD = 948.0 and DIC = 10426.2
## DIC is an estimate of expected predictive error (lower deviance is better).
plot(Q1mBB.fit)
fit.mcmc <- as.mcmc(Q1mBB.fit)
summary(fit.mcmc)
##
## Iterations = 1:900
## Thinning interval = 1
## Number of chains = 4
## Sample size per chain = 900
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## b.znas8 6.22e-02 0.0199 0.000332 0.00102
## deviance 9.48e+03 43.8263 0.730439 3.35483
## mu 6.69e-01 0.0300 0.000500 0.00153
## sigma.epsilon 4.28e-01 0.0357 0.000595 0.00369
## sigma.znas8 5.00e+01 28.9098 0.481830 0.51810
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## b.znas8 0.025 4.81e-02 6.19e-02 7.55e-02 0.101
## deviance 9397.550 9.45e+03 9.48e+03 9.51e+03 9570.271
## mu 0.609 6.49e-01 6.70e-01 6.89e-01 0.727
## sigma.epsilon 0.353 4.06e-01 4.28e-01 4.52e-01 0.497
## sigma.znas8 2.563 2.51e+01 4.92e+01 7.57e+01 97.829
xyplot(fit.mcmc)
densityplot(fit.mcmc)
# autocorr.plot(fit.mcmc)
options(width = 200)
Q1mBBs.model <- function() {
for (i in 1:n) {
znas8[i] ~ dnorm(0, 0.01)
Q1_male[i] ~ dpois(lambda[i])
log(lambda[i]) <- mu + b.znas8 * znas8[i] + b.schoolMAIN[school[i]] +
epsilon[i]
epsilon[i] ~ dnorm(0, tau.epsilon)
}
mu ~ dnorm(0, 1e-04)
mu.adj <- mu + mean(b.schoolMAIN[])
tau.epsilon <- pow(sigma.epsilon, -2)
sigma.epsilon ~ dunif(0, 100)
b.znas8 ~ dnorm(0, 0.01)
tau.znas8 <- pow(sigma.znas8, -2)
sigma.znas8 ~ dunif(0, 100)
for (j in 1:n.school) {
b.schoolMAIN[j] ~ dnorm(0, tau.schoolMAIN)
b.schoolMAIN.adj[j] <- b.schoolMAIN[j] - mean(b.schoolMAIN[])
}
tau.schoolMAIN <- pow(sigma.schoolMAIN, -2)
sigma.schoolMAIN ~ dunif(0, 100)
}
library(R2jags)
n <- length(Boys$id) # of Y10 survey respondents
n.school <- length(unique(Boys$schoolMAIN))
Q1_male <- Boys$Q1_male
znas8 <- Boys$znas8
school <- Boys$school
Q1mBBs.data <- list("n", "n.school", "Q1_male", "znas8", "school")
Q1mBBs.params <- c("mu", "mu.adj", "b.znas8", "b.schoolMAIN", "b.schoolMAIN.adj",
"sigma.znas8", "sigma.schoolMAIN", "sigma.epsilon")
Q1mBBs.inits <- function() {
list(b.znas8 = c(0), b.schoolMAIN = rnorm(n.school))
}
set.seed(999)
Q1mBBs.fit <- jags(data = Q1mBBs.data, inits = Q1mBBs.inits, Q1mBBs.params,
model.file = Q1mBBs.model, n.chains = 4, n.iter = 1000, n.burnin = 100)
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph Size: 6118
##
## Initializing model
print(Q1mBBs.fit)
## Inference for Bugs model at "/var/folders/mn/jsy0lvks0117hn0pl7ysl4380000gp/T//Rtmp1SRtO7/model56ec1d39b931.txt", fit using jags,
## 4 chains, each with 1000 iterations (first 100 discarded)
## n.sims = 3600 iterations saved
## mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
## b.schoolMAIN[1] 0.030 0.059 -0.058 -0.003 0.016 0.056 0.164 1.033 150
## b.schoolMAIN[2] 0.020 0.055 -0.079 -0.009 0.007 0.046 0.146 1.036 140
## b.schoolMAIN[3] -0.005 0.053 -0.116 -0.031 -0.002 0.020 0.097 1.019 2000
## b.schoolMAIN[4] -0.002 0.056 -0.117 -0.029 -0.001 0.021 0.115 1.021 430
## b.schoolMAIN[5] -0.005 0.065 -0.149 -0.032 -0.001 0.023 0.132 1.013 2800
## b.schoolMAIN[6] 0.000 0.059 -0.118 -0.027 0.000 0.026 0.127 1.019 2000
## b.schoolMAIN[7] -0.021 0.054 -0.145 -0.050 -0.012 0.007 0.081 1.014 540
## b.schoolMAIN[8] -0.028 0.056 -0.157 -0.058 -0.017 0.003 0.070 1.012 640
## b.schoolMAIN[9] 0.018 0.060 -0.088 -0.013 0.007 0.042 0.155 1.022 520
## b.schoolMAIN[10] -0.017 0.054 -0.139 -0.042 -0.009 0.008 0.083 1.017 820
## b.schoolMAIN[11] -0.043 0.064 -0.196 -0.079 -0.026 0.000 0.050 1.014 220
## b.schoolMAIN[12] 0.050 0.064 -0.036 0.002 0.036 0.083 0.192 1.043 83
## b.schoolMAIN[13] 0.029 0.054 -0.055 -0.002 0.017 0.053 0.156 1.033 210
## b.schoolMAIN.adj[1] 0.028 0.049 -0.054 -0.002 0.016 0.055 0.147 1.016 190
## b.schoolMAIN.adj[2] 0.018 0.049 -0.071 -0.008 0.008 0.044 0.134 1.023 220
## b.schoolMAIN.adj[3] -0.007 0.048 -0.113 -0.031 -0.002 0.016 0.087 1.010 1200
## b.schoolMAIN.adj[4] -0.004 0.049 -0.110 -0.028 -0.001 0.019 0.100 1.012 880
## b.schoolMAIN.adj[5] -0.006 0.062 -0.146 -0.031 -0.001 0.021 0.117 1.014 3600
## b.schoolMAIN.adj[6] -0.001 0.054 -0.113 -0.025 0.000 0.022 0.114 1.010 3600
## b.schoolMAIN.adj[7] -0.023 0.050 -0.141 -0.049 -0.013 0.005 0.067 1.017 260
## b.schoolMAIN.adj[8] -0.030 0.052 -0.152 -0.058 -0.018 0.001 0.055 1.015 240
## b.schoolMAIN.adj[9] 0.016 0.052 -0.084 -0.012 0.006 0.041 0.139 1.007 1200
## b.schoolMAIN.adj[10] -0.019 0.049 -0.134 -0.044 -0.010 0.006 0.073 1.015 340
## b.schoolMAIN.adj[11] -0.045 0.063 -0.198 -0.081 -0.028 -0.001 0.045 1.022 140
## b.schoolMAIN.adj[12] 0.048 0.055 -0.030 0.003 0.037 0.083 0.176 1.029 93
## b.schoolMAIN.adj[13] 0.027 0.046 -0.051 -0.001 0.017 0.052 0.136 1.010 440
## b.znas8 0.058 0.021 0.018 0.045 0.058 0.072 0.102 1.022 120
## mu 0.656 0.042 0.578 0.636 0.659 0.681 0.725 1.073 120
## mu.adj 0.658 0.031 0.595 0.638 0.659 0.679 0.717 1.015 180
## sigma.epsilon 0.435 0.039 0.362 0.409 0.435 0.461 0.514 1.036 78
## sigma.schoolMAIN 0.058 0.043 0.001 0.028 0.053 0.080 0.150 1.283 18
## sigma.znas8 48.957 28.584 2.122 24.232 49.053 73.151 97.198 1.001 3600
## deviance 9471.816 44.947 9384.761 9441.019 9471.726 9503.325 9560.992 1.015 180
##
## For each parameter, n.eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
##
## DIC info (using the rule, pD = var(deviance)/2)
## pD = 994.2 and DIC = 10466.0
## DIC is an estimate of expected predictive error (lower deviance is better).
plot(Q1mBBs.fit)
# autocorr.plot(sfit.mcmc)
library(R2jags)
sfit.mcmc <- as.mcmc(Q1mBBs.fit)
summary(sfit.mcmc)
##
## Iterations = 1:900
## Thinning interval = 1
## Number of chains = 4
## Sample size per chain = 900
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## b.schoolMAIN[1] 3.00e-02 0.0591 0.000984 0.00337
## b.schoolMAIN[2] 1.98e-02 0.0553 0.000922 0.00265
## b.schoolMAIN[3] -5.19e-03 0.0531 0.000885 0.00180
## b.schoolMAIN[4] -2.46e-03 0.0558 0.000930 0.00201
## b.schoolMAIN[5] -4.54e-03 0.0650 0.001084 0.00175
## b.schoolMAIN[6] 4.39e-04 0.0593 0.000989 0.00203
## b.schoolMAIN[7] -2.14e-02 0.0542 0.000903 0.00233
## b.schoolMAIN[8] -2.79e-02 0.0561 0.000936 0.00246
## b.schoolMAIN[9] 1.75e-02 0.0603 0.001005 0.00261
## b.schoolMAIN[10] -1.72e-02 0.0540 0.000900 0.00209
## b.schoolMAIN[11] -4.30e-02 0.0637 0.001062 0.00385
## b.schoolMAIN[12] 5.01e-02 0.0644 0.001074 0.00482
## b.schoolMAIN[13] 2.86e-02 0.0541 0.000902 0.00290
## b.schoolMAIN.adj[1] 2.81e-02 0.0491 0.000818 0.00206
## b.schoolMAIN.adj[2] 1.79e-02 0.0490 0.000816 0.00163
## b.schoolMAIN.adj[3] -7.09e-03 0.0477 0.000795 0.00122
## b.schoolMAIN.adj[4] -4.36e-03 0.0491 0.000818 0.00127
## b.schoolMAIN.adj[5] -6.45e-03 0.0617 0.001028 0.00157
## b.schoolMAIN.adj[6] -1.46e-03 0.0535 0.000892 0.00121
## b.schoolMAIN.adj[7] -2.33e-02 0.0503 0.000839 0.00203
## b.schoolMAIN.adj[8] -2.98e-02 0.0518 0.000864 0.00207
## b.schoolMAIN.adj[9] 1.56e-02 0.0521 0.000869 0.00160
## b.schoolMAIN.adj[10] -1.91e-02 0.0486 0.000811 0.00134
## b.schoolMAIN.adj[11] -4.49e-02 0.0629 0.001048 0.00413
## b.schoolMAIN.adj[12] 4.82e-02 0.0554 0.000924 0.00425
## b.schoolMAIN.adj[13] 2.67e-02 0.0460 0.000767 0.00203
## b.znas8 5.84e-02 0.0207 0.000345 0.00111
## deviance 9.47e+03 44.9475 0.749124 2.88412
## mu 6.56e-01 0.0421 0.000701 0.00252
## mu.adj 6.58e-01 0.0310 0.000517 0.00138
## sigma.epsilon 4.35e-01 0.0387 0.000645 0.00393
## sigma.schoolMAIN 5.80e-02 0.0426 0.000711 0.00504
## sigma.znas8 4.90e+01 28.5841 0.476402 0.47648
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## b.schoolMAIN[1] -5.77e-02 -2.87e-03 1.65e-02 5.55e-02 1.64e-01
## b.schoolMAIN[2] -7.88e-02 -8.94e-03 7.39e-03 4.64e-02 1.46e-01
## b.schoolMAIN[3] -1.16e-01 -3.09e-02 -1.69e-03 1.96e-02 9.69e-02
## b.schoolMAIN[4] -1.17e-01 -2.89e-02 -1.09e-03 2.06e-02 1.15e-01
## b.schoolMAIN[5] -1.49e-01 -3.18e-02 -8.20e-04 2.34e-02 1.32e-01
## b.schoolMAIN[6] -1.18e-01 -2.65e-02 -5.81e-05 2.55e-02 1.27e-01
## b.schoolMAIN[7] -1.45e-01 -5.00e-02 -1.18e-02 6.55e-03 8.08e-02
## b.schoolMAIN[8] -1.57e-01 -5.83e-02 -1.66e-02 3.01e-03 6.96e-02
## b.schoolMAIN[9] -8.80e-02 -1.26e-02 6.62e-03 4.17e-02 1.55e-01
## b.schoolMAIN[10] -1.39e-01 -4.23e-02 -9.33e-03 7.95e-03 8.32e-02
## b.schoolMAIN[11] -1.96e-01 -7.92e-02 -2.56e-02 -5.91e-05 5.03e-02
## b.schoolMAIN[12] -3.57e-02 2.47e-03 3.63e-02 8.32e-02 1.92e-01
## b.schoolMAIN[13] -5.55e-02 -1.88e-03 1.69e-02 5.27e-02 1.56e-01
## b.schoolMAIN.adj[1] -5.37e-02 -1.98e-03 1.60e-02 5.47e-02 1.47e-01
## b.schoolMAIN.adj[2] -7.06e-02 -7.83e-03 7.77e-03 4.36e-02 1.34e-01
## b.schoolMAIN.adj[3] -1.13e-01 -3.05e-02 -1.97e-03 1.65e-02 8.66e-02
## b.schoolMAIN.adj[4] -1.10e-01 -2.85e-02 -1.23e-03 1.88e-02 9.96e-02
## b.schoolMAIN.adj[5] -1.46e-01 -3.15e-02 -1.07e-03 2.13e-02 1.17e-01
## b.schoolMAIN.adj[6] -1.13e-01 -2.54e-02 -3.09e-04 2.22e-02 1.14e-01
## b.schoolMAIN.adj[7] -1.41e-01 -4.94e-02 -1.31e-02 4.58e-03 6.72e-02
## b.schoolMAIN.adj[8] -1.52e-01 -5.75e-02 -1.85e-02 1.46e-03 5.47e-02
## b.schoolMAIN.adj[9] -8.38e-02 -1.16e-02 6.30e-03 4.08e-02 1.39e-01
## b.schoolMAIN.adj[10] -1.34e-01 -4.36e-02 -1.03e-02 5.88e-03 7.29e-02
## b.schoolMAIN.adj[11] -1.98e-01 -8.10e-02 -2.82e-02 -5.87e-04 4.51e-02
## b.schoolMAIN.adj[12] -3.05e-02 3.07e-03 3.69e-02 8.30e-02 1.76e-01
## b.schoolMAIN.adj[13] -5.06e-02 -1.36e-03 1.73e-02 5.20e-02 1.36e-01
## b.znas8 1.84e-02 4.49e-02 5.80e-02 7.16e-02 1.02e-01
## deviance 9.38e+03 9.44e+03 9.47e+03 9.50e+03 9.56e+03
## mu 5.78e-01 6.36e-01 6.59e-01 6.81e-01 7.25e-01
## mu.adj 5.95e-01 6.38e-01 6.59e-01 6.79e-01 7.17e-01
## sigma.epsilon 3.62e-01 4.09e-01 4.35e-01 4.61e-01 5.14e-01
## sigma.schoolMAIN 1.31e-03 2.77e-02 5.35e-02 7.99e-02 1.50e-01
## sigma.znas8 2.12e+00 2.42e+01 4.91e+01 7.32e+01 9.72e+01
xyplot(sfit.mcmc, layout = c(2, 10), aspect = "fill")
densityplot(sfit.mcmc)
options(width = 200)
Q1mBBc.model <- function() {
for (i in 1:n) {
znas8[i] ~ dnorm(0, 0.01)
Q1_male[i] ~ dpois(lambda[i])
log(lambda[i]) <- mu + b.znas8 * znas8[i] + b.boys[n_boys[i]] + epsilon[i]
epsilon[i] ~ dnorm(0, tau.epsilon)
}
mu ~ dnorm(0, 1e-04)
mu.adj <- mu + mean(b.boys[])
tau.epsilon <- pow(sigma.epsilon, -2)
sigma.epsilon ~ dunif(0, 100)
b.znas8 ~ dnorm(0, 0.01)
tau.znas8 <- pow(sigma.znas8, -2)
sigma.znas8 ~ dunif(0, 100)
for (j in 1:n.boys) {
b.boys[j] ~ dnorm(0, tau.boys)
b.boys.adj[j] <- b.boys[j] - mean(b.boys[])
}
tau.boys <- pow(sigma.boys, -2)
sigma.boys ~ dunif(0, 100)
}
library(R2jags)
n <- length(Boys$id) # of Y10 survey respondents
n.boys <- length(unique(Boys$n_boys))
Q1_male <- Boys$Q1_male
znas8 <- Boys$znas8
n_boys <- as.factor(Boys$zboys)
Q1mBBc.data <- list("n", "n.boys", "Q1_male", "znas8", "n_boys")
Q1mBBc.params <- c("mu", "mu.adj", "b.znas8", "b.boys", "b.boys.adj", "sigma.znas8", "sigma.boys", "sigma.epsilon")
Q1mBBc.inits <- function() {
list(b.znas8 = c(0), b.boys = rnorm(n.boys))
}
set.seed(500)
Q1mBBc.fit <- jags(data = Q1mBBc.data, inits = Q1mBBc.inits, Q1mBBc.params, model.file = Q1mBBc.model, n.chains = 4, n.iter = 1000, n.burnin = 100)
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph Size: 6140
##
## Initializing model
print(Q1mBBc.fit)
## Inference for Bugs model at "/var/folders/mn/jsy0lvks0117hn0pl7ysl4380000gp/T//Rtmp1SRtO7/model56ec38ad4ef4.txt", fit using jags,
## 4 chains, each with 1000 iterations (first 100 discarded)
## n.sims = 3600 iterations saved
## mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
## b.boys[1] -0.028 0.083 -0.233 -0.055 -0.009 0.011 0.100 1.032 190
## b.boys[2] -0.051 0.099 -0.328 -0.079 -0.019 0.003 0.068 1.047 100
## b.boys[3] 0.007 0.068 -0.119 -0.021 0.002 0.031 0.156 1.027 2000
## b.boys[4] 0.020 0.073 -0.107 -0.013 0.007 0.044 0.199 1.035 380
## b.boys[5] -0.008 0.063 -0.148 -0.034 -0.003 0.020 0.112 1.021 790
## b.boys[6] 0.029 0.071 -0.076 -0.007 0.011 0.054 0.204 1.055 110
## b.boys[7] -0.033 0.061 -0.174 -0.064 -0.019 0.002 0.065 1.038 120
## b.boys[8] -0.013 0.058 -0.141 -0.038 -0.006 0.013 0.094 1.021 500
## b.boys[9] 0.000 0.055 -0.115 -0.026 -0.001 0.024 0.119 1.017 1800
## b.boys[10] 0.017 0.056 -0.082 -0.010 0.008 0.042 0.142 1.037 210
## b.boys[11] -0.020 0.070 -0.182 -0.048 -0.007 0.012 0.103 1.025 250
## b.boys[12] -0.014 0.056 -0.142 -0.040 -0.007 0.012 0.085 1.030 230
## b.boys[13] -0.009 0.060 -0.152 -0.035 -0.003 0.016 0.109 1.019 1200
## b.boys[14] -0.027 0.068 -0.188 -0.054 -0.013 0.007 0.078 1.027 170
## b.boys[15] 0.033 0.082 -0.083 -0.007 0.012 0.061 0.234 1.049 160
## b.boys[16] -0.046 0.088 -0.288 -0.076 -0.019 0.003 0.076 1.048 78
## b.boys[17] 0.007 0.064 -0.114 -0.023 0.002 0.031 0.153 1.022 1100
## b.boys[18] -0.003 0.059 -0.125 -0.029 -0.002 0.020 0.123 1.025 3600
## b.boys[19] 0.013 0.058 -0.083 -0.015 0.005 0.036 0.144 1.031 950
## b.boys[20] 0.013 0.064 -0.104 -0.017 0.004 0.037 0.162 1.030 370
## b.boys[21] 0.027 0.072 -0.086 -0.009 0.010 0.051 0.201 1.039 150
## b.boys[22] 0.052 0.076 -0.036 0.002 0.030 0.082 0.242 1.063 74
## b.boys[23] 0.019 0.067 -0.097 -0.014 0.006 0.045 0.176 1.031 260
## b.boys[24] 0.047 0.072 -0.048 0.000 0.025 0.079 0.220 1.055 74
## b.boys.adj[1] -0.029 0.084 -0.237 -0.057 -0.010 0.011 0.096 1.036 170
## b.boys.adj[2] -0.052 0.102 -0.334 -0.082 -0.019 0.003 0.065 1.056 100
## b.boys.adj[3] 0.006 0.062 -0.123 -0.021 0.002 0.030 0.151 1.024 1200
## b.boys.adj[4] 0.019 0.067 -0.106 -0.013 0.006 0.044 0.191 1.024 420
## b.boys.adj[5] -0.009 0.060 -0.149 -0.033 -0.003 0.018 0.108 1.021 410
## b.boys.adj[6] 0.028 0.064 -0.075 -0.006 0.011 0.054 0.191 1.050 98
## b.boys.adj[7] -0.034 0.056 -0.168 -0.064 -0.020 0.001 0.055 1.036 100
## b.boys.adj[8] -0.014 0.052 -0.137 -0.037 -0.006 0.012 0.082 1.020 510
## b.boys.adj[9] -0.002 0.051 -0.113 -0.025 -0.001 0.022 0.109 1.011 3600
## b.boys.adj[10] 0.016 0.049 -0.082 -0.009 0.009 0.040 0.131 1.023 210
## b.boys.adj[11] -0.021 0.068 -0.188 -0.046 -0.008 0.011 0.098 1.024 230
## b.boys.adj[12] -0.016 0.051 -0.138 -0.040 -0.008 0.011 0.079 1.026 230
## b.boys.adj[13] -0.011 0.056 -0.145 -0.033 -0.003 0.016 0.095 1.017 1300
## b.boys.adj[14] -0.028 0.063 -0.186 -0.054 -0.014 0.006 0.068 1.027 150
## b.boys.adj[15] 0.032 0.074 -0.079 -0.006 0.012 0.058 0.227 1.033 160
## b.boys.adj[16] -0.048 0.091 -0.295 -0.075 -0.018 0.003 0.068 1.047 81
## b.boys.adj[17] 0.005 0.060 -0.119 -0.022 0.001 0.031 0.143 1.017 1400
## b.boys.adj[18] -0.004 0.055 -0.127 -0.030 -0.002 0.020 0.112 1.015 3600
## b.boys.adj[19] 0.012 0.050 -0.083 -0.015 0.005 0.035 0.129 1.013 920
## b.boys.adj[20] 0.012 0.058 -0.101 -0.016 0.004 0.036 0.153 1.017 500
## b.boys.adj[21] 0.025 0.065 -0.081 -0.008 0.010 0.050 0.197 1.028 150
## b.boys.adj[22] 0.051 0.069 -0.034 0.002 0.030 0.082 0.232 1.059 62
## b.boys.adj[23] 0.017 0.062 -0.096 -0.014 0.007 0.044 0.170 1.021 310
## b.boys.adj[24] 0.045 0.065 -0.043 0.000 0.026 0.078 0.215 1.050 65
## b.znas8 0.059 0.020 0.021 0.046 0.059 0.072 0.101 1.014 200
## mu 0.661 0.039 0.592 0.641 0.663 0.685 0.725 1.093 580
## mu.adj 0.662 0.031 0.601 0.642 0.663 0.683 0.722 1.003 1100
## sigma.boys 0.062 0.051 0.003 0.024 0.051 0.086 0.182 1.128 30
## sigma.epsilon 0.429 0.036 0.352 0.406 0.430 0.453 0.494 1.029 120
## sigma.znas8 50.443 28.922 2.297 25.436 51.007 75.611 97.651 1.001 3600
## deviance 9475.433 43.133 9394.861 9445.884 9473.723 9503.671 9563.547 1.009 330
##
## For each parameter, n.eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
##
## DIC info (using the rule, pD = var(deviance)/2)
## pD = 922.5 and DIC = 10397.9
## DIC is an estimate of expected predictive error (lower deviance is better).
plot(Q1mBBc.fit)
cfit.mcmc <- as.mcmc(Q1mBBc.fit)
summary(cfit.mcmc)
##
## Iterations = 1:900
## Thinning interval = 1
## Number of chains = 4
## Sample size per chain = 900
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## b.boys[1] -2.81e-02 0.0826 0.001377 0.00369
## b.boys[2] -5.07e-02 0.0988 0.001647 0.00705
## b.boys[3] 7.24e-03 0.0676 0.001126 0.00192
## b.boys[4] 2.04e-02 0.0728 0.001214 0.00316
## b.boys[5] -7.63e-03 0.0627 0.001045 0.00181
## b.boys[6] 2.92e-02 0.0706 0.001177 0.00369
## b.boys[7] -3.26e-02 0.0608 0.001014 0.00242
## b.boys[8] -1.32e-02 0.0575 0.000959 0.00215
## b.boys[9] -4.93e-04 0.0554 0.000924 0.00167
## b.boys[10] 1.74e-02 0.0561 0.000935 0.00235
## b.boys[11] -2.02e-02 0.0702 0.001170 0.00236
## b.boys[12] -1.44e-02 0.0560 0.000933 0.00233
## b.boys[13] -9.27e-03 0.0603 0.001004 0.00227
## b.boys[14] -2.70e-02 0.0680 0.001133 0.00275
## b.boys[15] 3.35e-02 0.0815 0.001359 0.00442
## b.boys[16] -4.65e-02 0.0885 0.001474 0.00482
## b.boys[17] 6.51e-03 0.0639 0.001066 0.00152
## b.boys[18] -2.91e-03 0.0591 0.000986 0.00190
## b.boys[19] 1.28e-02 0.0577 0.000962 0.00217
## b.boys[20] 1.29e-02 0.0644 0.001073 0.00283
## b.boys[21] 2.67e-02 0.0719 0.001198 0.00384
## b.boys[22] 5.19e-02 0.0758 0.001263 0.00550
## b.boys[23] 1.86e-02 0.0669 0.001115 0.00258
## b.boys[24] 4.65e-02 0.0723 0.001205 0.00433
## b.boys.adj[1] -2.94e-02 0.0839 0.001399 0.00418
## b.boys.adj[2] -5.20e-02 0.1021 0.001701 0.00817
## b.boys.adj[3] 5.95e-03 0.0624 0.001039 0.00133
## b.boys.adj[4] 1.91e-02 0.0672 0.001120 0.00264
## b.boys.adj[5] -8.92e-03 0.0603 0.001005 0.00171
## b.boys.adj[6] 2.80e-02 0.0640 0.001066 0.00287
## b.boys.adj[7] -3.39e-02 0.0558 0.000929 0.00256
## b.boys.adj[8] -1.45e-02 0.0518 0.000863 0.00138
## b.boys.adj[9] -1.78e-03 0.0510 0.000851 0.00114
## b.boys.adj[10] 1.61e-02 0.0491 0.000818 0.00181
## b.boys.adj[11] -2.15e-02 0.0679 0.001131 0.00263
## b.boys.adj[12] -1.57e-02 0.0515 0.000858 0.00151
## b.boys.adj[13] -1.05e-02 0.0558 0.000930 0.00157
## b.boys.adj[14] -2.82e-02 0.0626 0.001043 0.00250
## b.boys.adj[15] 3.22e-02 0.0744 0.001240 0.00374
## b.boys.adj[16] -4.78e-02 0.0907 0.001511 0.00534
## b.boys.adj[17] 5.23e-03 0.0600 0.001000 0.00130
## b.boys.adj[18] -4.19e-03 0.0552 0.000920 0.00117
## b.boys.adj[19] 1.15e-02 0.0503 0.000838 0.00157
## b.boys.adj[20] 1.16e-02 0.0576 0.000960 0.00193
## b.boys.adj[21] 2.54e-02 0.0648 0.001080 0.00362
## b.boys.adj[22] 5.07e-02 0.0686 0.001143 0.00471
## b.boys.adj[23] 1.74e-02 0.0618 0.001030 0.00179
## b.boys.adj[24] 4.52e-02 0.0654 0.001090 0.00389
## b.znas8 5.94e-02 0.0203 0.000339 0.00104
## deviance 9.48e+03 43.1334 0.718890 2.79290
## mu 6.61e-01 0.0392 0.000653 0.00223
## mu.adj 6.62e-01 0.0306 0.000510 0.00123
## sigma.boys 6.15e-02 0.0507 0.000845 0.00546
## sigma.epsilon 4.29e-01 0.0362 0.000603 0.00361
## sigma.znas8 5.04e+01 28.9221 0.482035 0.47312
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## b.boys[1] -2.33e-01 -5.53e-02 -9.49e-03 1.10e-02 1.00e-01
## b.boys[2] -3.28e-01 -7.95e-02 -1.89e-02 3.40e-03 6.84e-02
## b.boys[3] -1.19e-01 -2.13e-02 1.57e-03 3.11e-02 1.56e-01
## b.boys[4] -1.07e-01 -1.29e-02 6.76e-03 4.44e-02 1.99e-01
## b.boys[5] -1.48e-01 -3.35e-02 -3.02e-03 1.96e-02 1.12e-01
## b.boys[6] -7.61e-02 -7.13e-03 1.12e-02 5.37e-02 2.04e-01
## b.boys[7] -1.74e-01 -6.45e-02 -1.90e-02 1.82e-03 6.52e-02
## b.boys[8] -1.41e-01 -3.75e-02 -5.96e-03 1.27e-02 9.35e-02
## b.boys[9] -1.15e-01 -2.60e-02 -8.19e-04 2.38e-02 1.19e-01
## b.boys[10] -8.20e-02 -9.73e-03 8.28e-03 4.21e-02 1.42e-01
## b.boys[11] -1.82e-01 -4.75e-02 -7.17e-03 1.23e-02 1.03e-01
## b.boys[12] -1.42e-01 -4.05e-02 -7.16e-03 1.23e-02 8.48e-02
## b.boys[13] -1.52e-01 -3.46e-02 -3.37e-03 1.64e-02 1.09e-01
## b.boys[14] -1.88e-01 -5.44e-02 -1.33e-02 7.23e-03 7.83e-02
## b.boys[15] -8.30e-02 -6.74e-03 1.24e-02 6.07e-02 2.34e-01
## b.boys[16] -2.88e-01 -7.60e-02 -1.87e-02 2.98e-03 7.57e-02
## b.boys[17] -1.14e-01 -2.27e-02 1.74e-03 3.14e-02 1.53e-01
## b.boys[18] -1.25e-01 -2.91e-02 -2.12e-03 2.03e-02 1.23e-01
## b.boys[19] -8.28e-02 -1.52e-02 4.92e-03 3.58e-02 1.44e-01
## b.boys[20] -1.04e-01 -1.66e-02 4.37e-03 3.69e-02 1.62e-01
## b.boys[21] -8.64e-02 -8.84e-03 9.79e-03 5.13e-02 2.01e-01
## b.boys[22] -3.63e-02 1.86e-03 2.99e-02 8.22e-02 2.42e-01
## b.boys[23] -9.69e-02 -1.41e-02 5.85e-03 4.47e-02 1.76e-01
## b.boys[24] -4.77e-02 -2.20e-04 2.55e-02 7.93e-02 2.20e-01
## b.boys.adj[1] -2.37e-01 -5.66e-02 -9.91e-03 1.10e-02 9.56e-02
## b.boys.adj[2] -3.34e-01 -8.20e-02 -1.93e-02 3.32e-03 6.50e-02
## b.boys.adj[3] -1.23e-01 -2.07e-02 1.72e-03 2.99e-02 1.51e-01
## b.boys.adj[4] -1.06e-01 -1.26e-02 6.24e-03 4.43e-02 1.91e-01
## b.boys.adj[5] -1.49e-01 -3.32e-02 -2.86e-03 1.83e-02 1.08e-01
## b.boys.adj[6] -7.47e-02 -6.49e-03 1.15e-02 5.41e-02 1.91e-01
## b.boys.adj[7] -1.68e-01 -6.45e-02 -2.00e-02 9.52e-04 5.45e-02
## b.boys.adj[8] -1.37e-01 -3.72e-02 -5.90e-03 1.21e-02 8.18e-02
## b.boys.adj[9] -1.13e-01 -2.52e-02 -1.04e-03 2.24e-02 1.09e-01
## b.boys.adj[10] -8.20e-02 -8.81e-03 8.60e-03 4.00e-02 1.31e-01
## b.boys.adj[11] -1.88e-01 -4.62e-02 -7.59e-03 1.15e-02 9.78e-02
## b.boys.adj[12] -1.38e-01 -4.02e-02 -8.02e-03 1.08e-02 7.85e-02
## b.boys.adj[13] -1.45e-01 -3.34e-02 -3.42e-03 1.56e-02 9.50e-02
## b.boys.adj[14] -1.86e-01 -5.39e-02 -1.38e-02 6.10e-03 6.85e-02
## b.boys.adj[15] -7.92e-02 -6.25e-03 1.21e-02 5.81e-02 2.27e-01
## b.boys.adj[16] -2.95e-01 -7.55e-02 -1.83e-02 3.25e-03 6.81e-02
## b.boys.adj[17] -1.19e-01 -2.19e-02 1.18e-03 3.10e-02 1.43e-01
## b.boys.adj[18] -1.27e-01 -2.96e-02 -2.13e-03 2.01e-02 1.12e-01
## b.boys.adj[19] -8.32e-02 -1.47e-02 5.13e-03 3.49e-02 1.29e-01
## b.boys.adj[20] -1.01e-01 -1.62e-02 4.23e-03 3.64e-02 1.53e-01
## b.boys.adj[21] -8.10e-02 -8.34e-03 9.81e-03 5.01e-02 1.97e-01
## b.boys.adj[22] -3.42e-02 2.08e-03 3.04e-02 8.24e-02 2.32e-01
## b.boys.adj[23] -9.62e-02 -1.41e-02 6.62e-03 4.36e-02 1.70e-01
## b.boys.adj[24] -4.31e-02 2.22e-04 2.57e-02 7.78e-02 2.15e-01
## b.znas8 2.10e-02 4.58e-02 5.85e-02 7.17e-02 1.01e-01
## deviance 9.39e+03 9.45e+03 9.47e+03 9.50e+03 9.56e+03
## mu 5.92e-01 6.41e-01 6.63e-01 6.85e-01 7.25e-01
## mu.adj 6.01e-01 6.42e-01 6.63e-01 6.83e-01 7.22e-01
## sigma.boys 3.04e-03 2.37e-02 5.06e-02 8.64e-02 1.82e-01
## sigma.epsilon 3.52e-01 4.06e-01 4.30e-01 4.53e-01 4.94e-01
## sigma.znas8 2.30e+00 2.54e+01 5.10e+01 7.56e+01 9.77e+01
# autocorr.plot(cfit.mcmc)
xyplot(cfit.mcmc, layout = c(2, 15), aspect = "fill")
densityplot(cfit.mcmc, layout = c(3, 10), aspect = "fill")
options(width = 200)
Q1mBBf.model <- function() {
for (i in 1:n) {
znas8[i] ~ dnorm(0, 0.01)
Q1_male[i] ~ dpois(lambda[i])
log(lambda[i]) <- mu + b.znas8 * znas8[i] + b.schoolMAIN[school[i]] + b.boys[zboys[i]] + epsilon[i]
epsilon[i] ~ dnorm(0, tau.epsilon)
}
mu ~ dnorm(0, 1e-04)
mu.adj <- mu + mean(b.schoolMAIN[])
tau.epsilon <- pow(sigma.epsilon, -2)
sigma.epsilon ~ dunif(0, 100)
b.znas8 ~ dnorm(0, 0.01)
tau.znas8 <- pow(sigma.znas8, -2)
sigma.znas8 ~ dunif(0, 100)
for (j in 1:n.boys) {
b.boys[j] ~ dnorm(0, tau.boys)
b.boys.adj[j] <- b.boys[j] - mean(b.boys[])
}
tau.boys <- pow(sigma.boys, -2)
sigma.boys ~ dunif(0, 100)
for (j in 1:n.school) {
b.schoolMAIN[j] ~ dnorm(0, tau.schoolMAIN)
b.schoolMAIN.adj[j] <- b.schoolMAIN[j] - mean(b.schoolMAIN[])
}
tau.schoolMAIN <- pow(sigma.schoolMAIN, -2)
sigma.schoolMAIN ~ dunif(0, 100)
}
library(R2jags)
n <- length(Boys$id)
n.boys <- length(unique(Boys$zboys))
n.school <- length(unique(Boys$schoolMAIN))
Q1_male <- Boys$Q1_male
znas8 <- Boys$znas8
zboys <- Boys$zboys
school <- Boys$school
Q1mBBf.data <- list("n", "n.boys", "n.school", "Q1_male", "znas8", "zboys", "school")
Q1mBBf.params <- c("mu", "mu.adj", "b.znas8", "b.boys", "b.boys.adj", "b.schoolMAIN", "b.schoolMAIN.adj", "sigma.znas8", "sigma.boys", "sigma.schoolMAIN", "sigma.epsilon")
Q1mBBf.inits <- function() {
list(b.znas8 = c(0), b.boys = rnorm(n.boys), b.schoolMAIN = rnorm(n.school))
}
set.seed(999)
Q1mBBf.fit <- jags(data = Q1mBBf.data, inits = Q1mBBf.inits, Q1mBBf.params, model.file = Q1mBBf.model, n.chains = 4, n.iter = 1000, n.burnin = 100)
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph Size: 7164
##
## Initializing model
print(Q1mBBf.fit)
## Inference for Bugs model at "/var/folders/mn/jsy0lvks0117hn0pl7ysl4380000gp/T//Rtmp1SRtO7/model56ec7a1a923d.txt", fit using jags,
## 4 chains, each with 1000 iterations (first 100 discarded)
## n.sims = 3600 iterations saved
## mu.vect sd.vect 2.5% 25% 50% 75% 97.5% Rhat n.eff
## b.boys[1] -0.025 0.078 -0.219 -0.058 -0.011 0.015 0.111 1.020 340
## b.boys[2] -0.053 0.091 -0.305 -0.087 -0.028 0.002 0.067 1.048 95
## b.boys[3] 0.004 0.068 -0.138 -0.028 0.002 0.036 0.156 1.015 3600
## b.boys[4] 0.020 0.072 -0.116 -0.016 0.011 0.054 0.193 1.021 410
## b.boys[5] -0.011 0.065 -0.160 -0.042 -0.006 0.022 0.113 1.008 1500
## b.boys[6] 0.033 0.071 -0.083 -0.008 0.018 0.066 0.201 1.035 130
## b.boys[7] -0.035 0.061 -0.183 -0.067 -0.024 0.003 0.066 1.020 190
## b.boys[8] -0.012 0.061 -0.150 -0.041 -0.006 0.019 0.105 1.014 1200
## b.boys[9] 0.002 0.057 -0.115 -0.028 0.001 0.032 0.124 1.017 3600
## b.boys[10] 0.024 0.057 -0.074 -0.010 0.014 0.054 0.164 1.031 150
## b.boys[11] -0.017 0.073 -0.191 -0.050 -0.008 0.019 0.118 1.020 500
## b.boys[12] -0.015 0.057 -0.146 -0.045 -0.009 0.015 0.092 1.010 680
## b.boys[13] -0.004 0.063 -0.146 -0.033 -0.002 0.027 0.121 1.021 710
## b.boys[14] -0.033 0.066 -0.199 -0.068 -0.018 0.007 0.076 1.030 160
## b.boys[15] 0.031 0.074 -0.092 -0.011 0.016 0.065 0.209 1.031 150
## b.boys[16] -0.045 0.081 -0.249 -0.079 -0.024 0.004 0.074 1.039 96
## b.boys[17] 0.007 0.068 -0.125 -0.028 0.003 0.037 0.165 1.021 1700
## b.boys[18] -0.009 0.062 -0.146 -0.042 -0.004 0.024 0.116 1.013 1200
## b.boys[19] 0.008 0.057 -0.105 -0.022 0.004 0.036 0.141 1.023 300
## b.boys[20] 0.015 0.061 -0.102 -0.016 0.008 0.045 0.159 1.016 630
## b.boys[21] 0.022 0.069 -0.104 -0.015 0.011 0.056 0.184 1.030 270
## b.boys[22] 0.050 0.069 -0.058 0.001 0.034 0.089 0.212 1.034 97
## b.boys[23] 0.019 0.069 -0.112 -0.017 0.009 0.052 0.184 1.026 330
## b.boys[24] 0.049 0.071 -0.052 0.001 0.031 0.087 0.220 1.046 77
## b.boys.adj[1] -0.026 0.077 -0.211 -0.060 -0.012 0.014 0.105 1.022 290
## b.boys.adj[2] -0.054 0.091 -0.296 -0.090 -0.029 0.001 0.064 1.052 88
## b.boys.adj[3] 0.003 0.067 -0.139 -0.027 0.001 0.034 0.151 1.014 3600
## b.boys.adj[4] 0.019 0.069 -0.114 -0.016 0.010 0.052 0.180 1.019 460
## b.boys.adj[5] -0.012 0.064 -0.160 -0.042 -0.007 0.020 0.111 1.009 1100
## b.boys.adj[6] 0.032 0.067 -0.077 -0.008 0.018 0.063 0.197 1.033 120
## b.boys.adj[7] -0.036 0.059 -0.181 -0.067 -0.025 0.001 0.062 1.022 160
## b.boys.adj[8] -0.013 0.057 -0.147 -0.042 -0.007 0.018 0.095 1.012 800
## b.boys.adj[9] 0.001 0.055 -0.113 -0.028 0.000 0.030 0.116 1.015 3600
## b.boys.adj[10] 0.023 0.055 -0.069 -0.009 0.014 0.053 0.154 1.026 160
## b.boys.adj[11] -0.018 0.070 -0.189 -0.051 -0.009 0.016 0.112 1.019 400
## b.boys.adj[12] -0.016 0.054 -0.143 -0.044 -0.010 0.014 0.085 1.010 520
## b.boys.adj[13] -0.005 0.061 -0.147 -0.033 -0.002 0.026 0.117 1.021 530
## b.boys.adj[14] -0.034 0.064 -0.191 -0.068 -0.020 0.006 0.071 1.032 140
## b.boys.adj[15] 0.030 0.072 -0.089 -0.011 0.015 0.063 0.204 1.028 150
## b.boys.adj[16] -0.046 0.079 -0.251 -0.080 -0.026 0.003 0.071 1.042 88
## b.boys.adj[17] 0.006 0.067 -0.132 -0.027 0.003 0.036 0.154 1.023 1800
## b.boys.adj[18] -0.010 0.061 -0.143 -0.042 -0.005 0.023 0.108 1.014 820
## b.boys.adj[19] 0.007 0.054 -0.105 -0.021 0.004 0.033 0.134 1.021 320
## b.boys.adj[20] 0.014 0.059 -0.100 -0.016 0.007 0.043 0.152 1.013 750
## b.boys.adj[21] 0.021 0.067 -0.103 -0.014 0.011 0.053 0.178 1.027 290
## b.boys.adj[22] 0.049 0.067 -0.055 0.002 0.034 0.086 0.207 1.034 97
## b.boys.adj[23] 0.018 0.067 -0.109 -0.017 0.009 0.051 0.173 1.026 350
## b.boys.adj[24] 0.048 0.069 -0.052 0.001 0.031 0.083 0.216 1.046 77
## b.schoolMAIN[1] 0.024 0.055 -0.058 -0.007 0.012 0.046 0.149 1.032 610
## b.schoolMAIN[2] 0.021 0.055 -0.072 -0.008 0.011 0.042 0.149 1.023 250
## b.schoolMAIN[3] -0.010 0.055 -0.135 -0.034 -0.005 0.015 0.098 1.002 1900
## b.schoolMAIN[4] -0.001 0.051 -0.103 -0.025 -0.001 0.021 0.106 1.008 890
## b.schoolMAIN[5] 0.000 0.059 -0.123 -0.024 -0.001 0.023 0.129 1.006 990
## b.schoolMAIN[6] 0.001 0.056 -0.118 -0.023 0.000 0.025 0.121 1.005 2200
## b.schoolMAIN[7] -0.017 0.052 -0.139 -0.043 -0.009 0.009 0.084 1.018 190
## b.schoolMAIN[8] -0.023 0.054 -0.155 -0.048 -0.013 0.007 0.070 1.020 220
## b.schoolMAIN[9] 0.016 0.056 -0.079 -0.012 0.008 0.039 0.146 1.010 1100
## b.schoolMAIN[10] -0.013 0.051 -0.131 -0.036 -0.007 0.013 0.087 1.009 810
## b.schoolMAIN[11] -0.034 0.059 -0.186 -0.058 -0.019 0.002 0.054 1.018 170
## b.schoolMAIN[12] 0.040 0.063 -0.045 0.001 0.024 0.067 0.198 1.029 250
## b.schoolMAIN[13] 0.026 0.056 -0.060 -0.005 0.014 0.047 0.158 1.032 240
## b.schoolMAIN.adj[1] 0.021 0.047 -0.051 -0.006 0.011 0.045 0.134 1.005 1000
## b.schoolMAIN.adj[2] 0.018 0.048 -0.068 -0.008 0.010 0.041 0.134 1.009 420
## b.schoolMAIN.adj[3] -0.012 0.051 -0.135 -0.034 -0.005 0.012 0.083 1.002 3600
## b.schoolMAIN.adj[4] -0.003 0.046 -0.105 -0.025 -0.002 0.019 0.091 1.006 1700
## b.schoolMAIN.adj[5] -0.002 0.055 -0.121 -0.025 -0.001 0.023 0.116 1.004 2200
## b.schoolMAIN.adj[6] -0.001 0.052 -0.117 -0.023 0.000 0.021 0.109 1.006 1300
## b.schoolMAIN.adj[7] -0.019 0.048 -0.136 -0.043 -0.010 0.007 0.067 1.015 250
## b.schoolMAIN.adj[8] -0.025 0.052 -0.159 -0.050 -0.013 0.005 0.063 1.013 340
## b.schoolMAIN.adj[9] 0.014 0.049 -0.077 -0.012 0.007 0.037 0.130 1.007 870
## b.schoolMAIN.adj[10] -0.015 0.048 -0.127 -0.037 -0.007 0.010 0.073 1.004 3600
## b.schoolMAIN.adj[11] -0.036 0.057 -0.192 -0.059 -0.021 0.000 0.043 1.014 230
## b.schoolMAIN.adj[12] 0.037 0.055 -0.042 0.001 0.023 0.065 0.174 1.021 160
## b.schoolMAIN.adj[13] 0.023 0.046 -0.055 -0.005 0.013 0.046 0.135 1.010 280
## b.znas8 0.059 0.020 0.020 0.045 0.058 0.072 0.100 1.002 1500
## mu 0.654 0.046 0.566 0.629 0.657 0.683 0.728 1.059 440
## mu.adj 0.656 0.037 0.582 0.633 0.657 0.681 0.724 1.003 3600
## sigma.boys 0.066 0.042 0.007 0.035 0.058 0.093 0.159 1.190 21
## sigma.epsilon 0.426 0.037 0.350 0.402 0.427 0.451 0.501 1.016 190
## sigma.schoolMAIN 0.054 0.040 0.005 0.025 0.045 0.072 0.149 1.082 48
## sigma.znas8 49.200 28.773 2.176 24.916 48.607 74.018 97.669 1.001 3600
## deviance 9476.712 43.896 9393.117 9447.341 9475.894 9505.949 9563.689 1.005 560
##
## For each parameter, n.eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor (at convergence, Rhat=1).
##
## DIC info (using the rule, pD = var(deviance)/2)
## pD = 959.0 and DIC = 10435.7
## DIC is an estimate of expected predictive error (lower deviance is better).
ffit.mcmc <- as.mcmc(Q1mBBf.fit)
summary(ffit.mcmc)
##
## Iterations = 1:900
## Thinning interval = 1
## Number of chains = 4
## Sample size per chain = 900
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## b.boys[1] -2.51e-02 0.0778 0.001297 0.002629
## b.boys[2] -5.35e-02 0.0910 0.001517 0.003948
## b.boys[3] 4.41e-03 0.0683 0.001139 0.001397
## b.boys[4] 2.01e-02 0.0717 0.001196 0.002226
## b.boys[5] -1.13e-02 0.0647 0.001078 0.001482
## b.boys[6] 3.29e-02 0.0706 0.001176 0.002777
## b.boys[7] -3.54e-02 0.0613 0.001022 0.002952
## b.boys[8] -1.23e-02 0.0609 0.001015 0.002012
## b.boys[9] 2.08e-03 0.0574 0.000957 0.001600
## b.boys[10] 2.44e-02 0.0573 0.000954 0.002191
## b.boys[11] -1.73e-02 0.0726 0.001210 0.001885
## b.boys[12] -1.53e-02 0.0572 0.000953 0.001636
## b.boys[13] -4.01e-03 0.0632 0.001053 0.001713
## b.boys[14] -3.27e-02 0.0663 0.001105 0.002563
## b.boys[15] 3.11e-02 0.0738 0.001231 0.002560
## b.boys[16] -4.49e-02 0.0807 0.001345 0.003531
## b.boys[17] 6.54e-03 0.0683 0.001139 0.001602
## b.boys[18] -8.84e-03 0.0625 0.001041 0.001432
## b.boys[19] 7.76e-03 0.0570 0.000950 0.001514
## b.boys[20] 1.54e-02 0.0610 0.001017 0.001605
## b.boys[21] 2.21e-02 0.0690 0.001151 0.002258
## b.boys[22] 4.96e-02 0.0688 0.001147 0.003739
## b.boys[23] 1.86e-02 0.0687 0.001146 0.001846
## b.boys[24] 4.92e-02 0.0713 0.001188 0.004139
## b.boys.adj[1] -2.61e-02 0.0769 0.001281 0.002710
## b.boys.adj[2] -5.44e-02 0.0905 0.001509 0.004200
## b.boys.adj[3] 3.43e-03 0.0668 0.001113 0.001343
## b.boys.adj[4] 1.91e-02 0.0693 0.001154 0.001775
## b.boys.adj[5] -1.23e-02 0.0638 0.001063 0.001467
## b.boys.adj[6] 3.19e-02 0.0672 0.001120 0.002479
## b.boys.adj[7] -3.64e-02 0.0586 0.000977 0.002762
## b.boys.adj[8] -1.33e-02 0.0574 0.000957 0.001732
## b.boys.adj[9] 1.09e-03 0.0547 0.000912 0.001363
## b.boys.adj[10] 2.35e-02 0.0546 0.000911 0.002065
## b.boys.adj[11] -1.83e-02 0.0699 0.001165 0.002039
## b.boys.adj[12] -1.63e-02 0.0543 0.000906 0.001382
## b.boys.adj[13] -5.00e-03 0.0609 0.001015 0.001359
## b.boys.adj[14] -3.37e-02 0.0641 0.001068 0.002555
## b.boys.adj[15] 3.01e-02 0.0720 0.001200 0.002564
## b.boys.adj[16] -4.59e-02 0.0794 0.001323 0.004270
## b.boys.adj[17] 5.55e-03 0.0669 0.001114 0.001534
## b.boys.adj[18] -9.82e-03 0.0605 0.001009 0.001370
## b.boys.adj[19] 6.77e-03 0.0545 0.000908 0.001388
## b.boys.adj[20] 1.44e-02 0.0587 0.000978 0.001505
## b.boys.adj[21] 2.11e-02 0.0668 0.001114 0.002165
## b.boys.adj[22] 4.86e-02 0.0666 0.001109 0.004007
## b.boys.adj[23] 1.76e-02 0.0666 0.001110 0.001762
## b.boys.adj[24] 4.83e-02 0.0691 0.001152 0.003858
## b.schoolMAIN[1] 2.36e-02 0.0550 0.000917 0.003648
## b.schoolMAIN[2] 2.07e-02 0.0552 0.000919 0.002728
## b.schoolMAIN[3] -9.86e-03 0.0551 0.000918 0.001794
## b.schoolMAIN[4] -9.87e-04 0.0513 0.000855 0.002275
## b.schoolMAIN[5] 3.90e-05 0.0588 0.000979 0.001798
## b.schoolMAIN[6] 7.91e-04 0.0556 0.000927 0.002050
## b.schoolMAIN[7] -1.71e-02 0.0524 0.000874 0.002339
## b.schoolMAIN[8] -2.29e-02 0.0544 0.000906 0.001975
## b.schoolMAIN[9] 1.62e-02 0.0563 0.000938 0.003508
## b.schoolMAIN[10] -1.31e-02 0.0515 0.000858 0.001973
## b.schoolMAIN[11] -3.36e-02 0.0586 0.000977 0.002455
## b.schoolMAIN[12] 3.96e-02 0.0629 0.001049 0.004848
## b.schoolMAIN[13] 2.55e-02 0.0557 0.000929 0.003461
## b.schoolMAIN.adj[1] 2.14e-02 0.0467 0.000778 0.002585
## b.schoolMAIN.adj[2] 1.85e-02 0.0481 0.000802 0.001528
## b.schoolMAIN.adj[3] -1.21e-02 0.0507 0.000845 0.001277
## b.schoolMAIN.adj[4] -3.21e-03 0.0459 0.000764 0.000921
## b.schoolMAIN.adj[5] -2.18e-03 0.0554 0.000923 0.001193
## b.schoolMAIN.adj[6] -1.43e-03 0.0519 0.000864 0.001186
## b.schoolMAIN.adj[7] -1.94e-02 0.0482 0.000803 0.001570
## b.schoolMAIN.adj[8] -2.51e-02 0.0524 0.000874 0.002684
## b.schoolMAIN.adj[9] 1.40e-02 0.0493 0.000822 0.001390
## b.schoolMAIN.adj[10] -1.54e-02 0.0477 0.000795 0.001627
## b.schoolMAIN.adj[11] -3.58e-02 0.0574 0.000957 0.002674
## b.schoolMAIN.adj[12] 3.73e-02 0.0546 0.000910 0.002897
## b.schoolMAIN.adj[13] 2.33e-02 0.0463 0.000772 0.002319
## b.znas8 5.89e-02 0.0200 0.000333 0.001024
## deviance 9.48e+03 43.8957 0.731595 3.378171
## mu 6.54e-01 0.0459 0.000766 0.003750
## mu.adj 6.56e-01 0.0367 0.000612 0.001888
## sigma.boys 6.64e-02 0.0415 0.000692 0.004167
## sigma.epsilon 4.26e-01 0.0369 0.000614 0.003925
## sigma.schoolMAIN 5.36e-02 0.0405 0.000674 0.004041
## sigma.znas8 4.92e+01 28.7727 0.479544 0.473893
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## b.boys[1] -2.19e-01 -5.79e-02 -1.08e-02 1.52e-02 1.11e-01
## b.boys[2] -3.05e-01 -8.70e-02 -2.83e-02 1.69e-03 6.72e-02
## b.boys[3] -1.38e-01 -2.83e-02 2.24e-03 3.56e-02 1.56e-01
## b.boys[4] -1.16e-01 -1.58e-02 1.09e-02 5.35e-02 1.93e-01
## b.boys[5] -1.60e-01 -4.18e-02 -5.61e-03 2.17e-02 1.13e-01
## b.boys[6] -8.32e-02 -8.40e-03 1.79e-02 6.62e-02 2.01e-01
## b.boys[7] -1.83e-01 -6.74e-02 -2.40e-02 2.58e-03 6.63e-02
## b.boys[8] -1.50e-01 -4.07e-02 -6.31e-03 1.93e-02 1.05e-01
## b.boys[9] -1.15e-01 -2.78e-02 8.03e-04 3.16e-02 1.24e-01
## b.boys[10] -7.42e-02 -9.99e-03 1.42e-02 5.44e-02 1.64e-01
## b.boys[11] -1.91e-01 -4.95e-02 -8.49e-03 1.90e-02 1.18e-01
## b.boys[12] -1.46e-01 -4.47e-02 -8.63e-03 1.51e-02 9.25e-02
## b.boys[13] -1.46e-01 -3.34e-02 -1.68e-03 2.70e-02 1.21e-01
## b.boys[14] -1.99e-01 -6.83e-02 -1.80e-02 7.27e-03 7.56e-02
## b.boys[15] -9.24e-02 -1.14e-02 1.56e-02 6.50e-02 2.09e-01
## b.boys[16] -2.49e-01 -7.85e-02 -2.42e-02 4.29e-03 7.42e-02
## b.boys[17] -1.25e-01 -2.82e-02 2.95e-03 3.66e-02 1.65e-01
## b.boys[18] -1.46e-01 -4.17e-02 -4.10e-03 2.40e-02 1.16e-01
## b.boys[19] -1.05e-01 -2.16e-02 4.08e-03 3.58e-02 1.41e-01
## b.boys[20] -1.02e-01 -1.62e-02 8.01e-03 4.48e-02 1.59e-01
## b.boys[21] -1.04e-01 -1.48e-02 1.13e-02 5.58e-02 1.84e-01
## b.boys[22] -5.76e-02 1.38e-03 3.37e-02 8.87e-02 2.12e-01
## b.boys[23] -1.12e-01 -1.72e-02 9.15e-03 5.24e-02 1.84e-01
## b.boys[24] -5.20e-02 8.59e-04 3.10e-02 8.69e-02 2.20e-01
## b.boys.adj[1] -2.11e-01 -6.03e-02 -1.16e-02 1.38e-02 1.05e-01
## b.boys.adj[2] -2.96e-01 -9.03e-02 -2.85e-02 1.03e-03 6.38e-02
## b.boys.adj[3] -1.39e-01 -2.74e-02 1.33e-03 3.41e-02 1.51e-01
## b.boys.adj[4] -1.14e-01 -1.61e-02 9.78e-03 5.18e-02 1.80e-01
## b.boys.adj[5] -1.60e-01 -4.23e-02 -6.80e-03 2.00e-02 1.11e-01
## b.boys.adj[6] -7.72e-02 -7.62e-03 1.78e-02 6.26e-02 1.97e-01
## b.boys.adj[7] -1.81e-01 -6.74e-02 -2.49e-02 7.67e-04 6.16e-02
## b.boys.adj[8] -1.47e-01 -4.19e-02 -7.09e-03 1.76e-02 9.52e-02
## b.boys.adj[9] -1.13e-01 -2.79e-02 4.85e-04 3.00e-02 1.16e-01
## b.boys.adj[10] -6.88e-02 -8.57e-03 1.45e-02 5.27e-02 1.54e-01
## b.boys.adj[11] -1.89e-01 -5.05e-02 -9.25e-03 1.63e-02 1.12e-01
## b.boys.adj[12] -1.43e-01 -4.44e-02 -1.02e-02 1.38e-02 8.48e-02
## b.boys.adj[13] -1.47e-01 -3.34e-02 -2.25e-03 2.62e-02 1.17e-01
## b.boys.adj[14] -1.91e-01 -6.82e-02 -1.97e-02 6.40e-03 7.15e-02
## b.boys.adj[15] -8.85e-02 -1.08e-02 1.45e-02 6.31e-02 2.04e-01
## b.boys.adj[16] -2.51e-01 -7.99e-02 -2.61e-02 2.98e-03 7.11e-02
## b.boys.adj[17] -1.32e-01 -2.72e-02 2.52e-03 3.58e-02 1.54e-01
## b.boys.adj[18] -1.43e-01 -4.22e-02 -5.33e-03 2.30e-02 1.08e-01
## b.boys.adj[19] -1.05e-01 -2.14e-02 3.77e-03 3.33e-02 1.34e-01
## b.boys.adj[20] -9.95e-02 -1.63e-02 7.47e-03 4.29e-02 1.52e-01
## b.boys.adj[21] -1.03e-01 -1.40e-02 1.07e-02 5.34e-02 1.78e-01
## b.boys.adj[22] -5.47e-02 1.89e-03 3.36e-02 8.63e-02 2.07e-01
## b.boys.adj[23] -1.09e-01 -1.68e-02 8.75e-03 5.14e-02 1.73e-01
## b.boys.adj[24] -5.18e-02 8.63e-04 3.05e-02 8.26e-02 2.16e-01
## b.schoolMAIN[1] -5.77e-02 -6.71e-03 1.19e-02 4.56e-02 1.49e-01
## b.schoolMAIN[2] -7.24e-02 -8.12e-03 1.06e-02 4.18e-02 1.49e-01
## b.schoolMAIN[3] -1.35e-01 -3.42e-02 -4.67e-03 1.53e-02 9.78e-02
## b.schoolMAIN[4] -1.03e-01 -2.53e-02 -1.36e-03 2.10e-02 1.06e-01
## b.schoolMAIN[5] -1.23e-01 -2.44e-02 -9.23e-04 2.29e-02 1.29e-01
## b.schoolMAIN[6] -1.18e-01 -2.26e-02 3.94e-04 2.46e-02 1.21e-01
## b.schoolMAIN[7] -1.39e-01 -4.29e-02 -9.48e-03 9.21e-03 8.40e-02
## b.schoolMAIN[8] -1.55e-01 -4.81e-02 -1.25e-02 6.95e-03 6.96e-02
## b.schoolMAIN[9] -7.90e-02 -1.21e-02 8.25e-03 3.86e-02 1.46e-01
## b.schoolMAIN[10] -1.31e-01 -3.63e-02 -6.55e-03 1.27e-02 8.69e-02
## b.schoolMAIN[11] -1.86e-01 -5.79e-02 -1.90e-02 2.08e-03 5.42e-02
## b.schoolMAIN[12] -4.55e-02 5.40e-04 2.36e-02 6.68e-02 1.98e-01
## b.schoolMAIN[13] -5.95e-02 -4.86e-03 1.41e-02 4.66e-02 1.58e-01
## b.schoolMAIN.adj[1] -5.12e-02 -6.15e-03 1.12e-02 4.50e-02 1.34e-01
## b.schoolMAIN.adj[2] -6.84e-02 -7.64e-03 1.00e-02 4.09e-02 1.34e-01
## b.schoolMAIN.adj[3] -1.35e-01 -3.43e-02 -5.05e-03 1.22e-02 8.29e-02
## b.schoolMAIN.adj[4] -1.05e-01 -2.48e-02 -2.00e-03 1.88e-02 9.14e-02
## b.schoolMAIN.adj[5] -1.21e-01 -2.50e-02 -5.43e-04 2.25e-02 1.16e-01
## b.schoolMAIN.adj[6] -1.17e-01 -2.29e-02 -1.94e-04 2.13e-02 1.09e-01
## b.schoolMAIN.adj[7] -1.36e-01 -4.34e-02 -1.02e-02 7.03e-03 6.72e-02
## b.schoolMAIN.adj[8] -1.59e-01 -4.98e-02 -1.32e-02 4.90e-03 6.30e-02
## b.schoolMAIN.adj[9] -7.74e-02 -1.20e-02 7.18e-03 3.67e-02 1.30e-01
## b.schoolMAIN.adj[10] -1.27e-01 -3.70e-02 -7.40e-03 1.03e-02 7.32e-02
## b.schoolMAIN.adj[11] -1.92e-01 -5.89e-02 -2.10e-02 4.96e-04 4.27e-02
## b.schoolMAIN.adj[12] -4.19e-02 8.82e-04 2.32e-02 6.45e-02 1.74e-01
## b.schoolMAIN.adj[13] -5.51e-02 -4.62e-03 1.34e-02 4.56e-02 1.35e-01
## b.znas8 2.03e-02 4.52e-02 5.84e-02 7.21e-02 1.00e-01
## deviance 9.39e+03 9.45e+03 9.48e+03 9.51e+03 9.56e+03
## mu 5.66e-01 6.29e-01 6.57e-01 6.83e-01 7.28e-01
## mu.adj 5.82e-01 6.33e-01 6.57e-01 6.81e-01 7.24e-01
## sigma.boys 7.03e-03 3.54e-02 5.76e-02 9.27e-02 1.59e-01
## sigma.epsilon 3.50e-01 4.02e-01 4.27e-01 4.51e-01 5.01e-01
## sigma.schoolMAIN 4.54e-03 2.55e-02 4.46e-02 7.25e-02 1.49e-01
## sigma.znas8 2.18e+00 2.49e+01 4.86e+01 7.40e+01 9.77e+01
# autocorr.plot(ffit.mcmc)
plot(Q1mBBf.fit)
xyplot(ffit.mcmc, layout = c(2, 21), aspect = "fill")
densityplot(ffit.mcmc, layout = c(2, 21), aspect = "fill")
options(width = 200)
library(lme4)
library(influence.ME)
# students within classes within schools; using individual-level random variable to deal with overdispersion
M8 <- glmer(Q1_male ~ znas8 + (1 + znas8 | zboys) + (1 + znas8 | schoolMAIN) + (1 | id), family = poisson, data = Boys)
summary(M8)
## Generalized linear mixed model fit by maximum likelihood ['glmerMod']
## Family: poisson ( log )
## Formula: Q1_male ~ znas8 + (1 + znas8 | zboys) + (1 + znas8 | schoolMAIN) + (1 | id)
## Data: Boys
##
## AIC BIC logLik deviance
## 3555 3599 -1769 3537
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 1.90e-01 4.35e-01
## zboys (Intercept) 1.86e-04 1.37e-02
## znas8 1.11e-03 3.34e-02 -1.00
## schoolMAIN (Intercept) 3.42e-13 5.85e-07
## znas8 5.63e-11 7.50e-06 -0.62
## Number of obs: 947, groups: id, 947; zboys, 24; schoolMAIN, 13
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.6774 0.0271 24.95 < 2e-16 ***
## znas8 0.0963 0.0285 3.38 0.00074 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## znas8 -0.131
coef(M8) # estimated model within each class (see $zboys coefficients)
## $id
## (Intercept) znas8
## 2 0.6620 0.09628
## 3 0.7925 0.09628
## 4 0.3804 0.09628
## 5 0.5456 0.09628
## 6 0.4052 0.09628
## 7 0.8185 0.09628
## 8 0.9403 0.09628
## 9 0.8478 0.09628
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## 1435 0.3926 0.09628
## 1436 1.0649 0.09628
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## 1443 0.6941 0.09628
## 1444 0.5366 0.09628
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## 1708 1.0811 0.09628
## 1715 0.3722 0.09628
## 1716 0.8554 0.09628
## 1717 0.7037 0.09628
## 1718 0.7795 0.09628
## 1719 0.7995 0.09628
## 1720 0.3993 0.09628
## 1725 0.5431 0.09628
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## 1728 0.5192 0.09628
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## 1730 1.0553 0.09628
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## 1733 0.3946 0.09628
## 1734 0.3977 0.09628
## 1736 0.6915 0.09628
## 1738 0.9483 0.09628
## 1739 1.0508 0.09628
## 1742 0.5778 0.09628
## 1743 0.8255 0.09628
## 1744 0.9316 0.09628
## 1745 0.7037 0.09628
## 1750 0.6443 0.09628
## 1751 0.5120 0.09628
## 1752 0.5332 0.09628
## 1756 0.8028 0.09628
## 1757 0.6604 0.09628
## 1758 0.8029 0.09628
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## 1760 0.5025 0.09628
## 1761 0.4237 0.09628
## 1762 0.3824 0.09628
## 1764 0.6409 0.09628
## 1766 0.8178 0.09628
## 1867 0.6688 0.09628
## 1868 0.5182 0.09628
## 1869 0.4018 0.09628
## 1870 0.6165 0.09628
## 1871 0.5444 0.09628
## 1872 0.9364 0.09628
## 1874 0.5143 0.09628
## 1875 0.7651 0.09628
## 1885 0.9798 0.09628
## 1889 0.7935 0.09628
## 1890 1.1553 0.09628
## 1891 0.4018 0.09628
## 1894 0.6971 0.09628
## 1895 0.5182 0.09628
## 1896 0.6561 0.09628
## 1897 0.8208 0.09628
## 1899 0.4354 0.09628
## 1904 0.6892 0.09628
##
## $zboys
## (Intercept) znas8
## -1.9403949176938 0.6777 0.09551
## -1.78915377536492 0.6756 0.10065
## -1.63791263303604 0.6810 0.08759
## -1.48667149070715 0.6791 0.09227
## -1.33543034837827 0.6741 0.10449
## -1.18418920604939 0.6802 0.08955
## -1.03294806372051 0.6712 0.11144
## -0.881706921391632 0.6748 0.10278
## -0.730465779062751 0.6730 0.10709
## -0.57922463673387 0.6750 0.10231
## -0.42798349440499 0.6766 0.09839
## -0.276742352076109 0.6755 0.10090
## -0.125501209747228 0.6861 0.07513
## 0.0257399325816523 0.6772 0.09687
## 0.176981074910533 0.6816 0.08596
## 0.479463359568294 0.6770 0.09725
## 0.630704501897175 0.6778 0.09547
## 0.781945644226056 0.6780 0.09492
## 0.933186786554936 0.6824 0.08403
## 1.08442792888382 0.6816 0.08598
## 1.2356690712127 0.6805 0.08881
## 1.38691021354158 0.6759 0.10000
## 1.53815135587046 0.6783 0.09420
## 1.68939249819934 0.6814 0.08660
##
## $schoolMAIN
## (Intercept) znas8
## 1 0.6774 0.09628
## 2 0.6774 0.09628
## 3 0.6774 0.09628
## 5 0.6774 0.09628
## 6 0.6774 0.09628
## 7 0.6774 0.09628
## 8 0.6774 0.09628
## 10 0.6774 0.09628
## 11 0.6774 0.09628
## 20 0.6774 0.09628
## 22 0.6774 0.09628
## 28 0.6774 0.09628
## 36 0.6774 0.09628
##
## attr(,"class")
## [1] "coef.mer"
fixef(M8) # estimated model averaging over classes in schools
## (Intercept) znas8
## 0.67742 0.09628
ranef(M8) # class-level and school-level errors
## $id
## (Intercept)
## 2 -0.0154670
## 3 0.1151111
## 4 -0.2969983
## 5 -0.1318433
## 6 -0.2722149
## 7 0.1410902
## 8 0.2629126
## 9 0.1704071
## 10 -0.0376231
## 11 0.0004589
## 12 0.1468352
## 13 0.1486475
## 14 0.1017286
## 15 0.4499399
## 16 -0.0047613
## 17 -0.0081737
## 18 0.1294082
## 19 0.2414635
## 20 0.0244692
## 21 -0.3244344
## 22 0.1547878
## 23 -0.1191496
## 24 0.0014382
## 25 0.0855659
## 26 -0.3007705
## 27 -0.1031108
## 28 -0.2996590
## 29 -0.2669259
## 30 -0.2969983
## 31 0.1487664
## 32 -0.1540551
## 33 0.2016627
## 34 -0.1475714
## 35 -0.1683175
## 36 -0.3035802
## 37 -0.1592474
## 38 -0.1191712
## 39 -0.1225513
## 40 -0.1416208
## 41 -0.3050353
## 42 -0.0483782
## 43 0.0139831
## 44 0.2544054
## 45 0.1217482
## 46 0.1399235
## 47 -0.1071107
## 48 0.1294082
## 49 0.1709925
## 50 0.0021993
## 51 0.0893285
## 52 0.0930380
## 54 -0.2747348
## 55 0.0772112
## 56 0.1468352
## 57 -0.0017464
## 58 0.2188883
## 59 0.0046034
## 60 -0.1246718
## 61 -0.0312834
## 62 0.0325367
## 63 -0.2713868
## 64 0.1329330
## 65 -0.3185569
## 66 -0.0264639
## 67 0.0170711
## 68 -0.1164485
## 69 -0.3244344
## 70 0.0129039
## 71 0.1490713
## 72 0.8198155
## 73 0.1709925
## 74 0.0108758
## 75 -0.2592485
## 76 -0.1274500
## 77 0.2414635
## 78 0.4069694
## 79 0.8627781
## 80 0.2775238
## 81 -0.0179606
## 83 0.0159134
## 84 0.1561103
## 85 -0.1137206
## 86 0.0139831
## 87 0.0094192
## 88 0.0440031
## 89 0.0059104
## 90 -0.0049503
## 91 -0.2696106
## 92 0.3987992
## 93 0.0231896
## 94 0.1138927
## 95 0.1294082
## 96 -0.2583824
## 97 -0.1540083
## 98 0.0976525
## 99 0.4909658
## 100 -0.2696106
## 101 -0.1540551
## 102 -0.1225513
## 103 0.0357926
## 104 1.0694224
## 105 0.6187197
## 106 0.3871339
## 107 0.3159114
## 108 0.2468075
## 109 0.0266022
## 110 0.1217822
## 111 -0.0081737
## 112 0.1452296
## 113 0.1435683
## 116 0.0106550
## 117 -0.2613230
## 118 0.3323044
## 119 -0.1241762
## 129 -0.1106057
## 131 -0.2429969
## 132 -0.1910139
## 133 -0.1019333
## 137 -0.0046212
## 139 0.2108789
## 140 -0.0384359
## 141 0.2545832
## 145 0.1609345
## 146 0.0291192
## 147 -0.2580682
## 150 0.0091979
## 153 -0.1511517
## 155 0.4069597
## 156 0.2723711
## 158 0.2515203
## 160 -0.1225419
## 161 0.0812366
## 168 0.1424295
## 169 -0.0595371
## 170 -0.2675788
## 171 -0.2765432
## 172 0.1382384
## 174 0.2678825
## 175 -0.0227986
## 178 -0.2920044
## 184 0.2746049
## 185 0.2812650
## 186 -0.2447943
## 189 0.1617744
## 190 -0.2643280
## 196 0.3779548
## 197 0.0066019
## 202 -0.1305024
## 206 0.1403381
## 207 -0.1372753
## 208 0.2882089
## 209 0.0304078
## 210 0.0925011
## 211 -0.2944911
## 212 -0.2954939
## 215 0.2929581
## 216 -0.1117981
## 218 0.2540444
## 219 0.0291192
## 228 0.1258024
## 230 -0.0203498
## 231 0.0363100
## 232 0.2765548
## 233 0.1128083
## 234 -0.0048959
## 235 0.0390271
## 236 0.0077580
## 237 -0.1789287
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## 241 0.0139757
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## 252 0.3935118
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## 254 0.3030150
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## 259 0.0172952
## 262 -0.2571924
## 265 -0.1442504
## 266 0.1299106
## 267 -0.1670341
## 276 -0.1307632
## 277 -0.3098349
## 279 0.0465290
## 280 0.3774188
## 283 -0.1722714
## 287 0.0279337
## 288 0.6200227
## 291 0.2588223
## 297 -0.1903609
## 304 -0.2538169
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## 309 0.1184078
## 313 -0.1510664
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## 316 0.2024819
## 319 -0.1118544
## 323 0.0049798
## 325 0.1445142
## 326 -0.1212583
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## 329 -0.2888596
## 330 0.1045144
## 331 -0.1342578
## 333 0.5501155
## 334 0.0348964
## 335 -0.1592631
## 336 -0.2826076
## 344 -0.2680401
## 345 -0.2278099
## 346 -0.1340425
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## 356 -0.2775376
## 359 -0.2797581
## 360 0.0062697
## 362 -0.1191496
## 364 0.0064220
## 368 0.1620269
## 369 -0.1653623
## 370 0.2405957
## 371 -0.1579875
## 375 0.0296841
## 380 -0.2454929
## 381 -0.1443408
## 382 0.0103778
## 383 0.0334942
## 384 0.0136969
## 386 -0.1117727
## 387 -0.1476638
## 388 0.0232136
## 389 -0.1323655
## 390 -0.1372139
## 391 -0.1100860
## 393 -0.1347463
## 396 -0.1375710
## 397 0.0603616
## 398 -0.1297207
## 400 0.1578582
## 401 0.0279337
## 402 -0.1208108
## 403 -0.0621853
## 404 -0.2803874
## 406 0.0086036
## 407 -0.2637452
## 408 0.2941643
## 412 0.1296975
## 413 0.0333077
## 414 -0.1442739
## 415 0.1419268
## 416 0.2514925
## 420 0.1383134
## 421 0.0246421
## 422 0.1172269
## 423 0.0246421
## 424 -0.1222169
## 427 0.2941643
## 429 0.3648168
## 430 -0.0122252
## 433 0.4374582
## 435 0.2852750
## 436 0.3470045
## 437 -0.2950107
## 440 -0.2799506
## 444 0.2938874
## 445 0.4690808
## 450 0.0066610
## 451 -0.1379025
## 455 -0.1212583
## 456 0.1296975
## 457 -0.1570244
## 459 0.1474794
## 460 -0.3106888
## 462 0.1105001
## 464 0.3011542
## 465 -0.1614804
## 466 -0.1253075
## 469 -0.2712069
## 471 -0.1176246
## 475 -0.1100860
## 476 0.1172269
## 486 0.1127399
## 496 0.2040940
## 498 0.5116665
## 501 -0.1164208
## 502 -0.2824586
## 503 -0.1335508
## 504 0.0275387
## 506 -0.2419783
## 507 -0.1587361
## 508 -0.2579037
## 511 0.0091444
## 512 0.2823965
## 513 0.0157657
## 514 0.3625304
## 515 -0.1652724
## 516 -0.0694753
## 519 -0.1209215
## 520 0.1647473
## 522 0.1532755
## 523 -0.1176927
## 530 -0.0084785
## 531 -0.1049567
## 532 0.1470542
## 534 0.4795008
## 538 -0.0318926
## 539 -0.1144897
## 540 0.3160359
## 541 -0.0085596
## 542 0.2067765
## 544 -0.0008541
## 547 0.1092551
## 548 0.2247957
## 551 0.0213652
## 560 0.0285550
## 561 -0.0543799
## 564 -0.2429969
## 566 0.0406112
## 567 -0.1511517
## 568 0.1582718
## 570 -0.2579037
## 571 0.0187214
## 572 0.0151165
## 573 -0.2738733
## 574 -0.2793185
## 575 0.4153299
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## 577 0.2723711
## 582 -0.1307632
## 583 0.1609267
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## 591 0.2396059
## 593 -0.1699654
## 594 0.2297628
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## 615 0.2587356
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## 623 0.0212420
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## 634 0.0029171
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## 694 0.0029171
## 697 0.1170792
## 698 -0.1407311
## 699 0.1709653
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## 705 0.0821369
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## 707 0.3564783
## 708 0.1542763
## 710 -0.1188722
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## 719 0.1329936
## 722 0.1675381
## 723 0.2636822
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## 1895 -0.1592631
## 1896 -0.0212793
## 1897 0.1433988
## 1899 -0.2419783
## 1904 0.0117778
##
## $zboys
## (Intercept) znas8
## -1.9403949176938 0.0003171 -0.0007753
## -1.78915377536492 -0.0017857 0.0043652
## -1.63791263303604 0.0035537 -0.0086870
## -1.48667149070715 0.0016399 -0.0040086
## -1.33543034837827 -0.0033596 0.0082127
## -1.18418920604939 0.0027529 -0.0067296
## -1.03294806372051 -0.0061999 0.0151559
## -0.881706921391632 -0.0026591 0.0065003
## -0.730465779062751 -0.0044200 0.0108049
## -0.57922463673387 -0.0024684 0.0060341
## -0.42798349440499 -0.0008614 0.0021058
## -0.276742352076109 -0.0018885 0.0046165
## -0.125501209747228 0.0086506 -0.0211467
## 0.0257399325816523 -0.0002406 0.0005881
## 0.176981074910533 0.0042217 -0.0103199
## 0.479463359568294 -0.0003959 0.0009677
## 0.630704501897175 0.0003334 -0.0008149
## 0.781945644226056 0.0005571 -0.0013618
## 0.933186786554936 0.0050132 -0.0122549
## 1.08442792888382 0.0042151 -0.0103038
## 1.2356690712127 0.0030553 -0.0074688
## 1.38691021354158 -0.0015203 0.0037165
## 1.53815135587046 0.0008503 -0.0020785
## 1.68939249819934 0.0039620 -0.0096852
##
## $schoolMAIN
## (Intercept) znas8
## 1 -8.312e-12 2.681e-10
## 2 4.538e-11 -9.021e-10
## 3 -3.825e-11 7.921e-10
## 5 -2.843e-12 4.639e-11
## 6 4.282e-11 -7.795e-10
## 7 4.159e-12 -7.084e-11
## 8 2.193e-12 -4.976e-11
## 10 -8.911e-12 2.352e-10
## 11 1.507e-11 -3.682e-10
## 20 -1.736e-11 5.146e-10
## 22 -4.461e-12 1.026e-10
## 28 -5.455e-12 1.117e-10
## 36 -1.637e-11 3.523e-10
##
## attr(,"class")
## [1] "ranef.mer"
se.fixef(M8) # SE of fixed effects
## [1] 0.02715 0.02852
fixef(M8)[2] + c(-2, 2) * se.fixef(M8)[2] # 95% CI of the slope
## [1] 0.03924 0.15332