library(readxl)
actitud_adultos <- read_excel("actitud_adultos.xlsx")
datos_raw <- actitud_adultos
head(datos_raw)
## # A tibble: 6 × 47
## P01 P02 P03 P04 P05 P06 P07 P08 P09 P10 P11 P12 P13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 4 5 2 3 3 2 3 2 2 4 3 4 5
## 2 3 3 4 3 4 1 3 1 1 3 3 3 3
## 3 3 4 5 4 4 2 3 4 3 3 4 4 3
## 4 3 4 4 4 5 1 4 2 3 4 3 4 4
## 5 3 4 3 3 2 2 3 3 2 3 3 4 4
## 6 2 4 2 3 4 2 3 2 2 3 3 4 4
## # ℹ 34 more variables: P14 <dbl>, P15 <dbl>, P16 <dbl>, P17 <dbl>, P18 <dbl>,
## # P19 <dbl>, P20 <dbl>, P21 <dbl>, P22 <dbl>, P23 <dbl>, P24 <dbl>,
## # P25 <dbl>, P26 <dbl>, P27 <dbl>, P28 <dbl>, P29 <dbl>, P30 <dbl>,
## # P31 <dbl>, P32 <dbl>, P33 <dbl>, P34 <dbl>, P35 <dbl>, P36 <dbl>,
## # P37 <dbl>, P38 <dbl>, P39 <dbl>, P40 <dbl>, P41 <dbl>, P42 <dbl>,
## # P43 <dbl>, P44 <dbl>, P45 <dbl>, P46 <dbl>, P47 <dbl>
glimpse(datos_raw)
## Rows: 156
## Columns: 47
## $ P01 <dbl> 4, 3, 3, 3, 3, 2, 3, 3, 2, 4, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 2, …
## $ P02 <dbl> 5, 3, 4, 4, 4, 4, 3, 2, 4, 4, 5, 4, 4, 4, 4, 4, 5, 4, 5, 3, 4, 4, …
## $ P03 <dbl> 2, 4, 5, 4, 3, 2, 3, 2, 4, 4, 5, 4, 2, 3, 4, 4, 4, 3, 5, 4, 5, 4, …
## $ P04 <dbl> 3, 3, 4, 4, 3, 3, 4, 2, 4, 5, 4, 4, 3, 4, 3, 3, 5, 3, 4, 3, 5, 4, …
## $ P05 <dbl> 3, 4, 4, 5, 2, 4, 1, 2, 4, 5, 3, 3, 2, 2, 3, 4, 4, 2, 5, 4, 2, 4, …
## $ P06 <dbl> 2, 1, 2, 1, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 4, 3, 1, 2, …
## $ P07 <dbl> 3, 3, 3, 4, 3, 3, 1, 3, 3, 4, 5, 3, 2, 3, 3, 4, 3, 3, 5, 2, 4, 3, …
## $ P08 <dbl> 2, 1, 4, 2, 3, 2, 3, 3, 2, 4, 2, 3, 2, 4, 2, 4, 3, 4, 4, 3, 4, 3, …
## $ P09 <dbl> 2, 1, 3, 3, 2, 2, 1, 3, 2, 3, 4, 4, 3, 5, 3, 2, 2, 2, 5, 4, 1, 3, …
## $ P10 <dbl> 4, 3, 3, 4, 3, 3, 5, 3, 4, 5, 2, 4, 2, 4, 3, 4, 3, 3, 4, 3, 4, 4, …
## $ P11 <dbl> 3, 3, 4, 3, 3, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 3, 2, 5, 4, 3, 3, …
## $ P12 <dbl> 4, 3, 4, 4, 4, 4, 4, 3, 4, 5, 4, 3, 2, 4, 2, 4, 3, 5, 4, 3, 4, 4, …
## $ P13 <dbl> 5, 3, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 3, 3, 2, 4, 2, 4, 5, 3, 4, 3, …
## $ P14 <dbl> 2, 3, 3, 3, 4, 2, 4, 4, 5, 2, 4, 4, 4, 4, 4, 3, 2, 2, 4, 4, 4, 3, …
## $ P15 <dbl> 2, 3, 2, 2, 2, 2, 1, 3, 1, 2, 2, 1, 3, 2, 3, 3, 2, 2, 5, 4, 1, 3, …
## $ P16 <dbl> 3, 3, 4, 3, 3, 4, 3, 3, 4, 5, 4, 4, 3, 3, 3, 3, 1, 3, 4, 3, 3, 3, …
## $ P17 <dbl> 3, 3, 4, 2, 4, 2, 3, 3, 2, 5, 2, 2, 2, 2, 2, 3, 1, 3, 5, 3, 4, 4, …
## $ P18 <dbl> 4, 3, 5, 4, 4, 4, 3, 4, 5, 4, 4, 4, 2, 2, 4, 4, 5, 4, 4, 4, 4, 4, …
## $ P19 <dbl> 3, 3, 3, 2, 2, 4, 3, 3, 1, 3, 2, 2, 3, 4, 3, 3, 2, 2, 5, 4, 2, 2, …
## $ P20 <dbl> 3, 3, 4, 4, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, …
## $ P21 <dbl> 3, 3, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 5, 3, 1, 1, …
## $ P22 <dbl> 3, 3, 3, 4, 3, 3, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 1, 3, 5, 3, 3, 2, …
## $ P23 <dbl> 2, 3, 2, 1, 3, 2, 5, 3, 2, 4, 2, 2, 4, 2, 3, 3, 2, 1, 2, 3, 2, 2, …
## $ P24 <dbl> 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 4, 2, 3, 4, 4, 4, 4, 5, 5, 4, 4, 4, …
## $ P25 <dbl> 2, 3, 3, 2, 2, 1, 3, 3, 2, 4, 3, 4, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, …
## $ P26 <dbl> 3, 3, 3, 2, 3, 1, 2, 3, 1, 4, 2, 3, 3, 2, 4, 3, 2, 2, 2, 3, 2, 3, …
## $ P27 <dbl> 3, 3, 1, 2, 3, 1, 4, 3, 1, 2, 2, 2, 4, 3, 4, 3, 2, 3, 2, 2, 2, 2, …
## $ P28 <dbl> 4, 3, 3, 4, 4, 4, 2, 3, 4, 4, 4, 4, 2, 3, 2, 3, 3, 4, 5, 3, 4, 3, …
## $ P29 <dbl> 4, 3, 3, 4, 4, 4, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 5, 3, 3, 3, …
## $ P30 <dbl> 4, 3, 3, 4, 3, 3, 2, 3, 4, 5, 3, 3, 2, 4, 3, 3, 3, 4, 5, 2, 3, 3, …
## $ P31 <dbl> 2, 3, 2, 2, 2, 1, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, …
## $ P32 <dbl> 2, 3, 2, 2, 2, 2, 3, 3, 1, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 3, …
## $ P33 <dbl> 3, 3, 2, 2, 2, 2, 3, 3, 1, 2, 4, 3, 3, 1, 2, 3, 2, 2, 2, 4, 2, 3, …
## $ P34 <dbl> 4, 3, 4, 4, 4, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 5, 3, 4, 3, …
## $ P35 <dbl> 2, 3, 1, 2, 2, 2, 3, 3, 1, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 3, 2, 3, …
## $ P36 <dbl> 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 4, 4, 2, 4, 1, 3, 3, 4, 5, 3, 3, 4, …
## $ P37 <dbl> 3, 3, 3, 2, 2, 2, 3, 3, 1, 1, 2, 2, 3, 2, 4, 3, 2, 2, 2, 4, 2, 3, …
## $ P38 <dbl> 2, 3, 3, 2, 2, 2, 3, 3, 1, 2, 2, 2, 3, 1, 4, 3, 2, 2, 2, 3, 4, 3, …
## $ P39 <dbl> 4, 3, 4, 4, 4, 3, 3, 3, 3, 5, 4, 4, 2, 4, 2, 3, 3, 4, 5, 2, 4, 3, …
## $ P40 <dbl> 3, 3, 3, 4, 4, 2, 3, 4, 4, 4, 3, 4, 2, 4, 2, 3, 3, 3, 2, 3, 4, 3, …
## $ P41 <dbl> 3, 3, 2, 2, 3, 3, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 4, 3, …
## $ P42 <dbl> 3, 3, 1, 2, 2, 3, 3, 3, 1, 3, 3, 2, 3, 1, 4, 3, 3, 2, 2, 3, 2, 3, …
## $ P43 <dbl> 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 3, 2, 4, 3, 3, 3, 3, 5, 3, 4, 3, …
## $ P44 <dbl> 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 2, 2, 4, 2, 3, 3, 4, 2, 3, 4, 3, …
## $ P45 <dbl> 4, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 2, 4, 2, 3, 3, 3, 5, 3, 4, 3, …
## $ P46 <dbl> 3, 3, 2, 2, 3, 1, 3, 3, 2, 3, 4, 2, 4, 3, 3, 3, 3, 3, 2, 3, 3, 2, …
## $ P47 <dbl> 3, 3, 4, 2, 3, 3, 3, 3, 2, 4, 2, 2, 4, 3, 3, 3, 1, 3, 5, 3, 4, 3, …
# Ítems AEE y negativos
aee_items <- sprintf("P%02d", 1:25)
aee_neg <- sprintf("P%02d", c(1, 3, 6, 9, 11, 14, 15, 19, 21, 23, 25))
AEE <- datos_raw |>
select(all_of(aee_items)) |>
mutate(across(all_of(aee_neg), ~ 6 - .x))
# Ítems AEC y negativos
aec_items <- sprintf("P%02d", 26:45)
aec_neg <- sprintf("P%02d", c(26, 27, 31, 32, 33, 35, 37, 38, 41, 42))
AEC <- datos_raw |>
select(all_of(aec_items)) |>
mutate(across(all_of(aec_neg), ~ 6 - .x))
# Remover NA
AEE_comp <- drop_na(AEE)
AEC_comp <- drop_na(AEC)
AEE_comp <- AEE_comp |>
mutate(score_AEE = rowSums(across(all_of(aee_items))))
AEC_comp <- AEC_comp |>
mutate(score_AEC = rowSums(across(all_of(aec_items))))
psych::describe(AEE_comp$score_AEE)
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 145 90.99 11.03 92 90.76 11.86 66 117 51 0.12 -0.52 0.92
psych::describe(AEC_comp$score_AEC)
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 151 71.93 11.28 74 72.04 10.38 44 99 55 -0.11 -0.32 0.92
summary(AEE_comp$score_AEE)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 66.00 83.00 92.00 90.99 98.00 117.00
summary(AEC_comp$score_AEC)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 44.00 63.00 74.00 71.93 79.00 99.00
alpha_AEC <- psych::alpha(AEC_comp[aec_items])
alpha_AEC$total$raw_alpha
## [1] 0.9349434
alpha_AEC$item.stats[, c("mean", "sd", "r.drop")]
## mean sd r.drop
## P26 3.589404 0.9679637 0.5684867
## P27 3.827815 0.9644452 0.7350424
## P28 3.662252 0.7906741 0.6624560
## P29 3.304636 0.7830996 0.5967302
## P30 3.291391 0.7446646 0.5350629
## P31 3.874172 0.8817001 0.6177823
## P32 3.788079 0.8764266 0.6255387
## P33 3.774834 0.9533952 0.6988111
## P34 3.774834 0.6549523 0.6023526
## P35 3.880795 0.8863946 0.7291180
## P36 3.397351 0.7666331 0.5507445
## P37 3.801325 0.8642520 0.6748035
## P38 3.741722 0.9413719 0.6560418
## P39 3.450331 0.8221009 0.7395269
## P40 3.331126 0.7721991 0.6133230
## P41 3.675497 0.8683292 0.5786988
## P42 3.860927 0.9168041 0.6274897
## P43 3.099338 0.7188414 0.4877000
## P44 3.311258 0.8180092 0.5216836
## P45 3.490066 0.7820277 0.6815302
cor_AEC <- cor(AEC_comp[aec_items])
round(cor_AEC, 2)
## P26 P27 P28 P29 P30 P31 P32 P33 P34 P35 P36 P37 P38 P39 P40
## P26 1.00 0.59 0.26 0.29 0.18 0.49 0.53 0.58 0.31 0.53 0.27 0.37 0.41 0.32 0.31
## P27 0.59 1.00 0.47 0.41 0.26 0.54 0.60 0.65 0.40 0.65 0.34 0.64 0.59 0.47 0.39
## P28 0.26 0.47 1.00 0.52 0.59 0.40 0.25 0.34 0.64 0.41 0.63 0.47 0.32 0.66 0.49
## P29 0.29 0.41 0.52 1.00 0.52 0.28 0.24 0.44 0.45 0.49 0.39 0.31 0.33 0.57 0.47
## P30 0.18 0.26 0.59 0.52 1.00 0.27 0.20 0.32 0.46 0.33 0.51 0.33 0.24 0.52 0.43
## P31 0.49 0.54 0.40 0.28 0.27 1.00 0.63 0.55 0.41 0.64 0.25 0.50 0.49 0.38 0.27
## P32 0.53 0.60 0.25 0.24 0.20 0.63 1.00 0.64 0.31 0.57 0.17 0.60 0.61 0.34 0.23
## P33 0.58 0.65 0.34 0.44 0.32 0.55 0.64 1.00 0.40 0.73 0.23 0.56 0.55 0.45 0.40
## P34 0.31 0.40 0.64 0.45 0.46 0.41 0.31 0.40 1.00 0.32 0.54 0.40 0.33 0.51 0.41
## P35 0.53 0.65 0.41 0.49 0.33 0.64 0.57 0.73 0.32 1.00 0.32 0.56 0.62 0.50 0.38
## P36 0.27 0.34 0.63 0.39 0.51 0.25 0.17 0.23 0.54 0.32 1.00 0.33 0.28 0.61 0.50
## P37 0.37 0.64 0.47 0.31 0.33 0.50 0.60 0.56 0.40 0.56 0.33 1.00 0.63 0.50 0.35
## P38 0.41 0.59 0.32 0.33 0.24 0.49 0.61 0.55 0.33 0.62 0.28 0.63 1.00 0.48 0.36
## P39 0.32 0.47 0.66 0.57 0.52 0.38 0.34 0.45 0.51 0.50 0.61 0.50 0.48 1.00 0.66
## P40 0.31 0.39 0.49 0.47 0.43 0.27 0.23 0.40 0.41 0.38 0.50 0.35 0.36 0.66 1.00
## P41 0.40 0.55 0.27 0.31 0.26 0.39 0.55 0.47 0.20 0.49 0.26 0.53 0.61 0.34 0.30
## P42 0.47 0.56 0.42 0.31 0.24 0.42 0.44 0.50 0.35 0.59 0.37 0.47 0.54 0.42 0.40
## P43 0.28 0.32 0.38 0.37 0.39 0.21 0.27 0.29 0.29 0.29 0.36 0.26 0.21 0.59 0.47
## P44 0.26 0.30 0.50 0.45 0.44 0.28 0.23 0.27 0.47 0.30 0.35 0.23 0.22 0.47 0.50
## P45 0.30 0.43 0.61 0.58 0.59 0.33 0.33 0.33 0.61 0.33 0.55 0.40 0.35 0.72 0.63
## P41 P42 P43 P44 P45
## P26 0.40 0.47 0.28 0.26 0.30
## P27 0.55 0.56 0.32 0.30 0.43
## P28 0.27 0.42 0.38 0.50 0.61
## P29 0.31 0.31 0.37 0.45 0.58
## P30 0.26 0.24 0.39 0.44 0.59
## P31 0.39 0.42 0.21 0.28 0.33
## P32 0.55 0.44 0.27 0.23 0.33
## P33 0.47 0.50 0.29 0.27 0.33
## P34 0.20 0.35 0.29 0.47 0.61
## P35 0.49 0.59 0.29 0.30 0.33
## P36 0.26 0.37 0.36 0.35 0.55
## P37 0.53 0.47 0.26 0.23 0.40
## P38 0.61 0.54 0.21 0.22 0.35
## P39 0.34 0.42 0.59 0.47 0.72
## P40 0.30 0.40 0.47 0.50 0.63
## P41 1.00 0.51 0.22 0.26 0.30
## P42 0.51 1.00 0.19 0.32 0.35
## P43 0.22 0.19 1.00 0.47 0.54
## P44 0.26 0.32 0.47 1.00 0.58
## P45 0.30 0.35 0.54 0.58 1.00
ggplot(AEC_comp, aes(x = score_AEC)) +
geom_histogram(binwidth = 2) +
labs(title = "Distribución del puntaje AEC", x = "Score", y = "Frecuencia")
AEC_mat <- as.matrix(AEC_comp[aec_items])
N <- nrow(AEC_mat)
J <- ncol(AEC_mat)
K <- 5
data_jags <- list(
N = N,
J = J,
K = K,
y = AEC_mat
)
N; J; K
## [1] 151
## [1] 20
## [1] 5
modelo_grm <- "
model {
for (i in 1:N) {
theta[i] ~ dnorm(0,1)
}
for (j in 1:J) {
log_a[j] ~ dnorm(0,0.5)
a[j] <- exp(log_a[j])
b_raw[j,1] ~ dnorm(0,0.01)
b[j,1] <- b_raw[j,1]
for (k in 2:(K-1)) {
delta[j,k] ~ dnorm(0,1) T(0,)
b[j,k] <- b[j,k-1] + delta[j,k]
}
}
for (i in 1:N) {
for (j in 1:J) {
for (k in 1:(K-1)) {
eta[i,j,k] <- a[j] * (theta[i] - b[j,k])
q[i,j,k] <- 1 / (1 + exp(-eta[i,j,k]))
}
p[i,j,1] <- 1 - q[i,j,1]
for (k in 2:(K-1)) {
p[i,j,k] <- max(1.0E-10, q[i,j,k-1] - q[i,j,k])
}
p[i,j,K] <- q[i,j,K-1]
y[i,j] ~ dcat(p[i,j,1:K])
}
}
}
"
writeLines(modelo_grm, "grm_2pl_aec.jags")
set.seed(123)
mod <- jags.model(
file = "grm_2pl_aec.jags",
data = data_jags,
n.chains = 3,
n.adapt = 3000
)
## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 3020
## Unobserved stochastic nodes: 251
## Total graph size: 99999
##
## Initializing model
update(mod, 7000)
params <- c("a", "b", "theta")
mcmc_samples <- coda.samples(
model = mod,
variable.names = params,
n.iter = 30000,
thin = 10
)
summary(mcmc_samples)
##
## Iterations = 10010:40000
## Thinning interval = 10
## Number of chains = 3
## Sample size per chain = 3000
##
## 1. Empirical mean and standard deviation for each variable,
## plus standard error of the mean:
##
## Mean SD Naive SE Time-series SE
## a[1] 1.92157 0.2768 0.002918 0.006135
## a[2] 3.03274 0.4320 0.004554 0.009283
## a[3] 2.46463 0.3395 0.003579 0.006564
## a[4] 2.10008 0.2888 0.003044 0.005989
## a[5] 1.84845 0.2530 0.002667 0.004635
## a[6] 2.35037 0.3511 0.003701 0.008421
## a[7] 2.44964 0.3463 0.003650 0.006828
## a[8] 3.00074 0.4200 0.004427 0.007986
## a[9] 2.22903 0.3145 0.003315 0.006577
## a[10] 3.36787 0.4764 0.005021 0.008598
## a[11] 1.80512 0.2617 0.002758 0.004882
## a[12] 2.74919 0.3839 0.004047 0.006835
## a[13] 2.45581 0.3440 0.003626 0.007519
## a[14] 2.97425 0.4092 0.004313 0.007612
## a[15] 2.14744 0.2918 0.003075 0.005613
## a[16] 2.02937 0.2866 0.003021 0.006778
## a[17] 2.47423 0.3454 0.003641 0.006309
## a[18] 1.53705 0.2196 0.002314 0.003797
## a[19] 1.82397 0.2521 0.002657 0.005217
## a[20] 2.51640 0.3469 0.003657 0.006961
## b[1,1] -2.60355 0.4006 0.004223 0.011235
## b[2,1] -2.48957 0.3827 0.004034 0.014892
## b[3,1] -3.14452 0.5288 0.005575 0.022450
## b[4,1] -2.44446 0.3625 0.003821 0.009243
## b[5,1] -3.09205 0.4851 0.005113 0.015823
## b[6,1] -2.81953 0.4914 0.005180 0.019222
## b[7,1] -3.09900 0.5730 0.006040 0.027255
## b[8,1] -2.88815 0.5196 0.005477 0.027567
## b[9,1] -2.93365 0.4966 0.005234 0.016166
## b[10,1] -2.95649 0.5830 0.006145 0.037214
## b[11,1] -2.69622 0.4134 0.004358 0.010694
## b[12,1] -2.98875 0.5308 0.005595 0.024763
## b[13,1] -2.67113 0.4570 0.004817 0.017962
## b[14,1] -2.47967 0.3662 0.003860 0.013257
## b[15,1] -2.58784 0.3883 0.004093 0.010936
## b[16,1] -2.93360 0.4937 0.005204 0.018838
## b[17,1] -3.20031 0.5809 0.006123 0.028672
## b[18,1] -2.78386 0.4168 0.004394 0.009239
## b[19,1] -2.82743 0.4367 0.004603 0.012587
## b[20,1] -2.45253 0.3639 0.003836 0.010705
## b[1,2] -1.39396 0.2084 0.002197 0.005310
## b[2,2] -1.25924 0.1607 0.001694 0.004494
## b[3,2] -1.45123 0.1938 0.002043 0.004909
## b[4,2] -1.37678 0.1953 0.002059 0.005139
## b[5,2] -1.56256 0.2206 0.002325 0.005692
## b[6,2] -1.84183 0.2540 0.002677 0.006949
## b[7,2] -1.43453 0.1964 0.002070 0.005249
## b[8,2] -1.19489 0.1562 0.001646 0.004290
## b[9,2] -2.08481 0.2873 0.003029 0.007070
## b[10,2] -1.42565 0.1736 0.001830 0.004904
## b[11,2] -1.86144 0.2644 0.002787 0.006146
## b[12,2] -1.36927 0.1809 0.001907 0.004735
## b[13,2] -1.37349 0.1844 0.001944 0.004831
## b[14,2] -1.19817 0.1550 0.001634 0.004139
## b[15,2] -1.39980 0.1950 0.002056 0.004869
## b[16,2] -1.54023 0.2185 0.002303 0.005882
## b[17,2] -1.58401 0.2081 0.002194 0.005309
## b[18,2] -1.47866 0.2281 0.002404 0.004801
## b[19,2] -1.33699 0.2030 0.002139 0.005067
## b[20,2] -1.50090 0.1928 0.002032 0.005145
## b[1,3] -0.25855 0.1328 0.001400 0.002787
## b[2,3] -0.46479 0.1180 0.001244 0.003128
## b[3,3] -0.40126 0.1232 0.001299 0.002931
## b[4,3] 0.24709 0.1286 0.001355 0.002543
## b[5,3] 0.46115 0.1420 0.001497 0.002661
## b[6,3] -0.45090 0.1280 0.001349 0.003142
## b[7,3] -0.50610 0.1279 0.001349 0.003202
## b[8,3] -0.46406 0.1157 0.001220 0.002981
## b[9,3] -0.70706 0.1418 0.001494 0.003600
## b[10,3] -0.48498 0.1138 0.001199 0.002965
## b[11,3] 0.26362 0.1367 0.001441 0.002580
## b[12,3] -0.53206 0.1233 0.001300 0.003301
## b[13,3] -0.45080 0.1262 0.001330 0.003032
## b[14,3] -0.03192 0.1110 0.001170 0.002466
## b[15,3] 0.21842 0.1270 0.001339 0.002534
## b[16,3] -0.42129 0.1334 0.001407 0.002877
## b[17,3] -0.42039 0.1238 0.001305 0.002991
## b[18,3] 0.93336 0.1845 0.001945 0.003025
## b[19,3] 0.21761 0.1372 0.001447 0.002683
## b[20,3] -0.07012 0.1175 0.001238 0.002590
## b[1,4] 1.10531 0.1906 0.002009 0.003428
## b[2,4] 0.60736 0.1262 0.001330 0.002509
## b[3,4] 1.35487 0.1897 0.002000 0.003216
## b[4,4] 2.15134 0.2860 0.003015 0.004412
## b[5,4] 2.10614 0.2915 0.003072 0.004437
## b[6,4] 0.63939 0.1419 0.001496 0.002607
## b[7,4] 0.85881 0.1510 0.001591 0.002652
## b[8,4] 0.66807 0.1312 0.001383 0.002508
## b[9,4] 1.62023 0.2204 0.002323 0.003647
## b[10,4] 0.57434 0.1202 0.001267 0.002433
## b[11,4] 1.98352 0.2794 0.002946 0.004362
## b[12,4] 0.84687 0.1432 0.001510 0.002501
## b[13,4] 0.80924 0.1487 0.001567 0.002695
## b[14,4] 1.51594 0.1916 0.002020 0.003278
## b[15,4] 2.02741 0.2703 0.002849 0.004275
## b[16,4] 1.20226 0.1918 0.002022 0.003172
## b[17,4] 0.58063 0.1353 0.001426 0.002444
## b[18,4] 2.87602 0.4346 0.004581 0.006163
## b[19,4] 2.07858 0.2953 0.003113 0.004822
## b[20,4] 1.67561 0.2190 0.002309 0.003396
## theta[1] -0.19726 0.1998 0.002106 0.003098
## theta[2] -0.82864 0.1864 0.001965 0.003381
## theta[3] -0.03087 0.2100 0.002214 0.003024
## theta[4] 0.41493 0.1984 0.002091 0.002940
## theta[5] 0.13057 0.2022 0.002131 0.002949
## theta[6] 0.14690 0.2117 0.002231 0.003068
## theta[7] -1.00650 0.1970 0.002076 0.003849
## theta[8] -0.78615 0.1882 0.001984 0.003683
## theta[9] 0.93151 0.2305 0.002430 0.003170
## theta[10] 0.22390 0.2178 0.002296 0.002919
## theta[11] 0.08575 0.2033 0.002143 0.002966
## theta[12] -0.04740 0.2043 0.002153 0.003262
## theta[13] -1.35854 0.1987 0.002095 0.004725
## theta[14] 0.40016 0.2118 0.002232 0.002914
## theta[15] -1.39700 0.2120 0.002235 0.004908
## theta[16] -0.83537 0.1892 0.001994 0.003603
## theta[17] -0.20274 0.1936 0.002041 0.003210
## theta[18] 0.02923 0.2007 0.002116 0.002912
## theta[19] 0.70723 0.2363 0.002491 0.003496
## theta[20] -1.01778 0.1978 0.002085 0.003878
## theta[21] 0.09512 0.2031 0.002141 0.002922
## theta[22] -0.72604 0.1895 0.001997 0.003689
## theta[23] 0.17037 0.1975 0.002082 0.002848
## theta[24] 0.13929 0.2013 0.002122 0.003015
## theta[25] 0.20636 0.2083 0.002195 0.003028
## theta[26] -0.10786 0.2002 0.002110 0.003241
## theta[27] 2.11400 0.3290 0.003468 0.004042
## theta[28] 0.72357 0.2402 0.002532 0.003258
## theta[29] -0.77194 0.2036 0.002146 0.003618
## theta[30] -1.54610 0.2109 0.002223 0.005038
## theta[31] 0.22540 0.1995 0.002103 0.002993
## theta[32] 0.54992 0.2253 0.002375 0.003268
## theta[33] 0.87874 0.2163 0.002280 0.003003
## theta[34] 0.06289 0.1981 0.002088 0.002879
## theta[35] 0.53762 0.2146 0.002263 0.003171
## theta[36] -0.99072 0.1967 0.002074 0.003793
## theta[37] -1.09222 0.2511 0.002647 0.004642
## theta[38] 1.42869 0.2441 0.002573 0.003431
## theta[39] 0.07490 0.2016 0.002125 0.002945
## theta[40] -0.06455 0.1986 0.002093 0.003052
## theta[41] -0.28596 0.1990 0.002097 0.003231
## theta[42] 0.17461 0.2709 0.002856 0.003831
## theta[43] 0.26598 0.1948 0.002054 0.003111
## theta[44] -1.55803 0.2065 0.002177 0.004965
## theta[45] -0.61020 0.1974 0.002081 0.003544
## theta[46] -1.33566 0.2131 0.002247 0.004468
## theta[47] -0.46789 0.2342 0.002469 0.003753
## theta[48] 0.04321 0.2001 0.002109 0.002950
## theta[49] 0.68935 0.2134 0.002249 0.002963
## theta[50] -0.61980 0.2270 0.002393 0.003696
## theta[51] 0.10500 0.2046 0.002156 0.002953
## theta[52] -1.50066 0.2145 0.002261 0.004900
## theta[53] 2.24198 0.3355 0.003537 0.004338
## theta[54] 0.37884 0.2082 0.002195 0.002837
## theta[55] -0.83045 0.2029 0.002139 0.003843
## theta[56] -0.98922 0.2483 0.002617 0.004325
## theta[57] -0.79297 0.1889 0.001991 0.003668
## theta[58] 1.46554 0.2627 0.002770 0.003509
## theta[59] 1.01670 0.2310 0.002435 0.003182
## theta[60] 2.36334 0.3606 0.003801 0.004624
## theta[61] 0.36482 0.1986 0.002093 0.002877
## theta[62] 0.62878 0.2090 0.002203 0.003040
## theta[63] 1.10761 0.2313 0.002438 0.003159
## theta[64] -0.21554 0.1950 0.002055 0.003310
## theta[65] 0.23777 0.1966 0.002072 0.002869
## theta[66] 0.10497 0.2054 0.002165 0.002997
## theta[67] -0.51415 0.2010 0.002119 0.003229
## theta[68] -0.81638 0.2016 0.002125 0.003729
## theta[69] 0.28793 0.2051 0.002162 0.002900
## theta[70] 0.85935 0.2259 0.002381 0.003105
## theta[71] 0.26262 0.2009 0.002117 0.002908
## theta[72] -1.48942 0.2476 0.002609 0.005278
## theta[73] -1.09737 0.1994 0.002102 0.003992
## theta[74] -0.13940 0.1984 0.002092 0.002967
## theta[75] -0.34617 0.1981 0.002088 0.003330
## theta[76] 0.43872 0.2244 0.002365 0.003407
## theta[77] 0.23397 0.2094 0.002208 0.003106
## theta[78] -0.41796 0.1953 0.002059 0.003077
## theta[79] -0.64555 0.2156 0.002273 0.003766
## theta[80] -0.71679 0.2053 0.002164 0.003540
## theta[81] -0.98390 0.2007 0.002116 0.003941
## theta[82] 0.05112 0.1954 0.002059 0.003065
## theta[83] 0.54793 0.2242 0.002363 0.003414
## theta[84] -0.89599 0.1907 0.002010 0.003785
## theta[85] -0.85943 0.2485 0.002619 0.004191
## theta[86] -0.61927 0.1967 0.002073 0.003671
## theta[87] 0.62731 0.2287 0.002411 0.003106
## theta[88] -0.76932 0.2816 0.002969 0.004082
## theta[89] -0.33276 0.2011 0.002120 0.003254
## theta[90] 0.38453 0.2009 0.002118 0.003035
## theta[91] -0.06282 0.2536 0.002673 0.003607
## theta[92] -1.76594 0.2140 0.002256 0.005718
## theta[93] 0.02610 0.2143 0.002259 0.002921
## theta[94] 0.43511 0.2059 0.002170 0.002938
## theta[95] 0.41849 0.2109 0.002223 0.003008
## theta[96] -1.09777 0.2078 0.002191 0.004052
## theta[97] 0.13343 0.2023 0.002132 0.002856
## theta[98] 0.53757 0.2280 0.002404 0.003121
## theta[99] -0.63697 0.2075 0.002187 0.003494
## theta[100] 0.90084 0.2172 0.002289 0.003046
## theta[101] -0.14899 0.1913 0.002016 0.003180
## theta[102] 0.01400 0.2219 0.002339 0.003257
## theta[103] -0.01375 0.2029 0.002139 0.003172
## theta[104] 1.50809 0.2519 0.002655 0.003507
## theta[105] -0.14464 0.2387 0.002516 0.003731
## theta[106] 0.35272 0.2004 0.002112 0.002794
## theta[107] 0.67329 0.2073 0.002186 0.003024
## theta[108] 1.18612 0.2314 0.002439 0.003250
## theta[109] 1.33071 0.2469 0.002602 0.003381
## theta[110] 2.76168 0.4224 0.004452 0.004634
## theta[111] 1.11719 0.2286 0.002410 0.003103
## theta[112] 0.24465 0.1960 0.002066 0.002879
## theta[113] 0.41253 0.1977 0.002084 0.002849
## theta[114] 0.43188 0.2068 0.002180 0.002855
## theta[115] 1.18534 0.2327 0.002453 0.003120
## theta[116] -0.39482 0.1978 0.002085 0.003138
## theta[117] -0.05803 0.2144 0.002260 0.003149
## theta[118] -0.06724 0.1948 0.002054 0.002973
## theta[119] 0.81732 0.2170 0.002287 0.003124
## theta[120] 0.31880 0.1996 0.002104 0.002931
## theta[121] 2.03235 0.3039 0.003204 0.004122
## theta[122] -0.35301 0.2019 0.002128 0.003396
## theta[123] -1.08740 0.2118 0.002233 0.004452
## theta[124] -1.01531 0.2050 0.002161 0.004028
## theta[125] 0.08491 0.2074 0.002186 0.003122
## theta[126] 0.47339 0.1990 0.002098 0.002848
## theta[127] 1.06209 0.2239 0.002360 0.003202
## theta[128] -0.15972 0.2081 0.002193 0.002977
## theta[129] 0.96362 0.2156 0.002272 0.003050
## theta[130] -1.08980 0.2081 0.002194 0.004152
## theta[131] -0.88441 0.1922 0.002026 0.003801
## theta[132] 0.24871 0.2088 0.002201 0.002938
## theta[133] 0.39190 0.2013 0.002122 0.002821
## theta[134] 0.32102 0.1973 0.002080 0.002735
## theta[135] 0.52570 0.2066 0.002178 0.002876
## theta[136] -0.55592 0.1975 0.002082 0.003711
## theta[137] -1.38067 0.2131 0.002246 0.004604
## theta[138] 0.12829 0.1956 0.002062 0.002885
## theta[139] 1.06972 0.2350 0.002477 0.003255
## theta[140] -0.38624 0.2001 0.002109 0.003148
## theta[141] 0.07869 0.1938 0.002043 0.002924
## theta[142] 0.22119 0.2052 0.002163 0.003023
## theta[143] -0.45785 0.1955 0.002060 0.003360
## theta[144] -0.31388 0.2052 0.002163 0.003308
## theta[145] -0.60121 0.1928 0.002032 0.003571
## theta[146] -0.72282 0.1889 0.001991 0.003650
## theta[147] -0.63843 0.2016 0.002125 0.003362
## theta[148] -0.25138 0.2085 0.002198 0.003101
## theta[149] -0.33864 0.1946 0.002051 0.003171
## theta[150] -0.25397 0.1922 0.002026 0.003078
## theta[151] 0.21301 0.1968 0.002075 0.002569
##
## 2. Quantiles for each variable:
##
## 2.5% 25% 50% 75% 97.5%
## a[1] 1.4123798 1.727525 1.91151 2.104758 2.4950765
## a[2] 2.2619483 2.730613 3.00877 3.307385 3.9553618
## a[3] 1.8498208 2.226266 2.44947 2.679395 3.1768714
## a[4] 1.5706220 1.902418 2.08358 2.285589 2.7067206
## a[5] 1.3825782 1.674691 1.83305 2.009105 2.3787570
## a[6] 1.7246755 2.101946 2.33368 2.571967 3.1019800
## a[7] 1.8304471 2.208777 2.43269 2.670162 3.1840702
## a[8] 2.2352037 2.716330 2.97778 3.259334 3.9138177
## a[9] 1.6755747 2.011766 2.21217 2.423709 2.8967864
## a[10] 2.5047597 3.027865 3.34126 3.682236 4.3795179
## a[11] 1.3327015 1.621588 1.79139 1.972340 2.3618588
## a[12] 2.0587530 2.480668 2.72494 2.999373 3.5502130
## a[13] 1.8214203 2.218015 2.44267 2.673621 3.1867611
## a[14] 2.2480721 2.688562 2.94709 3.230727 3.8368368
## a[15] 1.6268813 1.944548 2.13255 2.329082 2.7770112
## a[16] 1.5109379 1.830940 2.01412 2.213070 2.6431156
## a[17] 1.8512870 2.231754 2.45820 2.696218 3.1932684
## a[18] 1.1492754 1.384155 1.52592 1.678487 1.9924335
## a[19] 1.3561758 1.646242 1.81090 1.985874 2.3421114
## a[20] 1.8866117 2.272706 2.49900 2.748760 3.2443340
## b[1,1] -3.5068092 -2.841845 -2.56547 -2.321275 -1.9351517
## b[2,1] -3.3475646 -2.713868 -2.45080 -2.215325 -1.8655414
## b[3,1] -4.2918130 -3.475877 -3.09076 -2.762334 -2.2574203
## b[4,1] -3.2339219 -2.661240 -2.41442 -2.190913 -1.8174259
## b[5,1] -4.1440455 -3.393032 -3.04718 -2.748134 -2.2589710
## b[6,1] -3.9665691 -3.108677 -2.76329 -2.475138 -2.0092598
## b[7,1] -4.4592579 -3.419221 -3.02987 -2.696653 -2.1733036
## b[8,1] -4.0351403 -3.206599 -2.83978 -2.514002 -2.0280395
## b[9,1] -4.0480685 -3.245119 -2.88149 -2.579599 -2.1030329
## b[10,1] -4.2324839 -3.309780 -2.88059 -2.527906 -2.0378384
## b[11,1] -3.5743200 -2.960571 -2.65575 -2.397258 -1.9809005
## b[12,1] -4.1997912 -3.297910 -2.93309 -2.609161 -2.0994958
## b[13,1] -3.7139963 -2.925008 -2.62132 -2.347755 -1.9294974
## b[14,1] -3.2909322 -2.703895 -2.45195 -2.222742 -1.8526833
## b[15,1] -3.4439766 -2.819684 -2.55489 -2.313468 -1.9164649
## b[16,1] -4.0197504 -3.227736 -2.87988 -2.578702 -2.1134852
## b[17,1] -4.5115153 -3.554766 -3.13463 -2.782421 -2.2555785
## b[18,1] -3.6839537 -3.049096 -2.75143 -2.489875 -2.0563041
## b[19,1] -3.7783343 -3.093729 -2.78854 -2.518229 -2.0943170
## b[20,1] -3.2596991 -2.667143 -2.42119 -2.197767 -1.8380079
## b[1,2] -1.8459628 -1.526043 -1.38173 -1.249182 -1.0214369
## b[2,2] -1.5884977 -1.364980 -1.25368 -1.149554 -0.9581866
## b[3,2] -1.8723973 -1.574071 -1.44115 -1.318080 -1.0969463
## b[4,2] -1.7870166 -1.499104 -1.36706 -1.242773 -1.0231020
## b[5,2] -2.0306215 -1.700836 -1.55040 -1.408850 -1.1716461
## b[6,2] -2.3974390 -1.999724 -1.82132 -1.665953 -1.3983695
## b[7,2] -1.8514367 -1.558883 -1.42644 -1.296698 -1.0794260
## b[8,2] -1.5186093 -1.295057 -1.18930 -1.088059 -0.9032869
## b[9,2] -2.7136328 -2.260160 -2.06077 -1.883594 -1.5972302
## b[10,2] -1.7820223 -1.536856 -1.41751 -1.305764 -1.1141678
## b[11,2] -2.4270764 -2.031863 -1.84552 -1.674255 -1.3963406
## b[12,2] -1.7477653 -1.484537 -1.35973 -1.243900 -1.0370533
## b[13,2] -1.7562491 -1.492566 -1.36458 -1.242895 -1.0402366
## b[14,2] -1.5082991 -1.301700 -1.19320 -1.092024 -0.9051765
## b[15,2] -1.8069433 -1.523886 -1.39092 -1.265967 -1.0431571
## b[16,2] -2.0058128 -1.678337 -1.52627 -1.388670 -1.1515133
## b[17,2] -2.0274291 -1.717723 -1.57140 -1.438163 -1.2092574
## b[18,2] -1.9579325 -1.626130 -1.46460 -1.319765 -1.0724012
## b[19,2] -1.7613813 -1.462031 -1.32450 -1.198562 -0.9726903
## b[20,2] -1.9109822 -1.621633 -1.48919 -1.369397 -1.1491495
## b[1,3] -0.5280678 -0.346007 -0.25644 -0.167327 -0.0073339
## b[2,3] -0.7015548 -0.542007 -0.46267 -0.385403 -0.2387607
## b[3,3] -0.6470232 -0.483596 -0.40236 -0.316554 -0.1642221
## b[4,3] -0.0045927 0.161249 0.24654 0.331962 0.5047976
## b[5,3] 0.1889514 0.365266 0.46027 0.553622 0.7477262
## b[6,3] -0.7087170 -0.535541 -0.44654 -0.364037 -0.2098318
## b[7,3] -0.7629883 -0.590548 -0.50460 -0.420108 -0.2584994
## b[8,3] -0.6967009 -0.540739 -0.46256 -0.385642 -0.2385324
## b[9,3] -0.9947614 -0.801760 -0.70242 -0.610968 -0.4397976
## b[10,3] -0.7141490 -0.560474 -0.48355 -0.409087 -0.2646762
## b[11,3] 0.0004338 0.169970 0.26201 0.353881 0.5418059
## b[12,3] -0.7794706 -0.614495 -0.53098 -0.449396 -0.2888060
## b[13,3] -0.7090804 -0.531908 -0.44924 -0.366407 -0.2129666
## b[14,3] -0.2485183 -0.105958 -0.03256 0.042405 0.1866396
## b[15,3] -0.0246869 0.132356 0.21550 0.304559 0.4707807
## b[16,3] -0.6906779 -0.509086 -0.42008 -0.329552 -0.1702260
## b[17,3] -0.6716268 -0.500998 -0.41739 -0.338641 -0.1820340
## b[18,3] 0.5864534 0.807668 0.92677 1.050110 1.3157504
## b[19,3] -0.0498279 0.124377 0.21519 0.308747 0.4928020
## b[20,3] -0.3010703 -0.149911 -0.06976 0.009998 0.1609295
## b[1,4] 0.7705103 0.969272 1.09294 1.226598 1.5061681
## b[2,4] 0.3676418 0.520853 0.60606 0.688770 0.8624392
## b[3,4] 1.0075179 1.223854 1.34794 1.476090 1.7560579
## b[4,4] 1.6392285 1.952862 2.13488 2.336197 2.7514917
## b[5,4] 1.5872831 1.903635 2.08788 2.291449 2.7325943
## b[6,4] 0.3714713 0.541862 0.63477 0.730221 0.9297779
## b[7,4] 0.5881496 0.752054 0.85283 0.955995 1.1657614
## b[8,4] 0.4142298 0.580786 0.66545 0.754087 0.9374457
## b[9,4] 1.2238585 1.465520 1.60931 1.762722 2.0769536
## b[10,4] 0.3408942 0.495087 0.57174 0.651814 0.8179007
## b[11,4] 1.4781178 1.786072 1.96798 2.161720 2.5632692
## b[12,4] 0.5818462 0.748870 0.84194 0.941313 1.1341764
## b[13,4] 0.5311741 0.706662 0.80321 0.906259 1.1154334
## b[14,4] 1.1612030 1.384088 1.50937 1.639174 1.9139606
## b[15,4] 1.5417655 1.837310 2.01363 2.200057 2.6005304
## b[16,4] 0.8527914 1.068278 1.19085 1.324362 1.6129393
## b[17,4] 0.3213505 0.488471 0.57818 0.668678 0.8532886
## b[18,4] 2.1105011 2.572121 2.84484 3.149421 3.8137970
## b[19,4] 1.5421988 1.870261 2.06224 2.266470 2.7106450
## b[20,4] 1.2826764 1.523313 1.66320 1.815526 2.1436278
## theta[1] -0.5890780 -0.329892 -0.20063 -0.066899 0.2017612
## theta[2] -1.1985536 -0.955374 -0.82612 -0.703214 -0.4656571
## theta[3] -0.4424722 -0.172953 -0.02927 0.110489 0.3871215
## theta[4] 0.0286568 0.275635 0.41443 0.548581 0.8053941
## theta[5] -0.2684478 -0.002960 0.13074 0.263833 0.5253892
## theta[6] -0.2647822 0.001957 0.14679 0.289092 0.5675770
## theta[7] -1.3964069 -1.137389 -1.00636 -0.873361 -0.6246925
## theta[8] -1.1524406 -0.911855 -0.78574 -0.662290 -0.4132757
## theta[9] 0.4889385 0.777257 0.92877 1.082738 1.3836261
## theta[10] -0.2086671 0.076994 0.22349 0.370053 0.6479493
## theta[11] -0.3199220 -0.051560 0.08650 0.222658 0.4831857
## theta[12] -0.4461501 -0.182861 -0.04693 0.087839 0.3596423
## theta[13] -1.7531896 -1.490747 -1.35662 -1.225019 -0.9750463
## theta[14] -0.0119098 0.254972 0.39793 0.544038 0.8144044
## theta[15] -1.8247521 -1.540532 -1.39623 -1.253756 -0.9854040
## theta[16] -1.2044953 -0.961449 -0.83385 -0.707149 -0.4629725
## theta[17] -0.5917898 -0.330576 -0.20178 -0.070524 0.1689150
## theta[18] -0.3676395 -0.105439 0.02801 0.161942 0.4236255
## theta[19] 0.2511797 0.544935 0.70287 0.863533 1.1856860
## theta[20] -1.4120157 -1.150518 -1.01749 -0.884370 -0.6308738
## theta[21] -0.2971201 -0.042345 0.09541 0.227834 0.4949221
## theta[22] -1.1046163 -0.854347 -0.72405 -0.596512 -0.3642308
## theta[23] -0.2138441 0.033452 0.17142 0.303957 0.5537630
## theta[24] -0.2505306 0.002763 0.13871 0.271077 0.5433020
## theta[25] -0.1917838 0.066206 0.20276 0.345324 0.6294598
## theta[26] -0.4922874 -0.245676 -0.10954 0.028803 0.2814123
## theta[27] 1.4987931 1.888255 2.10186 2.325485 2.7962267
## theta[28] 0.2656280 0.560487 0.71688 0.881383 1.2036752
## theta[29] -1.1789181 -0.910613 -0.77192 -0.635259 -0.3718411
## theta[30] -1.9716789 -1.684547 -1.54163 -1.403877 -1.1465073
## theta[31] -0.1698367 0.091411 0.22359 0.360719 0.6148555
## theta[32] 0.1080348 0.399483 0.55114 0.698318 0.9927883
## theta[33] 0.4686392 0.729023 0.87585 1.023238 1.3049828
## theta[34] -0.3265120 -0.066896 0.06036 0.192862 0.4586709
## theta[35] 0.1133039 0.391837 0.54001 0.678354 0.9631759
## theta[36] -1.3810870 -1.120168 -0.99077 -0.855734 -0.6061775
## theta[37] -1.5906086 -1.259733 -1.09022 -0.920345 -0.6097415
## theta[38] 0.9700099 1.263250 1.42043 1.585806 1.9353722
## theta[39] -0.3234806 -0.058314 0.07677 0.207649 0.4730053
## theta[40] -0.4529509 -0.201269 -0.06252 0.067065 0.3332204
## theta[41] -0.6790089 -0.419074 -0.28396 -0.153286 0.1015218
## theta[42] -0.3362956 -0.011489 0.16683 0.357566 0.7279885
## theta[43] -0.1136183 0.135570 0.26668 0.396544 0.6465488
## theta[44] -1.9771089 -1.696777 -1.55684 -1.420078 -1.1558097
## theta[45] -1.0078484 -0.740242 -0.60834 -0.478412 -0.2319346
## theta[46] -1.7609021 -1.475136 -1.33329 -1.193909 -0.9187569
## theta[47] -0.9247243 -0.628220 -0.46527 -0.307104 -0.0167256
## theta[48] -0.3455201 -0.093849 0.04222 0.176754 0.4370503
## theta[49] 0.2794055 0.541510 0.68937 0.833265 1.1028488
## theta[50] -1.0804115 -0.774070 -0.61552 -0.465696 -0.1802284
## theta[51] -0.2945073 -0.033441 0.10477 0.243272 0.5028290
## theta[52] -1.9265535 -1.647476 -1.49916 -1.352841 -1.0858102
## theta[53] 1.6253318 2.010384 2.22626 2.454220 2.9623978
## theta[54] -0.0323901 0.239358 0.38166 0.515534 0.7906051
## theta[55] -1.2305520 -0.966135 -0.82919 -0.695682 -0.4335014
## theta[56] -1.4702387 -1.154049 -0.99108 -0.819800 -0.5042699
## theta[57] -1.1673848 -0.923225 -0.79160 -0.664018 -0.4237436
## theta[58] 0.9678050 1.281630 1.45867 1.640314 1.9930121
## theta[59] 0.5770371 0.861829 1.01641 1.171237 1.4830783
## theta[60] 1.7146575 2.109888 2.34625 2.591938 3.1354724
## theta[61] -0.0264993 0.230650 0.36378 0.498770 0.7546243
## theta[62] 0.2161055 0.488581 0.62563 0.764966 1.0393989
## theta[63] 0.6664131 0.948846 1.10094 1.260711 1.5779680
## theta[64] -0.6037079 -0.344375 -0.21455 -0.086293 0.1686392
## theta[65] -0.1472347 0.105358 0.23576 0.369870 0.6260207
## theta[66] -0.2914051 -0.033430 0.10328 0.241322 0.5145779
## theta[67] -0.9070242 -0.651466 -0.51768 -0.376118 -0.1191829
## theta[68] -1.2118196 -0.949225 -0.81546 -0.681268 -0.4173447
## theta[69] -0.1194047 0.151204 0.28844 0.424241 0.6937267
## theta[70] 0.4332426 0.704523 0.85405 1.013777 1.3065703
## theta[71] -0.1270246 0.125316 0.26002 0.396070 0.6598701
## theta[72] -1.9733847 -1.653678 -1.48952 -1.320744 -1.0090133
## theta[73] -1.5007503 -1.228851 -1.09200 -0.962917 -0.7087462
## theta[74] -0.5279432 -0.274142 -0.13819 -0.006017 0.2478008
## theta[75] -0.7340924 -0.480932 -0.34315 -0.212523 0.0344943
## theta[76] 0.0001164 0.287263 0.43720 0.590519 0.8837093
## theta[77] -0.1773825 0.093196 0.23210 0.378202 0.6363645
## theta[78] -0.8023255 -0.549763 -0.41944 -0.287970 -0.0371128
## theta[79] -1.0774182 -0.790012 -0.64071 -0.501364 -0.2266917
## theta[80] -1.1237745 -0.852729 -0.71496 -0.575791 -0.3195425
## theta[81] -1.3751027 -1.119243 -0.98365 -0.847391 -0.5910412
## theta[82] -0.3332492 -0.079133 0.05056 0.181167 0.4383199
## theta[83] 0.1104607 0.396665 0.54693 0.698106 0.9923403
## theta[84] -1.2686677 -1.022614 -0.89477 -0.768995 -0.5230395
## theta[85] -1.3511440 -1.026539 -0.85875 -0.688082 -0.3822081
## theta[86] -1.0061178 -0.751174 -0.61832 -0.487160 -0.2343517
## theta[87] 0.1800947 0.476732 0.62840 0.779773 1.0800887
## theta[88] -1.3002468 -0.961892 -0.77680 -0.580562 -0.2014956
## theta[89] -0.7350627 -0.466796 -0.33182 -0.200229 0.0583892
## theta[90] -0.0053424 0.248525 0.38332 0.520198 0.7833365
## theta[91] -0.5539197 -0.234559 -0.06792 0.111979 0.4387790
## theta[92] -2.1870269 -1.908252 -1.76493 -1.620737 -1.3503968
## theta[93] -0.3937961 -0.115329 0.02209 0.168872 0.4569972
## theta[94] 0.0268225 0.295875 0.43505 0.576119 0.8375679
## theta[95] 0.0014277 0.277667 0.42051 0.559913 0.8328720
## theta[96] -1.5088791 -1.239718 -1.09626 -0.954336 -0.7005171
## theta[97] -0.2596233 -0.003111 0.12971 0.267431 0.5344933
## theta[98] 0.0921559 0.381555 0.53735 0.687745 0.9893122
## theta[99] -1.0494616 -0.775070 -0.63559 -0.496130 -0.2355664
## theta[100] 0.4826262 0.753317 0.89668 1.045048 1.3400448
## theta[101] -0.5209780 -0.281413 -0.14932 -0.016905 0.2185573
## theta[102] -0.4181811 -0.135586 0.01724 0.163355 0.4488881
## theta[103] -0.3995226 -0.151176 -0.01746 0.120539 0.3960003
## theta[104] 1.0450338 1.335712 1.50266 1.674350 2.0157969
## theta[105] -0.6092207 -0.302836 -0.14553 0.014198 0.3256597
## theta[106] -0.0323714 0.216410 0.35058 0.489351 0.7473272
## theta[107] 0.2690222 0.532625 0.67331 0.810095 1.0817713
## theta[108] 0.7565675 1.029171 1.18090 1.335366 1.6564912
## theta[109] 0.8647356 1.162445 1.32582 1.489696 1.8401227
## theta[110] 2.0094600 2.467647 2.73463 3.028995 3.6679498
## theta[111] 0.6862401 0.962087 1.11068 1.265217 1.5726818
## theta[112] -0.1367985 0.112524 0.24280 0.373402 0.6407420
## theta[113] 0.0299407 0.277250 0.41243 0.542177 0.8026991
## theta[114] 0.0313054 0.290936 0.43156 0.573034 0.8379051
## theta[115] 0.7457030 1.027384 1.17760 1.337445 1.6513866
## theta[116] -0.7867967 -0.523956 -0.39334 -0.264813 0.0002296
## theta[117] -0.4822215 -0.199239 -0.05915 0.088278 0.3557629
## theta[118] -0.4534925 -0.196858 -0.06606 0.062687 0.3157891
## theta[119] 0.3981095 0.670869 0.81542 0.958221 1.2539886
## theta[120] -0.0693390 0.182501 0.31760 0.450378 0.7062116
## theta[121] 1.4679033 1.820906 2.02139 2.224841 2.6663962
## theta[122] -0.7528152 -0.485908 -0.35026 -0.217955 0.0389936
## theta[123] -1.5025370 -1.230377 -1.08177 -0.944118 -0.6745882
## theta[124] -1.4205757 -1.152509 -1.01722 -0.876224 -0.6099482
## theta[125] -0.3308240 -0.049382 0.08723 0.223925 0.4924390
## theta[126] 0.0845990 0.338631 0.47423 0.607756 0.8594435
## theta[127] 0.6313063 0.908682 1.05600 1.210360 1.5125730
## theta[128] -0.5672725 -0.299853 -0.16254 -0.020258 0.2507235
## theta[129] 0.5608515 0.815794 0.95664 1.108099 1.4018803
## theta[130] -1.5002447 -1.231907 -1.08959 -0.951219 -0.6796971
## theta[131] -1.2694793 -1.012820 -0.88261 -0.753861 -0.5092860
## theta[132] -0.1605504 0.109934 0.24768 0.388705 0.6583814
## theta[133] -0.0005497 0.254085 0.39374 0.521690 0.7927449
## theta[134] -0.0580917 0.186050 0.31912 0.452434 0.7131032
## theta[135] 0.1204235 0.384402 0.52521 0.663715 0.9342039
## theta[136] -0.9426592 -0.688738 -0.55524 -0.423256 -0.1650538
## theta[137] -1.8070011 -1.518098 -1.37834 -1.235351 -0.9666753
## theta[138] -0.2512072 -0.005110 0.12833 0.260845 0.5114613
## theta[139] 0.6169476 0.912797 1.06337 1.225905 1.5437747
## theta[140] -0.7785781 -0.519236 -0.38547 -0.255360 0.0114182
## theta[141] -0.3031487 -0.051908 0.07841 0.210866 0.4529100
## theta[142] -0.1742004 0.085938 0.22059 0.358438 0.6207114
## theta[143] -0.8382601 -0.589578 -0.45721 -0.330832 -0.0667517
## theta[144] -0.7137901 -0.450771 -0.31630 -0.172877 0.0875341
## theta[145] -0.9845570 -0.731485 -0.60323 -0.471550 -0.2199668
## theta[146] -1.0978833 -0.845992 -0.72238 -0.595806 -0.3530948
## theta[147] -1.0375618 -0.773556 -0.63536 -0.500995 -0.2507904
## theta[148] -0.6621210 -0.392694 -0.25085 -0.109219 0.1560749
## theta[149] -0.7175159 -0.471142 -0.33651 -0.206940 0.0412230
## theta[150] -0.6342940 -0.383773 -0.25231 -0.126805 0.1185560
## theta[151] -0.1736390 0.084348 0.21134 0.342781 0.6047469
gelman.diag(mcmc_samples, multivariate = FALSE)
## Potential scale reduction factors:
##
## Point est. Upper C.I.
## a[1] 1.00 1.01
## a[2] 1.00 1.01
## a[3] 1.00 1.00
## a[4] 1.00 1.01
## a[5] 1.00 1.01
## a[6] 1.01 1.02
## a[7] 1.00 1.01
## a[8] 1.01 1.02
## a[9] 1.00 1.01
## a[10] 1.00 1.00
## a[11] 1.00 1.01
## a[12] 1.00 1.01
## a[13] 1.00 1.00
## a[14] 1.00 1.01
## a[15] 1.00 1.00
## a[16] 1.00 1.01
## a[17] 1.01 1.02
## a[18] 1.00 1.01
## a[19] 1.00 1.01
## a[20] 1.00 1.00
## b[1,1] 1.01 1.04
## b[2,1] 1.00 1.02
## b[3,1] 1.00 1.00
## b[4,1] 1.01 1.03
## b[5,1] 1.00 1.01
## b[6,1] 1.01 1.02
## b[7,1] 1.02 1.06
## b[8,1] 1.04 1.08
## b[9,1] 1.01 1.02
## b[10,1] 1.03 1.07
## b[11,1] 1.00 1.01
## b[12,1] 1.02 1.08
## b[13,1] 1.00 1.01
## b[14,1] 1.00 1.01
## b[15,1] 1.00 1.01
## b[16,1] 1.00 1.01
## b[17,1] 1.01 1.04
## b[18,1] 1.01 1.02
## b[19,1] 1.02 1.07
## b[20,1] 1.00 1.01
## b[1,2] 1.01 1.03
## b[2,2] 1.01 1.02
## b[3,2] 1.00 1.01
## b[4,2] 1.01 1.02
## b[5,2] 1.00 1.01
## b[6,2] 1.01 1.02
## b[7,2] 1.00 1.02
## b[8,2] 1.01 1.02
## b[9,2] 1.00 1.00
## b[10,2] 1.00 1.01
## b[11,2] 1.00 1.02
## b[12,2] 1.01 1.03
## b[13,2] 1.00 1.01
## b[14,2] 1.00 1.01
## b[15,2] 1.00 1.01
## b[16,2] 1.01 1.02
## b[17,2] 1.01 1.02
## b[18,2] 1.01 1.02
## b[19,2] 1.01 1.03
## b[20,2] 1.00 1.01
## b[1,3] 1.00 1.01
## b[2,3] 1.00 1.01
## b[3,3] 1.00 1.01
## b[4,3] 1.00 1.00
## b[5,3] 1.00 1.00
## b[6,3] 1.00 1.01
## b[7,3] 1.00 1.01
## b[8,3] 1.00 1.01
## b[9,3] 1.00 1.01
## b[10,3] 1.00 1.01
## b[11,3] 1.00 1.00
## b[12,3] 1.00 1.01
## b[13,3] 1.00 1.01
## b[14,3] 1.00 1.01
## b[15,3] 1.00 1.01
## b[16,3] 1.00 1.01
## b[17,3] 1.00 1.01
## b[18,3] 1.00 1.00
## b[19,3] 1.00 1.01
## b[20,3] 1.00 1.01
## b[1,4] 1.00 1.00
## b[2,4] 1.00 1.01
## b[3,4] 1.00 1.01
## b[4,4] 1.00 1.00
## b[5,4] 1.00 1.00
## b[6,4] 1.00 1.01
## b[7,4] 1.00 1.01
## b[8,4] 1.00 1.02
## b[9,4] 1.00 1.01
## b[10,4] 1.00 1.00
## b[11,4] 1.00 1.00
## b[12,4] 1.00 1.00
## b[13,4] 1.00 1.01
## b[14,4] 1.00 1.01
## b[15,4] 1.00 1.00
## b[16,4] 1.00 1.00
## b[17,4] 1.00 1.01
## b[18,4] 1.00 1.00
## b[19,4] 1.00 1.01
## b[20,4] 1.00 1.00
## theta[1] 1.00 1.00
## theta[2] 1.00 1.01
## theta[3] 1.00 1.01
## theta[4] 1.00 1.01
## theta[5] 1.00 1.00
## theta[6] 1.00 1.00
## theta[7] 1.00 1.01
## theta[8] 1.00 1.00
## theta[9] 1.00 1.00
## theta[10] 1.00 1.01
## theta[11] 1.00 1.00
## theta[12] 1.00 1.00
## theta[13] 1.00 1.02
## theta[14] 1.00 1.00
## theta[15] 1.00 1.01
## theta[16] 1.00 1.01
## theta[17] 1.00 1.00
## theta[18] 1.00 1.00
## theta[19] 1.00 1.01
## theta[20] 1.00 1.01
## theta[21] 1.00 1.00
## theta[22] 1.00 1.00
## theta[23] 1.00 1.00
## theta[24] 1.00 1.01
## theta[25] 1.00 1.00
## theta[26] 1.00 1.00
## theta[27] 1.00 1.00
## theta[28] 1.00 1.00
## theta[29] 1.00 1.01
## theta[30] 1.00 1.01
## theta[31] 1.00 1.00
## theta[32] 1.00 1.00
## theta[33] 1.00 1.00
## theta[34] 1.00 1.00
## theta[35] 1.00 1.00
## theta[36] 1.00 1.01
## theta[37] 1.00 1.01
## theta[38] 1.00 1.00
## theta[39] 1.00 1.00
## theta[40] 1.00 1.00
## theta[41] 1.00 1.00
## theta[42] 1.00 1.00
## theta[43] 1.00 1.00
## theta[44] 1.00 1.01
## theta[45] 1.00 1.02
## theta[46] 1.00 1.00
## theta[47] 1.00 1.01
## theta[48] 1.00 1.00
## theta[49] 1.00 1.00
## theta[50] 1.00 1.00
## theta[51] 1.00 1.00
## theta[52] 1.00 1.01
## theta[53] 1.00 1.00
## theta[54] 1.00 1.00
## theta[55] 1.00 1.01
## theta[56] 1.00 1.01
## theta[57] 1.00 1.00
## theta[58] 1.00 1.00
## theta[59] 1.00 1.00
## theta[60] 1.00 1.01
## theta[61] 1.00 1.00
## theta[62] 1.00 1.00
## theta[63] 1.00 1.00
## theta[64] 1.00 1.00
## theta[65] 1.00 1.00
## theta[66] 1.00 1.01
## theta[67] 1.00 1.00
## theta[68] 1.00 1.01
## theta[69] 1.00 1.00
## theta[70] 1.00 1.00
## theta[71] 1.00 1.01
## theta[72] 1.01 1.02
## theta[73] 1.00 1.01
## theta[74] 1.00 1.00
## theta[75] 1.00 1.00
## theta[76] 1.00 1.00
## theta[77] 1.00 1.00
## theta[78] 1.00 1.01
## theta[79] 1.00 1.02
## theta[80] 1.00 1.01
## theta[81] 1.00 1.01
## theta[82] 1.00 1.01
## theta[83] 1.00 1.00
## theta[84] 1.00 1.00
## theta[85] 1.00 1.00
## theta[86] 1.00 1.01
## theta[87] 1.00 1.00
## theta[88] 1.00 1.00
## theta[89] 1.00 1.01
## theta[90] 1.00 1.01
## theta[91] 1.00 1.01
## theta[92] 1.00 1.02
## theta[93] 1.00 1.00
## theta[94] 1.00 1.00
## theta[95] 1.00 1.00
## theta[96] 1.00 1.01
## theta[97] 1.00 1.00
## theta[98] 1.00 1.00
## theta[99] 1.00 1.01
## theta[100] 1.00 1.00
## theta[101] 1.00 1.00
## theta[102] 1.00 1.01
## theta[103] 1.00 1.01
## theta[104] 1.00 1.00
## theta[105] 1.00 1.01
## theta[106] 1.00 1.00
## theta[107] 1.00 1.00
## theta[108] 1.00 1.00
## theta[109] 1.00 1.00
## theta[110] 1.00 1.00
## theta[111] 1.00 1.00
## theta[112] 1.00 1.00
## theta[113] 1.00 1.01
## theta[114] 1.00 1.00
## theta[115] 1.00 1.00
## theta[116] 1.00 1.00
## theta[117] 1.00 1.00
## theta[118] 1.00 1.00
## theta[119] 1.00 1.00
## theta[120] 1.00 1.00
## theta[121] 1.00 1.00
## theta[122] 1.00 1.00
## theta[123] 1.00 1.01
## theta[124] 1.00 1.01
## theta[125] 1.00 1.00
## theta[126] 1.00 1.01
## theta[127] 1.00 1.00
## theta[128] 1.00 1.00
## theta[129] 1.00 1.00
## theta[130] 1.00 1.01
## theta[131] 1.00 1.01
## theta[132] 1.00 1.01
## theta[133] 1.00 1.01
## theta[134] 1.00 1.00
## theta[135] 1.00 1.00
## theta[136] 1.00 1.01
## theta[137] 1.00 1.00
## theta[138] 1.00 1.00
## theta[139] 1.00 1.00
## theta[140] 1.00 1.01
## theta[141] 1.00 1.00
## theta[142] 1.00 1.00
## theta[143] 1.00 1.00
## theta[144] 1.00 1.00
## theta[145] 1.00 1.00
## theta[146] 1.00 1.01
## theta[147] 1.00 1.00
## theta[148] 1.00 1.00
## theta[149] 1.00 1.01
## theta[150] 1.00 1.01
## theta[151] 1.00 1.01
s_mat <- as.matrix(mcmc_samples)
# Extraer a_j
a_cols <- grep("^a\\[", colnames(s_mat))
post_a <- s_mat[, a_cols]
a_summary <- t(apply(post_a, 2, function(x)
c(mean = mean(x), sd = sd(x),
q025 = quantile(x, .025), q975 = quantile(x, .975))
))
rownames(a_summary) <- aec_items
# Extraer b_jk
b_cols <- grep("^b\\[", colnames(s_mat))
post_b <- s_mat[, b_cols]
b_summary <- t(apply(post_b, 2, function(x)
c(mean = mean(x), sd = sd(x),
q025 = quantile(x, .025), q975 = quantile(x, .975))
))
item_stats <- alpha_AEC$item.stats[, c("mean","sd","r.drop")]
# Matriz de umbrales reorganizada
J <- length(aec_items)
K <- 5
b_means <- matrix(NA, nrow = J, ncol = K-1)
rownames(b_means) <- aec_items
colnames(b_means) <- paste0("b", 1:(K-1))
for (j in 1:J) {
for (k in 1:(K-1)) {
name_jk <- paste0("b[", j, ",", k, "]")
b_means[j,k] <- mean(s_mat[, name_jk])
}
}
a_means <- a_summary[, "mean"]
tabla_final <- cbind(
item_stats,
b_means,
a = a_means
)
tabla_final
## mean sd r.drop b1 b2 b3 b4
## P26 3.589404 0.9679637 0.5684867 -2.603553 -1.393960 -0.25854788 1.1053071
## P27 3.827815 0.9644452 0.7350424 -2.489567 -1.259236 -0.46478646 0.6073623
## P28 3.662252 0.7906741 0.6624560 -3.144520 -1.451230 -0.40125948 1.3548668
## P29 3.304636 0.7830996 0.5967302 -2.444456 -1.376779 0.24709495 2.1513448
## P30 3.291391 0.7446646 0.5350629 -3.092049 -1.562561 0.46114604 2.1061445
## P31 3.874172 0.8817001 0.6177823 -2.819528 -1.841832 -0.45089614 0.6393898
## P32 3.788079 0.8764266 0.6255387 -3.099004 -1.434530 -0.50609662 0.8588112
## P33 3.774834 0.9533952 0.6988111 -2.888154 -1.194894 -0.46405716 0.6680677
## P34 3.774834 0.6549523 0.6023526 -2.933651 -2.084810 -0.70705530 1.6202343
## P35 3.880795 0.8863946 0.7291180 -2.956494 -1.425650 -0.48497502 0.5743391
## P36 3.397351 0.7666331 0.5507445 -2.696216 -1.861445 0.26361688 1.9835231
## P37 3.801325 0.8642520 0.6748035 -2.988747 -1.369268 -0.53206442 0.8468713
## P38 3.741722 0.9413719 0.6560418 -2.671131 -1.373495 -0.45080238 0.8092431
## P39 3.450331 0.8221009 0.7395269 -2.479669 -1.198165 -0.03192079 1.5159385
## P40 3.331126 0.7721991 0.6133230 -2.587842 -1.399796 0.21842016 2.0274099
## P41 3.675497 0.8683292 0.5786988 -2.933596 -1.540234 -0.42129318 1.2022557
## P42 3.860927 0.9168041 0.6274897 -3.200306 -1.584011 -0.42039476 0.5806310
## P43 3.099338 0.7188414 0.4877000 -2.783864 -1.478662 0.93335633 2.8760236
## P44 3.311258 0.8180092 0.5216836 -2.827434 -1.336986 0.21761130 2.0785824
## P45 3.490066 0.7820277 0.6815302 -2.452532 -1.500902 -0.07012094 1.6756064
## a
## P26 1.921568
## P27 3.032739
## P28 2.464626
## P29 2.100083
## P30 1.848447
## P31 2.350373
## P32 2.449644
## P33 3.000743
## P34 2.229031
## P35 3.367869
## P36 1.805115
## P37 2.749188
## P38 2.455811
## P39 2.974253
## P40 2.147437
## P41 2.029367
## P42 2.474233
## P43 1.537054
## P44 1.823965
## P45 2.516398