Modelling non-Gaussian data
We will return to running generalised mixed-effects models (glmer) in rstanarm as we did in the first practical, this time considering non-Gaussian distributed-data, specified with the argument family.
Example 1: Roaches
First we examine a dataset with a count response variable, roaches (Gelman & Hill 2007), which is available in the rstanarm package and for which there is a vignette for the glm analysis. We will adapt this for our exercise to make this a hierarchical model using glmer.
The dataset is intended to explore the efficacy of roach pest management treatment. Our response \(y~{i}\) is the count of the number of roaches caught in traps, in apartments \(i\) . Either a treatment (1) or control (0) was applied to each apartment, and the variable roaches gives the number of roaches caught pre-treatment. There is also a variable indicating whether the apartment is in a building restricted to elderly residents:�senior. Because the number of days for which the roach traps were used is not the same for all apartments in the sample (i.e. there were different levels of opportunity to catch the roaches), we also include that as an ‘exposure’ term, and it can be specified using the�offset�argument to�stan_glm.
Following the vignette example, we rescale the roaches variable. We additionally generate and add a new grouping variable to denote clustered locations of the apartments: loc so that we can demonstrate a hierarchical model. Spatial clustering of apartments could have an effect if roach population sizes vary over space, (e.g. due to habitat or breeding success factors) thereby having an effect on the number of roaches caught beyond the experimental treatments we are trying to observe.
Warning: package 'ggplot2' was built under R version 4.4.3
library (bayesplot) # you may need to install this one!
This is bayesplot version 1.13.0
- Online documentation and vignettes at mc-stan.org/bayesplot
- bayesplot theme set to bayesplot::theme_default()
* Does _not_ affect other ggplot2 plots
* See ?bayesplot_theme_set for details on theme setting
Warning: package 'rstanarm' was built under R version 4.4.3
Loading required package: Rcpp
Warning: package 'Rcpp' was built under R version 4.4.3
This is rstanarm version 2.32.1
- See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!
- Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.
- For execution on a local, multicore CPU with excess RAM we recommend calling
options(mc.cores = parallel::detectCores())
data (roaches)head (roaches)
y roach1 treatment senior exposure2
1 153 308.00 1 0 0.800000
2 127 331.25 1 0 0.600000
3 7 1.67 1 0 1.000000
4 7 3.00 1 0 1.000000
5 0 2.00 1 0 1.142857
6 0 0.00 1 0 1.000000
# Rescale $ roach1 <- roaches$ roach1 / 100 # Randomly assign 'location' number as a new grouping term set.seed (2 ) # to ensure we get the same numbers each time <- sample (1 : 12 , size= 262 , replace= TRUE )
[1] 5 6 6 8 1 1 12 9 2 11 1 3 6 2 3 7 8 7 1 6 9 4 11 6 9
[26] 8 6 3 9 7 8 6 2 7 2 3 4 3 1 7 9 1 2 8 4 5 12 2 5 6
[51] 7 2 6 12 4 12 4 9 10 2 6 6 3 3 8 6 1 5 6 1 10 9 5 8 4
[76] 1 1 5 11 9 10 5 11 1 12 9 2 9 7 12 4 1 4 6 8 9 6 7 12 7
[101] 3 5 4 5 9 5 10 3 11 1 7 9 11 5 3 3 6 1 12 2 10 4 11 9 1
[126] 7 3 5 8 4 12 2 8 1 5 4 7 8 3 8 10 1 11 1 4 10 2 4 2 12
[151] 6 6 12 3 5 11 5 2 2 6 3 5 2 4 11 2 7 2 5 8 12 12 11 11 3
[176] 6 9 8 6 9 6 7 11 6 8 6 11 2 12 3 3 11 6 10 7 2 8 7 4 1
[201] 4 10 3 1 9 1 4 8 10 10 11 2 11 5 3 4 11 5 7 4 8 10 8 6 2
[226] 12 4 6 6 2 9 3 12 10 5 4 5 12 6 10 4 9 6 9 7 10 4 5 8 7
[251] 10 6 3 10 3 10 7 5 9 1 5 12
<- cbind (roaches, loc)head (roaches_new)
y roach1 treatment senior exposure2 loc
1 153 3.0800 1 0 0.800000 5
2 127 3.3125 1 0 0.600000 6
3 7 0.0167 1 0 1.000000 6
4 7 0.0300 1 0 1.000000 8
5 0 0.0200 1 0 1.142857 1
6 0 0.0000 1 0 1.000000 1
First, let’s run the models using the function glm (without the grouping term) and glmer (with the grouping term loc). Notice, in comparison to the first practical, we have specified the Poisson distribution using a log link function family = poisson(link = "log"), one of the families suitable for count data, but where there is quite a stringent assumption that the mean and variance are equal.
As with the example in the first practical, we can choose how to specify the random effects. Do we expect location to just shift the intercepts of the relationships between pre-treatment roaches and post-treatment roaches, or could the slopes of those relationships also vary across locations? We produce two versions of the glmer model. Other combinations could be possible, for example treatment efficacy having a different effect across locations.
Warning: package 'lme4' was built under R version 4.4.3
Loading required package: Matrix
# Estimate original model <- glm (y ~ roach1 + treatment + senior, offset = log (exposure2),data = roaches_new, family = poisson (link = "log" ))summary (glm1)
Call:
glm(formula = y ~ roach1 + treatment + senior, family = poisson(link = "log"),
data = roaches_new, offset = log(exposure2))
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.089246 0.021234 145.49 <2e-16 ***
roach1 0.698289 0.008874 78.69 <2e-16 ***
treatment -0.516726 0.024739 -20.89 <2e-16 ***
senior -0.379875 0.033418 -11.37 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 16954 on 261 degrees of freedom
Residual deviance: 11429 on 258 degrees of freedom
AIC: 12192
Number of Fisher Scoring iterations: 6
# Estimate candidate mixed-effects models <- glmer (y ~ roach1 + treatment + senior + (1 | loc), offset = log (exposure2),data = roaches_new, family = poisson (link = "log" ))summary (glm2)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: poisson ( log )
Formula: y ~ roach1 + treatment + senior + (1 | loc)
Data: roaches_new
Offset: log(exposure2)
AIC BIC logLik -2*log(L) df.resid
11646.4 11664.2 -5818.2 11636.4 257
Scaled residuals:
Min 1Q Median 3Q Max
-11.724 -3.885 -2.556 0.106 45.003
Random effects:
Groups Name Variance Std.Dev.
loc (Intercept) 0.1192 0.3453
Number of obs: 262, groups: loc, 12
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.024587 0.102076 29.63 <2e-16 ***
roach1 0.747000 0.009907 75.40 <2e-16 ***
treatment -0.534992 0.025625 -20.88 <2e-16 ***
senior -0.456364 0.034395 -13.27 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) roach1 trtmnt
roach1 -0.120
treatment -0.106 -0.050
senior -0.061 0.169 -0.124
$loc
(Intercept)
1 -0.228774670
2 -0.010197754
3 0.003867703
4 0.410392652
5 0.262560694
6 -0.004889566
7 -0.424295616
8 0.279652316
9 -0.720059821
10 0.397487779
11 -0.275254016
12 0.321418319
with conditional variances for "loc"
<- glmer (y ~ roach1 + treatment + senior + (roach1| loc), offset = log (exposure2),data = roaches_new, family = poisson (link = "log" ))summary (glm3)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: poisson ( log )
Formula: y ~ roach1 + treatment + senior + (roach1 | loc)
Data: roaches_new
Offset: log(exposure2)
AIC BIC logLik -2*log(L) df.resid
11097.0 11122.0 -5541.5 11083.0 255
Scaled residuals:
Min 1Q Median 3Q Max
-10.591 -3.662 -2.624 0.753 44.072
Random effects:
Groups Name Variance Std.Dev. Corr
loc (Intercept) 0.1211 0.3480
roach1 0.0604 0.2458 -0.58
Number of obs: 262, groups: loc, 12
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.91616 0.10347 28.18 <2e-16 ***
roach1 0.82682 0.07215 11.46 <2e-16 ***
treatment -0.48798 0.02823 -17.29 <2e-16 ***
senior -0.38332 0.03602 -10.64 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) roach1 trtmnt
roach1 -0.574
treatment -0.124 -0.006
senior -0.063 0.016 -0.124
$loc
(Intercept) roach1
1 -0.38402166 0.16363544
2 0.12793470 -0.11873824
3 -0.13447383 0.09681217
4 0.61808995 -0.33537557
5 0.16990675 0.06697628
6 0.15750920 -0.12989373
7 0.31700678 -0.39350123
8 0.35363777 -0.08569835
9 -0.48875228 -0.20979966
10 0.03441243 0.33278494
11 -0.49885510 0.24390528
12 -0.25279834 0.37263770
with conditional variances for "loc"
For simplicity, let’s proceed with model 2, this time using stan_glmer. The below code just uses the default settings for chains (4) and iterations (2000) because we have not explicitly stated them. What information could be used to help inform our priors?
# Estimate Bayesian version with stan_glm <- stan_glmer (y ~ roach1 + treatment + senior + (1 | loc), offset = log (exposure2),data = roaches_new, family = poisson (link = "log" ),prior = normal (0 , 2.5 ),prior_intercept = normal (0 , 5 ),seed = 12345 )
SAMPLING FOR MODEL 'count' NOW (CHAIN 1).
Chain 1:
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Priors for model 'stan_glm2'
------
Intercept (after predictors centered)
~ normal(location = 0, scale = 5)
Coefficients
~ normal(location = [0,0,0], scale = [2.5,2.5,2.5])
Covariance
~ decov(reg. = 1, conc. = 1, shape = 1, scale = 1)
------
See help('prior_summary.stanreg') for more details
Interpreting the model
$loc
(Intercept) roach1 treatment senior
1 2.795812 0.7470005 -0.5349923 -0.4563642
2 3.014389 0.7470005 -0.5349923 -0.4563642
3 3.028454 0.7470005 -0.5349923 -0.4563642
4 3.434979 0.7470005 -0.5349923 -0.4563642
5 3.287147 0.7470005 -0.5349923 -0.4563642
6 3.019697 0.7470005 -0.5349923 -0.4563642
7 2.600291 0.7470005 -0.5349923 -0.4563642
8 3.304239 0.7470005 -0.5349923 -0.4563642
9 2.304527 0.7470005 -0.5349923 -0.4563642
10 3.422074 0.7470005 -0.5349923 -0.4563642
11 2.749332 0.7470005 -0.5349923 -0.4563642
12 3.346005 0.7470005 -0.5349923 -0.4563642
attr(,"class")
[1] "coef.mer"
$loc
(Intercept) roach1 treatment senior
1 2.793090 0.7473234 -0.5336443 -0.4575336
2 3.012650 0.7473234 -0.5336443 -0.4575336
3 3.026102 0.7473234 -0.5336443 -0.4575336
4 3.433441 0.7473234 -0.5336443 -0.4575336
5 3.282963 0.7473234 -0.5336443 -0.4575336
6 3.017244 0.7473234 -0.5336443 -0.4575336
7 2.597886 0.7473234 -0.5336443 -0.4575336
8 3.303320 0.7473234 -0.5336443 -0.4575336
9 2.295207 0.7473234 -0.5336443 -0.4575336
10 3.417976 0.7473234 -0.5336443 -0.4575336
11 2.745987 0.7473234 -0.5336443 -0.4575336
12 3.344886 0.7473234 -0.5336443 -0.4575336
attr(,"class")
[1] "coef.mer"
print (stan_glm2) # for further information on interpretation: ?print.stanreg
stan_glmer
family: poisson [log]
formula: y ~ roach1 + treatment + senior + (1 | loc)
observations: 262
------
Median MAD_SD
(Intercept) 3.0 0.1
roach1 0.7 0.0
treatment -0.5 0.0
senior -0.5 0.0
Error terms:
Groups Name Std.Dev.
loc (Intercept) 0.41
Num. levels: loc 12
------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg
summary (stan_glm2, digits = 5 )
Model Info:
function: stan_glmer
family: poisson [log]
formula: y ~ roach1 + treatment + senior + (1 | loc)
algorithm: sampling
sample: 4000 (posterior sample size)
priors: see help('prior_summary')
observations: 262
groups: loc (12)
Estimates:
mean sd 10% 50% 90%
(Intercept) 3.02760 0.12105 2.88069 3.02444 3.17537
roach1 0.74714 0.00969 0.73455 0.74732 0.75962
treatment -0.53433 0.02504 -0.56689 -0.53364 -0.50278
senior -0.45723 0.03482 -0.50208 -0.45753 -0.41175
b[(Intercept) loc:1] -0.23333 0.12765 -0.39094 -0.23135 -0.07800
b[(Intercept) loc:2] -0.01484 0.12411 -0.16746 -0.01179 0.13655
b[(Intercept) loc:3] -0.00110 0.12488 -0.15464 0.00166 0.14660
b[(Intercept) loc:4] 0.40655 0.12494 0.25540 0.40900 0.55636
b[(Intercept) loc:5] 0.25814 0.12555 0.10281 0.25852 0.41148
b[(Intercept) loc:6] -0.00833 0.12365 -0.15715 -0.00720 0.14336
b[(Intercept) loc:7] -0.42857 0.12637 -0.58643 -0.42655 -0.27513
b[(Intercept) loc:8] 0.27573 0.12521 0.12424 0.27888 0.42535
b[(Intercept) loc:9] -0.72949 0.13203 -0.89339 -0.72923 -0.56643
b[(Intercept) loc:10] 0.39339 0.12543 0.24198 0.39353 0.54486
b[(Intercept) loc:11] -0.28010 0.13118 -0.44270 -0.27845 -0.11774
b[(Intercept) loc:12] 0.31766 0.12500 0.16285 0.32045 0.46735
Sigma[loc:(Intercept),(Intercept)] 0.16604 0.08730 0.08493 0.14647 0.26780
Fit Diagnostics:
mean sd 10% 50% 90%
mean_PPD 25.65330 0.45286 25.06107 25.65649 26.23282
The mean_ppd is the sample average posterior predictive distribution of the outcome variable (for details see help('summary.stanreg')).
MCMC diagnostics
mcse Rhat n_eff
(Intercept) 0.00463 1.00397 684
roach1 0.00016 1.00080 3896
treatment 0.00043 0.99965 3380
senior 0.00067 1.00072 2686
b[(Intercept) loc:1] 0.00469 1.00363 741
b[(Intercept) loc:2] 0.00467 1.00350 706
b[(Intercept) loc:3] 0.00464 1.00316 725
b[(Intercept) loc:4] 0.00464 1.00331 726
b[(Intercept) loc:5] 0.00467 1.00441 724
b[(Intercept) loc:6] 0.00468 1.00343 699
b[(Intercept) loc:7] 0.00457 1.00303 764
b[(Intercept) loc:8] 0.00461 1.00301 737
b[(Intercept) loc:9] 0.00452 1.00242 855
b[(Intercept) loc:10] 0.00461 1.00416 741
b[(Intercept) loc:11] 0.00467 1.00325 788
b[(Intercept) loc:12] 0.00462 1.00374 733
Sigma[loc:(Intercept),(Intercept)] 0.00279 1.00489 976
mean_PPD 0.00724 0.99955 3909
log-posterior 0.14779 1.00788 668
For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
plot (stan_glm2, "trace" ) # nice hairy catepillars!
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
<- posterior_predict (stan_glm2)# yrep will be an S x N matrix, where S is the size of the posterior sample and N is the number of data points. Each row of yrep represents a full dataset generated from the posterior predictive distribution. dim (yrep)pp_check (stan_glm2) # this does not look great! Can you describe what is happening here? <- function (y) mean (y == 0 )<- pp_check (stan_glm2, plotfun = "stat" , stat = "prop_zero" , binwidth = .005 ))
The proportion of zeros computed from the sample�y�is the dark blue vertical line (>35% zeros) and the light blue bars are those from the replicated datasets from the model, what do you we think of our model?
We should consider a model that more accurately accounts for the large proportion of zeros in the data - one option is to use a negative binomial distribution for the data which is often used for zero-inflated or overdispersed count data. It is more flexible than Poisson because the (conditional) mean and variance of \(y\) can differ. We update the model with the new family, as follows:
<- update (stan_glm2, family = neg_binomial_2)
SAMPLING FOR MODEL 'count' NOW (CHAIN 1).
Chain 1:
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SAMPLING FOR MODEL 'count' NOW (CHAIN 4).
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Chain 4: Gradient evaluation took 0.000144 seconds
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<- pp_check (stan_glm_nb, plotfun = "stat" , stat = "prop_zero" ,binwidth = 0.01 )prior_summary (stan_glm_nb)
Priors for model 'stan_glm_nb'
------
Intercept (after predictors centered)
~ normal(location = 0, scale = 5)
Coefficients
~ normal(location = [0,0,0], scale = [2.5,2.5,2.5])
Auxiliary (reciprocal_dispersion)
~ exponential(rate = 1)
Covariance
~ decov(reg. = 1, conc. = 1, shape = 1, scale = 1)
------
See help('prior_summary.stanreg') for more details
$loc
(Intercept) roach1 treatment senior
1 2.849141 1.314065 -0.7997935 -0.4109909
2 2.853071 1.314065 -0.7997935 -0.4109909
3 2.834623 1.314065 -0.7997935 -0.4109909
4 3.000969 1.314065 -0.7997935 -0.4109909
5 2.883617 1.314065 -0.7997935 -0.4109909
6 2.867341 1.314065 -0.7997935 -0.4109909
7 2.853989 1.314065 -0.7997935 -0.4109909
8 2.875434 1.314065 -0.7997935 -0.4109909
9 2.805406 1.314065 -0.7997935 -0.4109909
10 2.877205 1.314065 -0.7997935 -0.4109909
11 2.823158 1.314065 -0.7997935 -0.4109909
12 2.862583 1.314065 -0.7997935 -0.4109909
attr(,"class")
[1] "coef.mer"
# Show graphs for Poisson and negative binomial side by side - we use this function from the bayesplot package bayesplot_grid (prop_zero_test1 + ggtitle ("Poisson" ),+ ggtitle ("Negative Binomial" ),grid_args = list (ncol = 2 ))
We can see clearly that the updated model is doing a better job. At this point
Example 2: Climbing expeditions (…or other success/survival outcomes)
For this part of the practical we make use of an example from Johnson, Ott and Dogucu (2021), which presents a subset of The Himalayan Database (2020) https://www.himalayandatabase.com/ .
The climbers.csv represents the outcomes (success of reaching the destination) from 200 climbing expeditions. Each row represents a climber (member_id) and their individual success outcome (true or false) for a given expedition_id. The other predictors of outcomes include climber age, season, expedition_role and oxygen_used. expedition_id groups members across the dataset, because each expedition has multiple climbers - this grouping variable can be considered structure within the dataset, because members within the team share similar conditions (same weather, same destination, same instructors.
Let’s read in the data and visually explore.
Warning: package 'bayesrules' was built under R version 4.4.3
<- read.csv (url ("https://raw.githubusercontent.com/NERC-CEH/beem_data/main/climbers.csv" ))head (climbers)
X expedition_id member_id success year season age expedition_role
1 1 AMAD81101 AMAD81101-03 TRUE 1981 Spring 28 Climber
2 2 AMAD81101 AMAD81101-04 TRUE 1981 Spring 27 Exp Doctor
3 3 AMAD81101 AMAD81101-02 TRUE 1981 Spring 35 Deputy Leader
4 4 AMAD81101 AMAD81101-05 TRUE 1981 Spring 37 Climber
5 5 AMAD81101 AMAD81101-06 TRUE 1981 Spring 43 Climber
6 6 AMAD81101 AMAD81101-07 FALSE 1981 Spring 38 Climber
oxygen_used
1 FALSE
2 FALSE
3 FALSE
4 FALSE
5 FALSE
6 FALSE
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── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr 1.1.4 ✔ readr 2.1.5
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── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
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✖ tidyr::unpack() masks Matrix::unpack()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
<- climbers %>% group_by (expedition_id) %>% summarise (success_rate= mean (success))ggplot (expedition_success, aes (x= success_rate))+ geom_histogram (color= "white" )
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
What type of distribution would be appropriate for modelling the outcomes?
<- stan_glmer (~ age + oxygen_used + (1 | expedition_id), data = climbers, family = binomial,prior_intercept = normal (0 , 2.5 , autoscale = TRUE ),prior = normal (0 , 2.5 , autoscale = TRUE ), prior_covariance = decov (reg = 1 , conc = 1 , shape = 1 , scale = 1 ),chains = 4 , iter = 2500 , seed = 84735
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.001143 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 11.43 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1:
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 2).
Chain 2:
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Chain 2:
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000668 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 6.68 seconds.
Chain 3: Adjust your expectations accordingly!
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Chain 3:
SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.000662 seconds
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Chain 4:
Let’s check our model. Some of the outputs are quite long because our population of random effects is quite large.
library (bayesplot)rhat (climb_stan_glm1) # ?rhat for further details
(Intercept)
1.0005532
age
0.9995728
oxygen_usedTRUE
1.0003627
b[(Intercept) expedition_id:AMAD03107]
0.9997726
b[(Intercept) expedition_id:AMAD03327]
0.9998950
b[(Intercept) expedition_id:AMAD05338]
1.0000518
b[(Intercept) expedition_id:AMAD06110]
0.9997008
b[(Intercept) expedition_id:AMAD06334]
0.9996629
b[(Intercept) expedition_id:AMAD07101]
0.9998991
b[(Intercept) expedition_id:AMAD07310]
1.0002853
b[(Intercept) expedition_id:AMAD07337]
1.0003666
b[(Intercept) expedition_id:AMAD07340]
0.9999155
b[(Intercept) expedition_id:AMAD09331]
0.9996659
b[(Intercept) expedition_id:AMAD09333]
0.9994012
b[(Intercept) expedition_id:AMAD11304]
0.9997037
b[(Intercept) expedition_id:AMAD11321]
0.9998430
b[(Intercept) expedition_id:AMAD11340]
1.0003190
b[(Intercept) expedition_id:AMAD12108]
0.9995780
b[(Intercept) expedition_id:AMAD12342]
1.0004821
b[(Intercept) expedition_id:AMAD14105]
0.9998667
b[(Intercept) expedition_id:AMAD14322]
0.9996353
b[(Intercept) expedition_id:AMAD16354]
0.9994518
b[(Intercept) expedition_id:AMAD17307]
1.0001298
b[(Intercept) expedition_id:AMAD81101]
1.0003451
b[(Intercept) expedition_id:AMAD84401]
0.9997012
b[(Intercept) expedition_id:AMAD89102]
0.9995925
b[(Intercept) expedition_id:AMAD93304]
0.9999750
b[(Intercept) expedition_id:AMAD98311]
0.9999970
b[(Intercept) expedition_id:AMAD98316]
1.0007296
b[(Intercept) expedition_id:AMAD98402]
0.9994348
b[(Intercept) expedition_id:ANN115106]
0.9998717
b[(Intercept) expedition_id:ANN115108]
1.0000472
b[(Intercept) expedition_id:ANN179301]
0.9994432
b[(Intercept) expedition_id:ANN185401]
0.9995715
b[(Intercept) expedition_id:ANN190101]
0.9996483
b[(Intercept) expedition_id:ANN193302]
1.0002134
b[(Intercept) expedition_id:ANN281302]
0.9995369
b[(Intercept) expedition_id:ANN283302]
0.9995802
b[(Intercept) expedition_id:ANN378301]
1.0005540
b[(Intercept) expedition_id:ANN402302]
0.9994685
b[(Intercept) expedition_id:ANN405301]
0.9998415
b[(Intercept) expedition_id:ANN409201]
1.0005906
b[(Intercept) expedition_id:ANN416101]
0.9995834
b[(Intercept) expedition_id:BARU01304]
1.0007201
b[(Intercept) expedition_id:BARU02101]
1.0001295
b[(Intercept) expedition_id:BARU02303]
0.9997006
b[(Intercept) expedition_id:BARU09102]
0.9999938
b[(Intercept) expedition_id:BARU10312]
0.9999667
b[(Intercept) expedition_id:BARU11303]
1.0006530
b[(Intercept) expedition_id:BARU92301]
1.0004625
b[(Intercept) expedition_id:BARU94301]
1.0007040
b[(Intercept) expedition_id:BARU94307]
0.9997854
b[(Intercept) expedition_id:BHRI86101]
0.9996264
b[(Intercept) expedition_id:CHAM18101]
0.9995013
b[(Intercept) expedition_id:CHAM91301]
1.0000014
b[(Intercept) expedition_id:CHOY02117]
1.0001804
b[(Intercept) expedition_id:CHOY03103]
1.0011492
b[(Intercept) expedition_id:CHOY03318]
1.0008072
b[(Intercept) expedition_id:CHOY04122]
0.9997353
b[(Intercept) expedition_id:CHOY04302]
1.0003967
b[(Intercept) expedition_id:CHOY06330]
1.0001162
b[(Intercept) expedition_id:CHOY07310]
1.0000940
b[(Intercept) expedition_id:CHOY07330]
0.9997409
b[(Intercept) expedition_id:CHOY07356]
0.9997544
b[(Intercept) expedition_id:CHOY07358]
0.9997619
b[(Intercept) expedition_id:CHOY10328]
0.9997056
b[(Intercept) expedition_id:CHOY10341]
0.9998975
b[(Intercept) expedition_id:CHOY93304]
0.9999339
b[(Intercept) expedition_id:CHOY96319]
1.0001085
b[(Intercept) expedition_id:CHOY97103]
1.0007538
b[(Intercept) expedition_id:CHOY98307]
0.9996961
b[(Intercept) expedition_id:CHOY99301]
1.0000512
b[(Intercept) expedition_id:DHA109113]
0.9996487
b[(Intercept) expedition_id:DHA116106]
0.9999480
b[(Intercept) expedition_id:DHA183302]
0.9999637
b[(Intercept) expedition_id:DHA193302]
0.9995715
b[(Intercept) expedition_id:DHA196104]
1.0000891
b[(Intercept) expedition_id:DHA197107]
0.9995235
b[(Intercept) expedition_id:DHA197307]
1.0005591
b[(Intercept) expedition_id:DHA198107]
0.9997476
b[(Intercept) expedition_id:DHA198302]
0.9997488
b[(Intercept) expedition_id:DHAM88301]
0.9999669
b[(Intercept) expedition_id:DZA215301]
1.0000358
b[(Intercept) expedition_id:EVER00116]
0.9996641
b[(Intercept) expedition_id:EVER00148]
0.9992599
b[(Intercept) expedition_id:EVER01108]
1.0005965
b[(Intercept) expedition_id:EVER02112]
0.9996763
b[(Intercept) expedition_id:EVER03124]
1.0001600
b[(Intercept) expedition_id:EVER03168]
1.0012481
b[(Intercept) expedition_id:EVER04150]
1.0003185
b[(Intercept) expedition_id:EVER04156]
0.9996000
b[(Intercept) expedition_id:EVER06133]
0.9998157
b[(Intercept) expedition_id:EVER06136]
1.0007162
b[(Intercept) expedition_id:EVER06152]
1.0001397
b[(Intercept) expedition_id:EVER06163]
1.0004249
b[(Intercept) expedition_id:EVER07107]
0.9998612
b[(Intercept) expedition_id:EVER07148]
0.9995514
b[(Intercept) expedition_id:EVER07175]
1.0012568
b[(Intercept) expedition_id:EVER07192]
1.0000522
b[(Intercept) expedition_id:EVER07194]
1.0001655
b[(Intercept) expedition_id:EVER08139]
1.0012186
b[(Intercept) expedition_id:EVER08152]
1.0009996
b[(Intercept) expedition_id:EVER08154]
0.9996120
b[(Intercept) expedition_id:EVER10121]
0.9995880
b[(Intercept) expedition_id:EVER10136]
0.9997021
b[(Intercept) expedition_id:EVER10154]
1.0018716
b[(Intercept) expedition_id:EVER11103]
1.0010148
b[(Intercept) expedition_id:EVER11134]
0.9997410
b[(Intercept) expedition_id:EVER11144]
0.9999872
b[(Intercept) expedition_id:EVER11152]
1.0000995
b[(Intercept) expedition_id:EVER12133]
0.9997449
b[(Intercept) expedition_id:EVER12141]
0.9996518
b[(Intercept) expedition_id:EVER14138]
0.9994947
b[(Intercept) expedition_id:EVER14165]
1.0000990
b[(Intercept) expedition_id:EVER15117]
0.9997793
b[(Intercept) expedition_id:EVER15123]
0.9996767
b[(Intercept) expedition_id:EVER16105]
1.0016690
b[(Intercept) expedition_id:EVER17123]
1.0016099
b[(Intercept) expedition_id:EVER17137]
0.9997361
b[(Intercept) expedition_id:EVER18118]
0.9995584
b[(Intercept) expedition_id:EVER18132]
0.9996551
b[(Intercept) expedition_id:EVER19104]
0.9993636
b[(Intercept) expedition_id:EVER19112]
1.0004859
b[(Intercept) expedition_id:EVER19120]
1.0001846
b[(Intercept) expedition_id:EVER81101]
0.9994650
b[(Intercept) expedition_id:EVER86101]
1.0004059
b[(Intercept) expedition_id:EVER89304]
0.9995315
b[(Intercept) expedition_id:EVER91108]
0.9998226
b[(Intercept) expedition_id:EVER96302]
1.0000293
b[(Intercept) expedition_id:EVER97105]
1.0006378
b[(Intercept) expedition_id:EVER98116]
1.0002699
b[(Intercept) expedition_id:EVER99107]
0.9993799
b[(Intercept) expedition_id:EVER99113]
1.0002634
b[(Intercept) expedition_id:EVER99116]
0.9995102
b[(Intercept) expedition_id:FANG97301]
0.9998397
b[(Intercept) expedition_id:GAN379301]
1.0004571
b[(Intercept) expedition_id:GAUR83101]
0.9998868
b[(Intercept) expedition_id:GURK03301]
1.0010562
b[(Intercept) expedition_id:GYAJ15101]
0.9999490
b[(Intercept) expedition_id:HIML03302]
0.9998998
b[(Intercept) expedition_id:HIML08301]
0.9998365
b[(Intercept) expedition_id:HIML08307]
0.9994337
b[(Intercept) expedition_id:HIML13303]
1.0003050
b[(Intercept) expedition_id:HIML13305]
0.9997714
b[(Intercept) expedition_id:HIML18310]
0.9995565
b[(Intercept) expedition_id:JANU02401]
0.9997431
b[(Intercept) expedition_id:JANU89401]
0.9996309
b[(Intercept) expedition_id:JANU97301]
0.9994237
b[(Intercept) expedition_id:JANU98102]
0.9999609
b[(Intercept) expedition_id:JETH78101]
0.9995684
b[(Intercept) expedition_id:KABD85101]
0.9997887
b[(Intercept) expedition_id:KAN180101]
0.9994865
b[(Intercept) expedition_id:KANG81101]
1.0000984
b[(Intercept) expedition_id:KANG94301]
1.0004965
b[(Intercept) expedition_id:KWAN82402]
0.9996882
b[(Intercept) expedition_id:LANG84101]
0.9996592
b[(Intercept) expedition_id:LEOE05301]
0.9994956
b[(Intercept) expedition_id:LHOT09108]
0.9999177
b[(Intercept) expedition_id:LHOT88301]
0.9996417
b[(Intercept) expedition_id:LNJU16301]
0.9997315
b[(Intercept) expedition_id:LSHR90301]
1.0004738
b[(Intercept) expedition_id:MAKA01104]
0.9997320
b[(Intercept) expedition_id:MAKA02102]
1.0005283
b[(Intercept) expedition_id:MAKA02103]
0.9996149
b[(Intercept) expedition_id:MAKA08112]
1.0013837
b[(Intercept) expedition_id:MAKA09108]
0.9998132
b[(Intercept) expedition_id:MAKA15106]
1.0003040
b[(Intercept) expedition_id:MAKA90306]
1.0005162
b[(Intercept) expedition_id:MANA06305]
1.0002866
b[(Intercept) expedition_id:MANA08324]
1.0004055
b[(Intercept) expedition_id:MANA09107]
1.0005475
b[(Intercept) expedition_id:MANA10319]
0.9997260
b[(Intercept) expedition_id:MANA11106]
0.9996387
b[(Intercept) expedition_id:MANA11318]
0.9994870
b[(Intercept) expedition_id:MANA17333]
0.9998609
b[(Intercept) expedition_id:MANA18306]
1.0006496
b[(Intercept) expedition_id:MANA80101]
0.9999937
b[(Intercept) expedition_id:MANA82401]
0.9997594
b[(Intercept) expedition_id:MANA84101]
1.0007098
b[(Intercept) expedition_id:MANA91301]
1.0002649
b[(Intercept) expedition_id:MANA97301]
1.0002763
b[(Intercept) expedition_id:NAMP79101]
0.9999770
b[(Intercept) expedition_id:NEMJ83101]
0.9995502
b[(Intercept) expedition_id:NILC79101]
0.9998732
b[(Intercept) expedition_id:NUPT99102]
0.9994055
b[(Intercept) expedition_id:OHMI89101]
1.0004379
b[(Intercept) expedition_id:PUMO06301]
0.9998749
b[(Intercept) expedition_id:PUMO80302]
1.0008513
b[(Intercept) expedition_id:PUMO92308]
0.9994772
b[(Intercept) expedition_id:PUMO96101]
1.0000502
b[(Intercept) expedition_id:PUTH02301]
0.9998146
b[(Intercept) expedition_id:PUTH97302]
0.9997939
b[(Intercept) expedition_id:SHAL05301]
0.9995011
b[(Intercept) expedition_id:SPHN93101]
0.9996239
b[(Intercept) expedition_id:SYKG12301]
0.9997353
b[(Intercept) expedition_id:TAWO83101]
0.9995015
b[(Intercept) expedition_id:TILI04301]
1.0003972
b[(Intercept) expedition_id:TILI05301]
1.0010002
b[(Intercept) expedition_id:TILI91302]
0.9999817
b[(Intercept) expedition_id:TILI92301]
0.9996376
b[(Intercept) expedition_id:TKPO02102]
1.0009627
b[(Intercept) expedition_id:TUKU05101]
0.9996587
b[(Intercept) expedition_id:TUKU16301]
0.9999838
Sigma[expedition_id:(Intercept),(Intercept)]
1.0012913
stan_glmer
family: binomial [logit]
formula: success ~ age + oxygen_used + (1 | expedition_id)
observations: 2076
------
Median MAD_SD
(Intercept) -1.4 0.5
age 0.0 0.0
oxygen_usedTRUE 5.8 0.5
Error terms:
Groups Name Std.Dev.
expedition_id (Intercept) 3.7
Num. levels: expedition_id 200
------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg
summary (climb_stan_glm1, digits = 5 )
Model Info:
function: stan_glmer
family: binomial [logit]
formula: success ~ age + oxygen_used + (1 | expedition_id)
algorithm: sampling
sample: 5000 (posterior sample size)
priors: see help('prior_summary')
observations: 2076
groups: expedition_id (200)
Estimates:
mean sd 10%
(Intercept) -1.42560 0.48108 -2.03863
age -0.04774 0.00926 -0.05941
oxygen_usedTRUE 5.81435 0.48572 5.19214
b[(Intercept) expedition_id:AMAD03107] 2.58462 1.05527 1.22886
b[(Intercept) expedition_id:AMAD03327] 6.09344 1.86907 4.00374
b[(Intercept) expedition_id:AMAD05338] 4.12540 0.74295 3.18067
b[(Intercept) expedition_id:AMAD06110] -2.12498 2.63546 -5.76218
b[(Intercept) expedition_id:AMAD06334] -2.66437 2.43445 -6.03105
b[(Intercept) expedition_id:AMAD07101] -2.59019 2.47853 -6.07242
b[(Intercept) expedition_id:AMAD07310] 4.99448 0.73104 4.07581
b[(Intercept) expedition_id:AMAD07337] 2.91814 0.90162 1.77134
b[(Intercept) expedition_id:AMAD07340] 3.00031 0.83291 1.94906
b[(Intercept) expedition_id:AMAD09331] 3.73837 1.04516 2.43805
b[(Intercept) expedition_id:AMAD09333] 3.38418 0.97764 2.17328
b[(Intercept) expedition_id:AMAD11304] 3.94162 1.04654 2.62305
b[(Intercept) expedition_id:AMAD11321] 6.68067 1.76248 4.63832
b[(Intercept) expedition_id:AMAD11340] 6.27161 1.83718 4.20223
b[(Intercept) expedition_id:AMAD12108] 4.53617 1.20439 3.12452
b[(Intercept) expedition_id:AMAD12342] 4.82718 1.09813 3.54095
b[(Intercept) expedition_id:AMAD14105] -2.14392 2.57195 -5.62741
b[(Intercept) expedition_id:AMAD14322] 2.60047 0.75703 1.61986
b[(Intercept) expedition_id:AMAD16354] 4.15790 1.00258 2.88666
b[(Intercept) expedition_id:AMAD17307] 2.35569 0.99396 1.07838
b[(Intercept) expedition_id:AMAD81101] 4.56264 0.84324 3.50710
b[(Intercept) expedition_id:AMAD84401] -2.47170 2.55421 -5.90571
b[(Intercept) expedition_id:AMAD89102] -2.23811 2.48509 -5.59346
b[(Intercept) expedition_id:AMAD93304] 3.01674 0.94991 1.82339
b[(Intercept) expedition_id:AMAD98311] 6.60274 1.78207 4.58420
b[(Intercept) expedition_id:AMAD98316] 3.41252 0.68715 2.54421
b[(Intercept) expedition_id:AMAD98402] 4.29294 1.18256 2.88351
b[(Intercept) expedition_id:ANN115106] -2.62241 2.43068 -5.91960
b[(Intercept) expedition_id:ANN115108] -2.51791 2.43742 -5.85671
b[(Intercept) expedition_id:ANN179301] -2.50727 2.47726 -5.90908
b[(Intercept) expedition_id:ANN185401] -2.95374 2.36391 -6.18820
b[(Intercept) expedition_id:ANN190101] -2.51231 2.46417 -5.94034
b[(Intercept) expedition_id:ANN193302] -2.72987 2.45709 -6.12101
b[(Intercept) expedition_id:ANN281302] -2.92771 2.31649 -6.05400
b[(Intercept) expedition_id:ANN283302] -2.41458 2.43588 -5.68305
b[(Intercept) expedition_id:ANN378301] -2.96780 2.25677 -6.05808
b[(Intercept) expedition_id:ANN402302] -2.26993 2.58118 -5.72633
b[(Intercept) expedition_id:ANN405301] -1.85081 2.67077 -5.48998
b[(Intercept) expedition_id:ANN409201] 6.52670 1.82761 4.44457
b[(Intercept) expedition_id:ANN416101] -2.22586 2.64460 -5.80876
b[(Intercept) expedition_id:BARU01304] -2.38045 2.56391 -5.92191
b[(Intercept) expedition_id:BARU02101] -2.50414 2.37743 -5.72888
b[(Intercept) expedition_id:BARU02303] 4.05808 0.98773 2.81271
b[(Intercept) expedition_id:BARU09102] -2.34920 2.46361 -5.67170
b[(Intercept) expedition_id:BARU10312] -2.59506 2.39015 -5.82289
b[(Intercept) expedition_id:BARU11303] 4.24257 0.69951 3.35606
b[(Intercept) expedition_id:BARU92301] 3.35737 0.77896 2.38168
b[(Intercept) expedition_id:BARU94301] -2.23281 2.47358 -5.52525
b[(Intercept) expedition_id:BARU94307] -2.64432 2.44704 -5.98007
b[(Intercept) expedition_id:BHRI86101] -2.84606 2.35327 -6.09613
b[(Intercept) expedition_id:CHAM18101] -2.13296 2.57182 -5.53569
b[(Intercept) expedition_id:CHAM91301] 2.16264 0.74801 1.19401
b[(Intercept) expedition_id:CHOY02117] 2.25046 1.01699 0.91867
b[(Intercept) expedition_id:CHOY03103] 0.86263 1.27007 -0.74262
b[(Intercept) expedition_id:CHOY03318] -2.71607 0.70731 -3.62055
b[(Intercept) expedition_id:CHOY04122] 1.73790 0.91294 0.52959
b[(Intercept) expedition_id:CHOY04302] 4.53732 1.11176 3.22077
b[(Intercept) expedition_id:CHOY06330] 3.56472 0.99278 2.32850
b[(Intercept) expedition_id:CHOY07310] 3.59713 0.91066 2.44213
b[(Intercept) expedition_id:CHOY07330] -2.54613 2.47200 -5.73410
b[(Intercept) expedition_id:CHOY07356] -2.46844 2.46461 -5.82493
b[(Intercept) expedition_id:CHOY07358] 2.36368 0.81869 1.30795
b[(Intercept) expedition_id:CHOY10328] -3.94541 2.17354 -6.74664
b[(Intercept) expedition_id:CHOY10341] -2.06983 2.60626 -5.55325
b[(Intercept) expedition_id:CHOY93304] -2.53428 2.47876 -5.93481
b[(Intercept) expedition_id:CHOY96319] 2.15476 0.84894 1.06193
b[(Intercept) expedition_id:CHOY97103] -1.60506 0.94099 -2.78598
b[(Intercept) expedition_id:CHOY98307] -0.67156 1.62200 -2.81071
b[(Intercept) expedition_id:CHOY99301] 3.21945 0.72672 2.29728
b[(Intercept) expedition_id:DHA109113] 2.47803 1.39299 0.70144
b[(Intercept) expedition_id:DHA116106] -2.75514 2.42024 -6.06898
b[(Intercept) expedition_id:DHA183302] -2.68137 2.46419 -6.04356
b[(Intercept) expedition_id:DHA193302] 1.41083 1.33568 -0.31465
b[(Intercept) expedition_id:DHA196104] -2.50787 2.47336 -5.89618
b[(Intercept) expedition_id:DHA197107] -2.26242 2.51313 -5.70526
b[(Intercept) expedition_id:DHA197307] -2.16984 2.53111 -5.56595
b[(Intercept) expedition_id:DHA198107] 1.52062 0.95932 0.29941
b[(Intercept) expedition_id:DHA198302] -2.16545 2.48544 -5.51961
b[(Intercept) expedition_id:DHAM88301] -2.27515 2.51886 -5.72877
b[(Intercept) expedition_id:DZA215301] 5.90687 1.91343 3.73474
b[(Intercept) expedition_id:EVER00116] -1.24262 1.14380 -2.66075
b[(Intercept) expedition_id:EVER00148] -2.24264 2.63015 -5.78662
b[(Intercept) expedition_id:EVER01108] -1.23053 0.95860 -2.44491
b[(Intercept) expedition_id:EVER02112] 0.13470 1.39529 -1.67925
b[(Intercept) expedition_id:EVER03124] 0.39413 1.25981 -1.22383
b[(Intercept) expedition_id:EVER03168] -1.79239 1.02179 -3.04329
b[(Intercept) expedition_id:EVER04150] 1.00525 1.38190 -0.76730
b[(Intercept) expedition_id:EVER04156] -0.01150 1.20505 -1.57930
b[(Intercept) expedition_id:EVER06133] -1.39418 0.97974 -2.57853
b[(Intercept) expedition_id:EVER06136] -0.52842 0.96092 -1.71345
b[(Intercept) expedition_id:EVER06152] -2.18320 1.45586 -4.02147
b[(Intercept) expedition_id:EVER06163] -0.44209 0.99629 -1.70323
b[(Intercept) expedition_id:EVER07107] 0.98772 1.39267 -0.76457
b[(Intercept) expedition_id:EVER07148] -1.12615 1.07818 -2.47970
b[(Intercept) expedition_id:EVER07175] -0.19697 1.02673 -1.50260
b[(Intercept) expedition_id:EVER07192] 2.55135 2.45645 -0.30989
b[(Intercept) expedition_id:EVER07194] -6.06487 1.84802 -8.58170
b[(Intercept) expedition_id:EVER08139] -0.51572 0.65713 -1.35592
b[(Intercept) expedition_id:EVER08152] 0.10731 0.97523 -1.10485
b[(Intercept) expedition_id:EVER08154] 1.08240 1.26193 -0.53868
b[(Intercept) expedition_id:EVER10121] -0.79711 1.22634 -2.31084
b[(Intercept) expedition_id:EVER10136] -1.12381 1.20661 -2.64941
b[(Intercept) expedition_id:EVER10154] -1.72121 0.70279 -2.58507
b[(Intercept) expedition_id:EVER11103] -0.43040 0.75076 -1.37400
b[(Intercept) expedition_id:EVER11134] 3.35726 2.23395 0.78463
b[(Intercept) expedition_id:EVER11144] -5.66962 1.90437 -8.17256
b[(Intercept) expedition_id:EVER11152] 3.46002 2.25145 0.84028
b[(Intercept) expedition_id:EVER12133] 2.59615 2.44363 -0.25746
b[(Intercept) expedition_id:EVER12141] 1.56961 1.55855 -0.34308
b[(Intercept) expedition_id:EVER14138] -2.07616 2.56915 -5.58432
b[(Intercept) expedition_id:EVER14165] 1.67658 1.51871 -0.25401
b[(Intercept) expedition_id:EVER15117] -3.44779 2.23474 -6.39809
b[(Intercept) expedition_id:EVER15123] -3.26395 2.28611 -6.38874
b[(Intercept) expedition_id:EVER16105] -1.29497 0.72135 -2.19193
b[(Intercept) expedition_id:EVER17123] -1.62202 0.75444 -2.55988
b[(Intercept) expedition_id:EVER17137] 1.88869 1.41177 0.13340
b[(Intercept) expedition_id:EVER18118] 1.13297 1.03975 -0.18107
b[(Intercept) expedition_id:EVER18132] 0.55218 1.50267 -1.42165
b[(Intercept) expedition_id:EVER19104] 3.50067 2.21724 1.00455
b[(Intercept) expedition_id:EVER19112] -7.10545 1.69123 -9.34800
b[(Intercept) expedition_id:EVER19120] 3.40326 2.19662 0.87558
b[(Intercept) expedition_id:EVER81101] -4.49580 2.24708 -7.48117
b[(Intercept) expedition_id:EVER86101] -2.52059 2.46650 -5.83292
b[(Intercept) expedition_id:EVER89304] -2.94335 2.30166 -6.05163
b[(Intercept) expedition_id:EVER91108] -5.19499 2.04781 -7.89789
b[(Intercept) expedition_id:EVER96302] -0.34112 1.12605 -1.83561
b[(Intercept) expedition_id:EVER97105] -4.89106 2.00601 -7.55148
b[(Intercept) expedition_id:EVER98116] -0.82013 1.30463 -2.38770
b[(Intercept) expedition_id:EVER99107] -4.83542 2.01746 -7.47788
b[(Intercept) expedition_id:EVER99113] -2.11439 1.08111 -3.46708
b[(Intercept) expedition_id:EVER99116] 0.62323 1.06335 -0.71814
b[(Intercept) expedition_id:FANG97301] -2.55724 2.49524 -5.85915
b[(Intercept) expedition_id:GAN379301] 4.82999 1.07065 3.55650
b[(Intercept) expedition_id:GAUR83101] -2.73787 2.44531 -6.03820
b[(Intercept) expedition_id:GURK03301] -2.38419 2.48927 -5.83719
b[(Intercept) expedition_id:GYAJ15101] -1.89392 2.63842 -5.45911
b[(Intercept) expedition_id:HIML03302] 1.87013 0.98935 0.63241
b[(Intercept) expedition_id:HIML08301] 1.62213 0.92275 0.42413
b[(Intercept) expedition_id:HIML08307] -2.05948 2.52706 -5.46311
b[(Intercept) expedition_id:HIML13303] 5.01627 0.89396 3.90170
b[(Intercept) expedition_id:HIML13305] -2.12441 2.52219 -5.53771
b[(Intercept) expedition_id:HIML18310] 6.13444 1.81690 4.03634
b[(Intercept) expedition_id:JANU02401] -2.33309 2.52900 -5.81345
b[(Intercept) expedition_id:JANU89401] -2.50137 2.39675 -5.75711
b[(Intercept) expedition_id:JANU97301] -2.63817 2.34921 -5.80643
b[(Intercept) expedition_id:JANU98102] -2.29479 2.60749 -5.79529
b[(Intercept) expedition_id:JETH78101] 3.04722 1.03428 1.71516
b[(Intercept) expedition_id:KABD85101] 3.23227 0.89003 2.12167
b[(Intercept) expedition_id:KAN180101] -2.25321 2.45660 -5.57622
b[(Intercept) expedition_id:KANG81101] -0.65444 0.95217 -1.89131
b[(Intercept) expedition_id:KANG94301] -2.81457 2.29015 -5.94033
b[(Intercept) expedition_id:KWAN82402] 6.01302 1.83099 3.90995
b[(Intercept) expedition_id:LANG84101] -2.57763 2.45793 -5.88549
b[(Intercept) expedition_id:LEOE05301] -2.48805 2.41866 -5.76391
b[(Intercept) expedition_id:LHOT09108] 0.49017 1.41259 -1.35811
b[(Intercept) expedition_id:LHOT88301] 0.96358 1.81097 -1.33758
b[(Intercept) expedition_id:LNJU16301] -2.21115 2.54756 -5.68762
b[(Intercept) expedition_id:LSHR90301] 1.44354 0.94455 0.22243
b[(Intercept) expedition_id:MAKA01104] -2.39303 2.55136 -5.82507
b[(Intercept) expedition_id:MAKA02102] 1.77533 0.91557 0.59526
b[(Intercept) expedition_id:MAKA02103] 4.01277 0.93763 2.87114
b[(Intercept) expedition_id:MAKA08112] -5.78147 1.98138 -8.37621
b[(Intercept) expedition_id:MAKA09108] 0.04369 1.27699 -1.63840
b[(Intercept) expedition_id:MAKA15106] -2.45891 2.36193 -5.74649
b[(Intercept) expedition_id:MAKA90306] -2.69351 2.43369 -5.97698
b[(Intercept) expedition_id:MANA06305] -2.19010 2.66128 -5.78084
b[(Intercept) expedition_id:MANA08324] -6.12757 1.83096 -8.60786
b[(Intercept) expedition_id:MANA09107] 1.09540 1.37288 -0.66396
b[(Intercept) expedition_id:MANA10319] 2.05427 0.75905 1.09071
b[(Intercept) expedition_id:MANA11106] 4.13254 1.17547 2.71277
b[(Intercept) expedition_id:MANA11318] 1.70900 1.50181 -0.17858
b[(Intercept) expedition_id:MANA17333] 4.68512 2.17516 2.11668
b[(Intercept) expedition_id:MANA18306] 0.56117 1.02102 -0.70021
b[(Intercept) expedition_id:MANA80101] -2.80372 1.48779 -4.69586
b[(Intercept) expedition_id:MANA82401] -5.70714 1.95846 -8.28752
b[(Intercept) expedition_id:MANA84101] 6.86763 1.73485 4.86400
b[(Intercept) expedition_id:MANA91301] -2.57618 2.49091 -5.98577
b[(Intercept) expedition_id:MANA97301] 2.36095 0.71477 1.45079
b[(Intercept) expedition_id:NAMP79101] -2.57539 2.38751 -5.78000
b[(Intercept) expedition_id:NEMJ83101] -3.07247 2.34057 -6.23095
b[(Intercept) expedition_id:NILC79101] 3.71212 0.92944 2.56146
b[(Intercept) expedition_id:NUPT99102] -2.06069 2.61315 -5.55042
b[(Intercept) expedition_id:OHMI89101] 1.04390 0.94223 -0.14927
b[(Intercept) expedition_id:PUMO06301] -2.48834 2.39867 -5.77160
b[(Intercept) expedition_id:PUMO80302] -2.34651 2.52391 -5.79957
b[(Intercept) expedition_id:PUMO92308] 0.91100 1.26573 -0.70110
b[(Intercept) expedition_id:PUMO96101] 2.40227 0.85084 1.31315
b[(Intercept) expedition_id:PUTH02301] 1.42460 0.94670 0.19956
b[(Intercept) expedition_id:PUTH97302] -2.17485 2.46824 -5.61945
b[(Intercept) expedition_id:SHAL05301] -2.22066 2.48735 -5.66395
b[(Intercept) expedition_id:SPHN93101] 6.97740 1.67091 5.04511
b[(Intercept) expedition_id:SYKG12301] 5.48408 1.16635 4.07766
b[(Intercept) expedition_id:TAWO83101] -2.33970 2.51099 -5.75163
b[(Intercept) expedition_id:TILI04301] -2.47153 2.43775 -5.85646
b[(Intercept) expedition_id:TILI05301] 3.00634 0.67185 2.15360
b[(Intercept) expedition_id:TILI91302] 1.66625 0.95907 0.41207
b[(Intercept) expedition_id:TILI92301] -2.79137 2.41713 -6.04761
b[(Intercept) expedition_id:TKPO02102] -2.68386 2.35963 -5.91667
b[(Intercept) expedition_id:TUKU05101] -2.19821 2.53377 -5.59160
b[(Intercept) expedition_id:TUKU16301] 7.34626 1.69095 5.40123
Sigma[expedition_id:(Intercept),(Intercept)] 13.33845 2.59298 10.23552
50% 90%
(Intercept) -1.41192 -0.82198
age -0.04775 -0.03594
oxygen_usedTRUE 5.79289 6.45734
b[(Intercept) expedition_id:AMAD03107] 2.60352 3.90450
b[(Intercept) expedition_id:AMAD03327] 5.85107 8.57738
b[(Intercept) expedition_id:AMAD05338] 4.10337 5.08953
b[(Intercept) expedition_id:AMAD06110] -1.82839 0.97721
b[(Intercept) expedition_id:AMAD06334] -2.28804 0.16739
b[(Intercept) expedition_id:AMAD07101] -2.26341 0.30262
b[(Intercept) expedition_id:AMAD07310] 4.95883 5.93282
b[(Intercept) expedition_id:AMAD07337] 2.92699 4.06368
b[(Intercept) expedition_id:AMAD07340] 3.00040 4.05665
b[(Intercept) expedition_id:AMAD09331] 3.71307 5.08337
b[(Intercept) expedition_id:AMAD09333] 3.36566 4.63363
b[(Intercept) expedition_id:AMAD11304] 3.93480 5.26917
b[(Intercept) expedition_id:AMAD11321] 6.42822 9.09689
b[(Intercept) expedition_id:AMAD11340] 5.99432 8.74311
b[(Intercept) expedition_id:AMAD12108] 4.45718 6.08586
b[(Intercept) expedition_id:AMAD12342] 4.71390 6.24749
b[(Intercept) expedition_id:AMAD14105] -1.82372 0.88862
b[(Intercept) expedition_id:AMAD14322] 2.61407 3.58390
b[(Intercept) expedition_id:AMAD16354] 4.12871 5.44188
b[(Intercept) expedition_id:AMAD17307] 2.40293 3.57466
b[(Intercept) expedition_id:AMAD81101] 4.52562 5.65835
b[(Intercept) expedition_id:AMAD84401] -2.13143 0.48100
b[(Intercept) expedition_id:AMAD89102] -1.91936 0.64199
b[(Intercept) expedition_id:AMAD93304] 3.03452 4.22036
b[(Intercept) expedition_id:AMAD98311] 6.35244 9.00501
b[(Intercept) expedition_id:AMAD98316] 3.39920 4.30832
b[(Intercept) expedition_id:AMAD98402] 4.21856 5.76427
b[(Intercept) expedition_id:ANN115106] -2.30974 0.22170
b[(Intercept) expedition_id:ANN115108] -2.19292 0.35736
b[(Intercept) expedition_id:ANN179301] -2.18305 0.33680
b[(Intercept) expedition_id:ANN185401] -2.61884 -0.20623
b[(Intercept) expedition_id:ANN190101] -2.16417 0.39680
b[(Intercept) expedition_id:ANN193302] -2.40063 0.16340
b[(Intercept) expedition_id:ANN281302] -2.59899 -0.22190
b[(Intercept) expedition_id:ANN283302] -2.05955 0.43584
b[(Intercept) expedition_id:ANN378301] -2.68386 -0.29656
b[(Intercept) expedition_id:ANN402302] -1.89174 0.76295
b[(Intercept) expedition_id:ANN405301] -1.50956 1.29538
b[(Intercept) expedition_id:ANN409201] 6.27023 8.88495
b[(Intercept) expedition_id:ANN416101] -1.86808 0.87726
b[(Intercept) expedition_id:BARU01304] -2.04732 0.62060
b[(Intercept) expedition_id:BARU02101] -2.17593 0.25221
b[(Intercept) expedition_id:BARU02303] 4.05070 5.30395
b[(Intercept) expedition_id:BARU09102] -2.00162 0.50670
b[(Intercept) expedition_id:BARU10312] -2.25827 0.16895
b[(Intercept) expedition_id:BARU11303] 4.21665 5.15335
b[(Intercept) expedition_id:BARU92301] 3.34215 4.35998
b[(Intercept) expedition_id:BARU94301] -1.90406 0.66350
b[(Intercept) expedition_id:BARU94307] -2.29813 0.19694
b[(Intercept) expedition_id:BHRI86101] -2.52021 -0.12015
b[(Intercept) expedition_id:CHAM18101] -1.79744 0.85024
b[(Intercept) expedition_id:CHAM91301] 2.17494 3.08284
b[(Intercept) expedition_id:CHOY02117] 2.29903 3.50377
b[(Intercept) expedition_id:CHOY03103] 0.98213 2.33766
b[(Intercept) expedition_id:CHOY03318] -2.72864 -1.81911
b[(Intercept) expedition_id:CHOY04122] 1.80004 2.86191
b[(Intercept) expedition_id:CHOY04302] 4.42978 5.95567
b[(Intercept) expedition_id:CHOY06330] 3.52705 4.84829
b[(Intercept) expedition_id:CHOY07310] 3.58155 4.75554
b[(Intercept) expedition_id:CHOY07330] -2.23207 0.38696
b[(Intercept) expedition_id:CHOY07356] -2.15475 0.42109
b[(Intercept) expedition_id:CHOY07358] 2.38792 3.38464
b[(Intercept) expedition_id:CHOY10328] -3.71653 -1.34706
b[(Intercept) expedition_id:CHOY10341] -1.78952 1.07661
b[(Intercept) expedition_id:CHOY93304] -2.21219 0.38625
b[(Intercept) expedition_id:CHOY96319] 2.18085 3.20424
b[(Intercept) expedition_id:CHOY97103] -1.62612 -0.38628
b[(Intercept) expedition_id:CHOY98307] -0.60162 1.32033
b[(Intercept) expedition_id:CHOY99301] 3.21349 4.14416
b[(Intercept) expedition_id:DHA109113] 2.52337 4.19736
b[(Intercept) expedition_id:DHA116106] -2.42782 0.05942
b[(Intercept) expedition_id:DHA183302] -2.35806 0.22906
b[(Intercept) expedition_id:DHA193302] 1.54021 2.99080
b[(Intercept) expedition_id:DHA196104] -2.20450 0.38921
b[(Intercept) expedition_id:DHA197107] -1.94735 0.66353
b[(Intercept) expedition_id:DHA197307] -1.81805 0.73661
b[(Intercept) expedition_id:DHA198107] 1.57332 2.68301
b[(Intercept) expedition_id:DHA198302] -1.85583 0.79508
b[(Intercept) expedition_id:DHAM88301] -1.93024 0.70582
b[(Intercept) expedition_id:DZA215301] 5.62274 8.51937
b[(Intercept) expedition_id:EVER00116] -1.29375 0.26604
b[(Intercept) expedition_id:EVER00148] -1.87023 0.77133
b[(Intercept) expedition_id:EVER01108] -1.25700 0.03744
b[(Intercept) expedition_id:EVER02112] 0.11444 1.94698
b[(Intercept) expedition_id:EVER03124] 0.37369 2.04093
b[(Intercept) expedition_id:EVER03168] -1.82813 -0.43307
b[(Intercept) expedition_id:EVER04150] 0.97591 2.81875
b[(Intercept) expedition_id:EVER04156] -0.00116 1.52459
b[(Intercept) expedition_id:EVER06133] -1.46107 -0.11852
b[(Intercept) expedition_id:EVER06136] -0.59515 0.74203
b[(Intercept) expedition_id:EVER06152] -2.16460 -0.30929
b[(Intercept) expedition_id:EVER06163] -0.48145 0.86137
b[(Intercept) expedition_id:EVER07107] 0.93200 2.81941
b[(Intercept) expedition_id:EVER07148] -1.17001 0.28781
b[(Intercept) expedition_id:EVER07175] -0.22610 1.11899
b[(Intercept) expedition_id:EVER07192] 2.23603 5.83878
b[(Intercept) expedition_id:EVER07194] -5.80114 -3.93296
b[(Intercept) expedition_id:EVER08139] -0.51858 0.33543
b[(Intercept) expedition_id:EVER08152] 0.05550 1.39783
b[(Intercept) expedition_id:EVER08154] 1.04568 2.74937
b[(Intercept) expedition_id:EVER10121] -0.84457 0.80925
b[(Intercept) expedition_id:EVER10136] -1.15700 0.44107
b[(Intercept) expedition_id:EVER10154] -1.71942 -0.81161
b[(Intercept) expedition_id:EVER11103] -0.46131 0.53649
b[(Intercept) expedition_id:EVER11134] 2.99186 6.36882
b[(Intercept) expedition_id:EVER11144] -5.45481 -3.50037
b[(Intercept) expedition_id:EVER11152] 3.11376 6.55527
b[(Intercept) expedition_id:EVER12133] 2.27028 5.94529
b[(Intercept) expedition_id:EVER12141] 1.49195 3.60985
b[(Intercept) expedition_id:EVER14138] -1.74165 0.96990
b[(Intercept) expedition_id:EVER14165] 1.61811 3.68014
b[(Intercept) expedition_id:EVER15117] -3.12642 -0.88116
b[(Intercept) expedition_id:EVER15123] -2.95575 -0.62246
b[(Intercept) expedition_id:EVER16105] -1.29851 -0.37027
b[(Intercept) expedition_id:EVER17123] -1.64254 -0.66254
b[(Intercept) expedition_id:EVER17137] 1.78487 3.72382
b[(Intercept) expedition_id:EVER18118] 1.13325 2.48055
b[(Intercept) expedition_id:EVER18132] 0.52606 2.52797
b[(Intercept) expedition_id:EVER19104] 3.16916 6.42689
b[(Intercept) expedition_id:EVER19112] -6.84926 -5.20830
b[(Intercept) expedition_id:EVER19120] 3.07646 6.36249
b[(Intercept) expedition_id:EVER81101] -4.37135 -1.80506
b[(Intercept) expedition_id:EVER86101] -2.16055 0.36308
b[(Intercept) expedition_id:EVER89304] -2.61683 -0.28986
b[(Intercept) expedition_id:EVER91108] -4.96137 -2.80011
b[(Intercept) expedition_id:EVER96302] -0.31367 1.11112
b[(Intercept) expedition_id:EVER97105] -4.64312 -2.55486
b[(Intercept) expedition_id:EVER98116] -0.92969 0.85268
b[(Intercept) expedition_id:EVER99107] -4.62386 -2.51354
b[(Intercept) expedition_id:EVER99113] -2.14146 -0.68395
b[(Intercept) expedition_id:EVER99116] 0.60054 2.02357
b[(Intercept) expedition_id:FANG97301] -2.24933 0.33341
b[(Intercept) expedition_id:GAN379301] 4.73523 6.24003
b[(Intercept) expedition_id:GAUR83101] -2.38363 0.13411
b[(Intercept) expedition_id:GURK03301] -2.09383 0.53663
b[(Intercept) expedition_id:GYAJ15101] -1.54912 1.23681
b[(Intercept) expedition_id:HIML03302] 1.92032 3.06507
b[(Intercept) expedition_id:HIML08301] 1.67346 2.74487
b[(Intercept) expedition_id:HIML08307] -1.75679 0.91221
b[(Intercept) expedition_id:HIML13303] 4.98342 6.15932
b[(Intercept) expedition_id:HIML13305] -1.78899 0.87577
b[(Intercept) expedition_id:HIML18310] 5.89126 8.59576
b[(Intercept) expedition_id:JANU02401] -2.03564 0.68094
b[(Intercept) expedition_id:JANU89401] -2.22067 0.26902
b[(Intercept) expedition_id:JANU97301] -2.35703 0.11369
b[(Intercept) expedition_id:JANU98102] -1.96793 0.79803
b[(Intercept) expedition_id:JETH78101] 3.03177 4.37319
b[(Intercept) expedition_id:KABD85101] 3.20543 4.36733
b[(Intercept) expedition_id:KAN180101] -1.93108 0.67332
b[(Intercept) expedition_id:KANG81101] -0.64019 0.53604
b[(Intercept) expedition_id:KANG94301] -2.48786 -0.17647
b[(Intercept) expedition_id:KWAN82402] 5.75913 8.36575
b[(Intercept) expedition_id:LANG84101] -2.28659 0.32833
b[(Intercept) expedition_id:LEOE05301] -2.17404 0.40218
b[(Intercept) expedition_id:LHOT09108] 0.47423 2.35159
b[(Intercept) expedition_id:LHOT88301] 0.90947 3.34501
b[(Intercept) expedition_id:LNJU16301] -1.87076 0.77245
b[(Intercept) expedition_id:LSHR90301] 1.49716 2.61088
b[(Intercept) expedition_id:MAKA01104] -2.06227 0.60099
b[(Intercept) expedition_id:MAKA02102] 1.81502 2.92835
b[(Intercept) expedition_id:MAKA02103] 3.96840 5.20634
b[(Intercept) expedition_id:MAKA08112] -5.50998 -3.54058
b[(Intercept) expedition_id:MAKA09108] 0.04397 1.69792
b[(Intercept) expedition_id:MAKA15106] -2.13195 0.29561
b[(Intercept) expedition_id:MAKA90306] -2.32791 0.12128
b[(Intercept) expedition_id:MANA06305] -1.86824 0.97669
b[(Intercept) expedition_id:MANA08324] -5.87554 -4.02942
b[(Intercept) expedition_id:MANA09107] 1.21853 2.69330
b[(Intercept) expedition_id:MANA10319] 2.07413 3.01967
b[(Intercept) expedition_id:MANA11106] 4.05689 5.68540
b[(Intercept) expedition_id:MANA11318] 1.64095 3.67266
b[(Intercept) expedition_id:MANA17333] 4.45821 7.52485
b[(Intercept) expedition_id:MANA18306] 0.49761 1.89373
b[(Intercept) expedition_id:MANA80101] -2.80639 -0.89838
b[(Intercept) expedition_id:MANA82401] -5.49871 -3.43017
b[(Intercept) expedition_id:MANA84101] 6.64794 9.19887
b[(Intercept) expedition_id:MANA91301] -2.20116 0.28774
b[(Intercept) expedition_id:MANA97301] 2.39142 3.24958
b[(Intercept) expedition_id:NAMP79101] -2.30309 0.24799
b[(Intercept) expedition_id:NEMJ83101] -2.72437 -0.39955
b[(Intercept) expedition_id:NILC79101] 3.67073 4.91033
b[(Intercept) expedition_id:NUPT99102] -1.75308 1.03903
b[(Intercept) expedition_id:OHMI89101] 1.11351 2.18579
b[(Intercept) expedition_id:PUMO06301] -2.15880 0.35458
b[(Intercept) expedition_id:PUMO80302] -1.99216 0.58421
b[(Intercept) expedition_id:PUMO92308] 1.02975 2.44220
b[(Intercept) expedition_id:PUMO96101] 2.42213 3.44336
b[(Intercept) expedition_id:PUTH02301] 1.48088 2.58479
b[(Intercept) expedition_id:PUTH97302] -1.86844 0.71155
b[(Intercept) expedition_id:SHAL05301] -1.90362 0.75929
b[(Intercept) expedition_id:SPHN93101] 6.74751 9.20353
b[(Intercept) expedition_id:SYKG12301] 5.41985 7.01032
b[(Intercept) expedition_id:TAWO83101] -2.00321 0.64331
b[(Intercept) expedition_id:TILI04301] -2.16266 0.40081
b[(Intercept) expedition_id:TILI05301] 3.01175 3.87822
b[(Intercept) expedition_id:TILI91302] 1.70879 2.82383
b[(Intercept) expedition_id:TILI92301] -2.43748 0.01766
b[(Intercept) expedition_id:TKPO02102] -2.33704 -0.00470
b[(Intercept) expedition_id:TUKU05101] -1.89147 0.83791
b[(Intercept) expedition_id:TUKU16301] 7.12427 9.64484
Sigma[expedition_id:(Intercept),(Intercept)] 13.02944 16.74825
Fit Diagnostics:
mean sd 10% 50% 90%
mean_PPD 0.38865 0.00797 0.37813 0.38873 0.39884
The mean_ppd is the sample average posterior predictive distribution of the outcome variable (for details see help('summary.stanreg')).
MCMC diagnostics
mcse Rhat n_eff
(Intercept) 0.01101 1.00055 1908
age 0.00011 0.99957 6498
oxygen_usedTRUE 0.01097 1.00036 1961
b[(Intercept) expedition_id:AMAD03107] 0.01553 0.99977 4615
b[(Intercept) expedition_id:AMAD03327] 0.02795 0.99990 4470
b[(Intercept) expedition_id:AMAD05338] 0.01245 1.00005 3564
b[(Intercept) expedition_id:AMAD06110] 0.03355 0.99970 6171
b[(Intercept) expedition_id:AMAD06334] 0.03204 0.99966 5772
b[(Intercept) expedition_id:AMAD07101] 0.03266 0.99990 5759
b[(Intercept) expedition_id:AMAD07310] 0.01254 1.00029 3397
b[(Intercept) expedition_id:AMAD07337] 0.01423 1.00037 4016
b[(Intercept) expedition_id:AMAD07340] 0.01349 0.99992 3811
b[(Intercept) expedition_id:AMAD09331] 0.01471 0.99967 5047
b[(Intercept) expedition_id:AMAD09333] 0.01366 0.99940 5123
b[(Intercept) expedition_id:AMAD11304] 0.01388 0.99970 5684
b[(Intercept) expedition_id:AMAD11321] 0.02591 0.99984 4627
b[(Intercept) expedition_id:AMAD11340] 0.02772 1.00032 4392
b[(Intercept) expedition_id:AMAD12108] 0.01528 0.99958 6214
b[(Intercept) expedition_id:AMAD12342] 0.01564 1.00048 4928
b[(Intercept) expedition_id:AMAD14105] 0.03367 0.99987 5835
b[(Intercept) expedition_id:AMAD14322] 0.01356 0.99964 3118
b[(Intercept) expedition_id:AMAD16354] 0.01399 0.99945 5135
b[(Intercept) expedition_id:AMAD17307] 0.01494 1.00013 4429
b[(Intercept) expedition_id:AMAD81101] 0.01364 1.00035 3820
b[(Intercept) expedition_id:AMAD84401] 0.03392 0.99970 5669
b[(Intercept) expedition_id:AMAD89102] 0.03613 0.99959 4732
b[(Intercept) expedition_id:AMAD93304] 0.01354 0.99997 4923
b[(Intercept) expedition_id:AMAD98311] 0.02641 1.00000 4555
b[(Intercept) expedition_id:AMAD98316] 0.01173 1.00073 3432
b[(Intercept) expedition_id:AMAD98402] 0.01586 0.99943 5563
b[(Intercept) expedition_id:ANN115106] 0.03715 0.99987 4280
b[(Intercept) expedition_id:ANN115108] 0.03240 1.00005 5660
b[(Intercept) expedition_id:ANN179301] 0.03462 0.99944 5120
b[(Intercept) expedition_id:ANN185401] 0.03327 0.99957 5050
b[(Intercept) expedition_id:ANN190101] 0.03342 0.99965 5435
b[(Intercept) expedition_id:ANN193302] 0.03548 1.00021 4797
b[(Intercept) expedition_id:ANN281302] 0.03114 0.99954 5532
b[(Intercept) expedition_id:ANN283302] 0.03240 0.99958 5653
b[(Intercept) expedition_id:ANN378301] 0.03105 1.00055 5284
b[(Intercept) expedition_id:ANN402302] 0.03473 0.99947 5524
b[(Intercept) expedition_id:ANN405301] 0.03370 0.99984 6280
b[(Intercept) expedition_id:ANN409201] 0.02797 1.00059 4268
b[(Intercept) expedition_id:ANN416101] 0.03433 0.99958 5933
b[(Intercept) expedition_id:BARU01304] 0.03776 1.00072 4611
b[(Intercept) expedition_id:BARU02101] 0.03332 1.00013 5090
b[(Intercept) expedition_id:BARU02303] 0.01373 0.99970 5178
b[(Intercept) expedition_id:BARU09102] 0.03184 0.99999 5986
b[(Intercept) expedition_id:BARU10312] 0.03410 0.99997 4914
b[(Intercept) expedition_id:BARU11303] 0.01285 1.00065 2963
b[(Intercept) expedition_id:BARU92301] 0.01280 1.00046 3705
b[(Intercept) expedition_id:BARU94301] 0.03242 1.00070 5821
b[(Intercept) expedition_id:BARU94307] 0.03561 0.99979 4721
b[(Intercept) expedition_id:BHRI86101] 0.03266 0.99963 5193
b[(Intercept) expedition_id:CHAM18101] 0.03496 0.99950 5412
b[(Intercept) expedition_id:CHAM91301] 0.01272 1.00000 3456
b[(Intercept) expedition_id:CHOY02117] 0.01502 1.00018 4587
b[(Intercept) expedition_id:CHOY03103] 0.02031 1.00115 3912
b[(Intercept) expedition_id:CHOY03318] 0.01425 1.00081 2464
b[(Intercept) expedition_id:CHOY04122] 0.01331 0.99974 4703
b[(Intercept) expedition_id:CHOY04302] 0.01632 1.00040 4641
b[(Intercept) expedition_id:CHOY06330] 0.01424 1.00012 4864
b[(Intercept) expedition_id:CHOY07310] 0.01302 1.00009 4891
b[(Intercept) expedition_id:CHOY07330] 0.03297 0.99974 5620
b[(Intercept) expedition_id:CHOY07356] 0.03442 0.99975 5126
b[(Intercept) expedition_id:CHOY07358] 0.01227 0.99976 4451
b[(Intercept) expedition_id:CHOY10328] 0.02780 0.99971 6114
b[(Intercept) expedition_id:CHOY10341] 0.03399 0.99990 5880
b[(Intercept) expedition_id:CHOY93304] 0.03519 0.99993 4963
b[(Intercept) expedition_id:CHOY96319] 0.01411 1.00011 3619
b[(Intercept) expedition_id:CHOY97103] 0.01523 1.00075 3818
b[(Intercept) expedition_id:CHOY98307] 0.01960 0.99970 6847
b[(Intercept) expedition_id:CHOY99301] 0.01227 1.00005 3510
b[(Intercept) expedition_id:DHA109113] 0.01653 0.99965 7101
b[(Intercept) expedition_id:DHA116106] 0.03204 0.99995 5707
b[(Intercept) expedition_id:DHA183302] 0.03423 0.99996 5181
b[(Intercept) expedition_id:DHA193302] 0.01863 0.99957 5139
b[(Intercept) expedition_id:DHA196104] 0.03612 1.00009 4690
b[(Intercept) expedition_id:DHA197107] 0.03334 0.99952 5683
b[(Intercept) expedition_id:DHA197307] 0.03692 1.00056 4700
b[(Intercept) expedition_id:DHA198107] 0.01539 0.99975 3884
b[(Intercept) expedition_id:DHA198302] 0.03291 0.99975 5702
b[(Intercept) expedition_id:DHAM88301] 0.03194 0.99997 6218
b[(Intercept) expedition_id:DZA215301] 0.03023 1.00004 4007
b[(Intercept) expedition_id:EVER00116] 0.01623 0.99966 4964
b[(Intercept) expedition_id:EVER00148] 0.03739 0.99926 4949
b[(Intercept) expedition_id:EVER01108] 0.01530 1.00060 3925
b[(Intercept) expedition_id:EVER02112] 0.01733 0.99968 6479
b[(Intercept) expedition_id:EVER03124] 0.01550 1.00016 6609
b[(Intercept) expedition_id:EVER03168] 0.01759 1.00125 3375
b[(Intercept) expedition_id:EVER04150] 0.01781 1.00032 6022
b[(Intercept) expedition_id:EVER04156] 0.01531 0.99960 6198
b[(Intercept) expedition_id:EVER06133] 0.01686 0.99982 3377
b[(Intercept) expedition_id:EVER06136] 0.01699 1.00072 3198
b[(Intercept) expedition_id:EVER06152] 0.01869 1.00014 6069
b[(Intercept) expedition_id:EVER06163] 0.01452 1.00042 4707
b[(Intercept) expedition_id:EVER07107] 0.01507 0.99986 8542
b[(Intercept) expedition_id:EVER07148] 0.01718 0.99955 3937
b[(Intercept) expedition_id:EVER07175] 0.01521 1.00126 4559
b[(Intercept) expedition_id:EVER07192] 0.03324 1.00005 5460
b[(Intercept) expedition_id:EVER07194] 0.02668 1.00017 4797
b[(Intercept) expedition_id:EVER08139] 0.01443 1.00122 2073
b[(Intercept) expedition_id:EVER08152] 0.01549 1.00100 3965
b[(Intercept) expedition_id:EVER08154] 0.01544 0.99961 6677
b[(Intercept) expedition_id:EVER10121] 0.01640 0.99959 5588
b[(Intercept) expedition_id:EVER10136] 0.01591 0.99970 5749
b[(Intercept) expedition_id:EVER10154] 0.01531 1.00187 2106
b[(Intercept) expedition_id:EVER11103] 0.01440 1.00101 2720
b[(Intercept) expedition_id:EVER11134] 0.03300 0.99974 4584
b[(Intercept) expedition_id:EVER11144] 0.03000 0.99999 4030
b[(Intercept) expedition_id:EVER11152] 0.03132 1.00010 5168
b[(Intercept) expedition_id:EVER12133] 0.03077 0.99974 6306
b[(Intercept) expedition_id:EVER12141] 0.01794 0.99965 7545
b[(Intercept) expedition_id:EVER14138] 0.03414 0.99949 5664
b[(Intercept) expedition_id:EVER14165] 0.01916 1.00010 6284
b[(Intercept) expedition_id:EVER15117] 0.03293 0.99978 4607
b[(Intercept) expedition_id:EVER15123] 0.03072 0.99968 5539
b[(Intercept) expedition_id:EVER16105] 0.01477 1.00167 2384
b[(Intercept) expedition_id:EVER17123] 0.01468 1.00161 2641
b[(Intercept) expedition_id:EVER17137] 0.01812 0.99974 6067
b[(Intercept) expedition_id:EVER18118] 0.01444 0.99956 5183
b[(Intercept) expedition_id:EVER18132] 0.01747 0.99966 7399
b[(Intercept) expedition_id:EVER19104] 0.03196 0.99936 4813
b[(Intercept) expedition_id:EVER19112] 0.02679 1.00049 3985
b[(Intercept) expedition_id:EVER19120] 0.03149 1.00018 4866
b[(Intercept) expedition_id:EVER81101] 0.02739 0.99946 6733
b[(Intercept) expedition_id:EVER86101] 0.03296 1.00041 5599
b[(Intercept) expedition_id:EVER89304] 0.03315 0.99953 4820
b[(Intercept) expedition_id:EVER91108] 0.02598 0.99982 6212
b[(Intercept) expedition_id:EVER96302] 0.01580 1.00003 5081
b[(Intercept) expedition_id:EVER97105] 0.02878 1.00064 4859
b[(Intercept) expedition_id:EVER98116] 0.01995 1.00027 4276
b[(Intercept) expedition_id:EVER99107] 0.02666 0.99938 5727
b[(Intercept) expedition_id:EVER99113] 0.01634 1.00026 4379
b[(Intercept) expedition_id:EVER99116] 0.01349 0.99951 6209
b[(Intercept) expedition_id:FANG97301] 0.03495 0.99984 5096
b[(Intercept) expedition_id:GAN379301] 0.01522 1.00046 4950
b[(Intercept) expedition_id:GAUR83101] 0.03340 0.99989 5359
b[(Intercept) expedition_id:GURK03301] 0.03371 1.00106 5453
b[(Intercept) expedition_id:GYAJ15101] 0.03394 0.99995 6045
b[(Intercept) expedition_id:HIML03302] 0.01479 0.99990 4472
b[(Intercept) expedition_id:HIML08301] 0.01487 0.99984 3849
b[(Intercept) expedition_id:HIML08307] 0.03400 0.99943 5524
b[(Intercept) expedition_id:HIML13303] 0.01398 1.00030 4088
b[(Intercept) expedition_id:HIML13305] 0.03334 0.99977 5723
b[(Intercept) expedition_id:HIML18310] 0.02631 0.99956 4768
b[(Intercept) expedition_id:JANU02401] 0.03297 0.99974 5885
b[(Intercept) expedition_id:JANU89401] 0.03119 0.99963 5906
b[(Intercept) expedition_id:JANU97301] 0.03033 0.99942 5998
b[(Intercept) expedition_id:JANU98102] 0.03345 0.99996 6075
b[(Intercept) expedition_id:JETH78101] 0.01348 0.99957 5883
b[(Intercept) expedition_id:KABD85101] 0.01395 0.99979 4071
b[(Intercept) expedition_id:KAN180101] 0.03107 0.99949 6250
b[(Intercept) expedition_id:KANG81101] 0.01342 1.00010 5033
b[(Intercept) expedition_id:KANG94301] 0.03487 1.00050 4313
b[(Intercept) expedition_id:KWAN82402] 0.02656 0.99969 4753
b[(Intercept) expedition_id:LANG84101] 0.03498 0.99966 4938
b[(Intercept) expedition_id:LEOE05301] 0.03143 0.99950 5923
b[(Intercept) expedition_id:LHOT09108] 0.01677 0.99992 7098
b[(Intercept) expedition_id:LHOT88301] 0.02034 0.99964 7931
b[(Intercept) expedition_id:LNJU16301] 0.03745 0.99973 4628
b[(Intercept) expedition_id:LSHR90301] 0.01488 1.00047 4029
b[(Intercept) expedition_id:MAKA01104] 0.03434 0.99973 5521
b[(Intercept) expedition_id:MAKA02102] 0.01406 1.00053 4239
b[(Intercept) expedition_id:MAKA02103] 0.01377 0.99961 4634
b[(Intercept) expedition_id:MAKA08112] 0.03095 1.00138 4099
b[(Intercept) expedition_id:MAKA09108] 0.01549 0.99981 6794
b[(Intercept) expedition_id:MAKA15106] 0.03229 1.00030 5352
b[(Intercept) expedition_id:MAKA90306] 0.03342 1.00052 5303
b[(Intercept) expedition_id:MANA06305] 0.03702 1.00029 5167
b[(Intercept) expedition_id:MANA08324] 0.02692 1.00041 4624
b[(Intercept) expedition_id:MANA09107] 0.02068 1.00055 4406
b[(Intercept) expedition_id:MANA10319] 0.01238 0.99973 3758
b[(Intercept) expedition_id:MANA11106] 0.01569 0.99964 5613
b[(Intercept) expedition_id:MANA11318] 0.01837 0.99949 6687
b[(Intercept) expedition_id:MANA17333] 0.02943 0.99986 5462
b[(Intercept) expedition_id:MANA18306] 0.01617 1.00065 3989
b[(Intercept) expedition_id:MANA80101] 0.01770 0.99999 7067
b[(Intercept) expedition_id:MANA82401] 0.02737 0.99976 5121
b[(Intercept) expedition_id:MANA84101] 0.02544 1.00071 4649
b[(Intercept) expedition_id:MANA91301] 0.03511 1.00026 5033
b[(Intercept) expedition_id:MANA97301] 0.01340 1.00028 2846
b[(Intercept) expedition_id:NAMP79101] 0.03329 0.99998 5143
b[(Intercept) expedition_id:NEMJ83101] 0.03165 0.99955 5470
b[(Intercept) expedition_id:NILC79101] 0.01345 0.99987 4776
b[(Intercept) expedition_id:NUPT99102] 0.03415 0.99941 5856
b[(Intercept) expedition_id:OHMI89101] 0.01699 1.00044 3075
b[(Intercept) expedition_id:PUMO06301] 0.03225 0.99987 5531
b[(Intercept) expedition_id:PUMO80302] 0.03567 1.00085 5006
b[(Intercept) expedition_id:PUMO92308] 0.01801 0.99948 4940
b[(Intercept) expedition_id:PUMO96101] 0.01325 1.00005 4126
b[(Intercept) expedition_id:PUTH02301] 0.01572 0.99981 3626
b[(Intercept) expedition_id:PUTH97302] 0.03213 0.99979 5902
b[(Intercept) expedition_id:SHAL05301] 0.03207 0.99950 6017
b[(Intercept) expedition_id:SPHN93101] 0.02526 0.99962 4375
b[(Intercept) expedition_id:SYKG12301] 0.01595 0.99974 5351
b[(Intercept) expedition_id:TAWO83101] 0.03326 0.99950 5698
b[(Intercept) expedition_id:TILI04301] 0.03343 1.00040 5317
b[(Intercept) expedition_id:TILI05301] 0.01209 1.00100 3087
b[(Intercept) expedition_id:TILI91302] 0.01501 0.99998 4082
b[(Intercept) expedition_id:TILI92301] 0.03477 0.99964 4833
b[(Intercept) expedition_id:TKPO02102] 0.03457 1.00096 4659
b[(Intercept) expedition_id:TUKU05101] 0.03283 0.99966 5958
b[(Intercept) expedition_id:TUKU16301] 0.02600 0.99998 4230
Sigma[expedition_id:(Intercept),(Intercept)] 0.07588 1.00129 1168
mean_PPD 0.00011 0.99984 4955
log-posterior 0.47469 1.00402 822
For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
#plot(climb_stan_glm1, "trace") #plot(climb_stan_glm1, "hist")
Now we can conduct our posterior predictive check. Does the model seem to represent our data well?
# Define success rate function <- function (x){mean (x == 1 )}# Posterior predictive check pp_check (climb_stan_glm1, plotfun = "stat" , stat = "success_rate" ) + xlab ("success rate" )
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
