library(broom) # for tidy output
library(knitr) # for kable
library(effects) # for partial effects plots
library(emmeans) # for estimating marginal means
library(MASS) # for glm.nb
library(tidyverse) # for data wrangling
library(brms)
library(tidybayes)
library(bayesplot)
library(broom.mixed)
library(rstan)
library(patchwork)
library(modelsummary)
library(DHARMa)
source("helperFunctions.R")Bayesian GLMM Part10
1 Preparations
Load the necessary libraries
2 Original data
3 Data processing
- Make a categorical version of Year
- Combine Scores 4 and 5 into a single Score of 4 to be consistent across years
- Make Score an ordered categorical variable
- Generate a numeric version of categorical Score (as required for the
ocatfamily. Note this must be a 1 indexed numeric. - Relevel Sector such that it is in the order North, Central, South
- Ensure that there is a categorical version of Reef
- Generate a numeric version of the categorical Reef
coral_fams <- ltmp |>
filter(HC > 0) |>
pull(FAMILY_2021) |>
unique()
ltmp <- ltmp |>
filter(FAMILY_2021 %in% coral_fams) |>
dplyr::rename(P_CODE = P_CODE.y) |>
distinct() |>
group_by(P_CODE, AIMS_REEF_NAME, REPORT_YEAR, SITE_NO, TRANSECT_NO) |>
summarise(
HC = sum(HC, na.rm = TRUE),
n.points = sum(n.points),
total.points = unique(total.points)
) |>
ungroup() |>
dplyr::select(AIMS_REEF_NAME, REPORT_YEAR, SITE_NO, TRANSECT_NO, HC, n.points, total.points) |>
filter(!is.na(AIMS_REEF_NAME)) |>
droplevels()
write_csv(ltmp, file = "../data/ltmp.csv")
rm("ltmp")
gc()4 Scenario
For over 35 years, the AIMS long term monitoring program has performed benthic surveys of coral reefs on the Great Barrier Reef (GBR). To do so the team uses two main survey techniques 1) Manta Tow and 2) Photo transects. The current example focuses on data collected using the later technique. Within each reef, there are three sites on the north east flank and within each site there are five permanent transects. Every year, the team return and take photos every meter along the transects. Once back in the laboratory, five points from every photo are scored according to what is represented underneath the point.
The main objective of long-term monitoring is to be able to report on status and trends. Specifically, what is the status of each major benthic group (such as hard coral, soft coral and macroalgae) and how are they changing (particularly in response to major disturbances).
For this example, we will focus on a single reef (Agincourt Reef No.1).
5 Read in the data
Rows: 22125 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (1): AIMS_REEF_NAME
dbl (6): REPORT_YEAR, SITE_NO, TRANSECT_NO, HC, n.points, total.points
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Rows: 22,125
Columns: 7
$ AIMS_REEF_NAME <chr> "Arlington Reef", "Arlington Reef", "Arlington Reef", "…
$ REPORT_YEAR <dbl> 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2…
$ SITE_NO <dbl> 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1…
$ TRANSECT_NO <dbl> 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4…
$ HC <dbl> 10.00000, 10.50000, 10.50000, 8.50000, 25.00000, 19.000…
$ n.points <dbl> 20, 21, 21, 17, 50, 38, 43, 28, 30, 40, 55, 35, 32, 40,…
$ total.points <dbl> 200, 200, 200, 200, 200, 200, 200, 200, 196, 200, 200, …| AIMS_REEF_NAME | REPORT_YEAR | SITE_NO | TRANSECT_NO | HC | n.points | total.points |
|---|---|---|---|---|---|---|
| Arlington Reef | 2006 | 1 | 1 | 10.0 | 20 | 200 |
| Arlington Reef | 2006 | 1 | 2 | 10.5 | 21 | 200 |
Rows: 22,125
Columns: 7
$ AIMS_REEF_NAME <chr> "Arlington Reef", "Arlington Reef", "Arlington Reef", "…
$ REPORT_YEAR <dbl> 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2006, 2…
$ SITE_NO <dbl> 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1…
$ TRANSECT_NO <dbl> 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4…
$ HC <dbl> 10.00000, 10.50000, 10.50000, 8.50000, 25.00000, 19.000…
$ n.points <dbl> 20, 21, 21, 17, 50, 38, 43, 28, 30, 40, 55, 35, 32, 40,…
$ total.points <dbl> 200, 200, 200, 200, 200, 200, 200, 200, 196, 200, 200, …# A tibble: 6 × 7
AIMS_REEF_NAME REPORT_YEAR SITE_NO TRANSECT_NO HC n.points total.points
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Arlington Reef 2006 1 1 10 20 200
2 Arlington Reef 2006 1 2 10.5 21 200
3 Arlington Reef 2006 1 3 10.5 21 200
4 Arlington Reef 2006 1 4 8.5 17 200
5 Arlington Reef 2006 1 5 25 50 200
6 Arlington Reef 2006 2 1 19 38 200spc_tbl_ [22,125 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
$ AIMS_REEF_NAME: chr [1:22125] "Arlington Reef" "Arlington Reef" "Arlington Reef" "Arlington Reef" ...
$ REPORT_YEAR : num [1:22125] 2006 2006 2006 2006 2006 ...
$ SITE_NO : num [1:22125] 1 1 1 1 1 2 2 2 2 2 ...
$ TRANSECT_NO : num [1:22125] 1 2 3 4 5 1 2 3 4 5 ...
$ HC : num [1:22125] 10 10.5 10.5 8.5 25 ...
$ n.points : num [1:22125] 20 21 21 17 50 38 43 28 30 40 ...
$ total.points : num [1:22125] 200 200 200 200 200 200 200 200 196 200 ...
- attr(*, "spec")=
.. cols(
.. AIMS_REEF_NAME = col_character(),
.. REPORT_YEAR = col_double(),
.. SITE_NO = col_double(),
.. TRANSECT_NO = col_double(),
.. HC = col_double(),
.. n.points = col_double(),
.. total.points = col_double()
.. )
- attr(*, "problems")=<externalptr> ltmp (22125 rows and 7 variables, 7 shown)
ID | Name | Type | Missings | Values | N
---+----------------+-----------+----------+------------------------+-------------
1 | AIMS_REEF_NAME | character | 0 (0.0%) | Agincourt Reef No.1 | 418 ( 1.9%)
| | | | Arlington Reef | 135 ( 0.6%)
| | | | Border Island | 315 ( 1.4%)
| | | | Boult Reef | 120 ( 0.5%)
| | | | Broomfield Reef | 435 ( 2.0%)
| | | | Carter Reef | 315 ( 1.4%)
| | | | Centipede Reef | 105 ( 0.5%)
| | | | Chicken Reef | 420 ( 1.9%)
| | | | Chinaman Reef (22-102) | 419 ( 1.9%)
| | | | Corbett Reef | 75 ( 0.3%)
| | | | (...) |
---+----------------+-----------+----------+------------------------+-------------
2 | REPORT_YEAR | numeric | 0 (0.0%) | [1995, 2023] | 22125
---+----------------+-----------+----------+------------------------+-------------
3 | SITE_NO | numeric | 0 (0.0%) | 1 | 7378 (33.3%)
| | | | 2 | 7374 (33.3%)
| | | | 3 | 7373 (33.3%)
---+----------------+-----------+----------+------------------------+-------------
4 | TRANSECT_NO | numeric | 0 (0.0%) | 1 | 4421 (20.0%)
| | | | 2 | 4427 (20.0%)
| | | | 3 | 4426 (20.0%)
| | | | 4 | 4427 (20.0%)
| | | | 5 | 4424 (20.0%)
---+----------------+-----------+----------+------------------------+-------------
5 | HC | numeric | 0 (0.0%) | [0, 93.97] | 22125
---+----------------+-----------+----------+------------------------+-------------
6 | n.points | numeric | 0 (0.0%) | [0, 239] | 22125
---+----------------+-----------+----------+------------------------+-------------
7 | total.points | numeric | 0 (0.0%) | [45, 458] | 22125
----------------------------------------------------------------------------------| SITE_NO | Unique | Missing Pct. | Mean | SD | Min | Median | Max | Histogram | |
|---|---|---|---|---|---|---|---|---|---|
| REPORT_YEAR | 1.0 | 29 | 0 | 2009.8 | 8.5 | 1995.0 | 2010.0 | 2023.0 |  |
| 2.0 | 29 | 0 | 2009.8 | 8.5 | 1995.0 | 2010.0 | 2023.0 |  |
|
| 3.0 | 29 | 0 | 2009.8 | 8.5 | 1995.0 | 2010.0 | 2023.0 |  |
|
| TRANSECT_NO | 1.0 | 5 | 0 | 3.0 | 1.4 | 1.0 | 3.0 | 5.0 |  |
| 2.0 | 5 | 0 | 3.0 | 1.4 | 1.0 | 3.0 | 5.0 |  |
|
| 3.0 | 5 | 0 | 3.0 | 1.4 | 1.0 | 3.0 | 5.0 | |
|
| HC | 1.0 | 1762 | 0 | 26.2 | 18.0 | 0.0 | 22.5 | 92.5 |  |
| 2.0 | 1686 | 0 | 25.2 | 17.0 | 0.0 | 22.0 | 94.0 |  |
|
| 3.0 | 1633 | 0 | 25.1 | 16.7 | 0.0 | 22.7 | 92.0 |  |
|
| n.points | 1.0 | 178 | 0 | 51.9 | 35.9 | 0.0 | 44.0 | 185.0 |  |
| 2.0 | 180 | 0 | 50.1 | 34.0 | 0.0 | 44.0 | 202.0 |  |
|
| 3.0 | 177 | 0 | 49.8 | 33.4 | 0.0 | 45.0 | 239.0 |  |
|
| total.points | 1.0 | 125 | 0 | 198.6 | 12.1 | 65.0 | 200.0 | 395.0 |  |
| 2.0 | 129 | 0 | 198.6 | 12.3 | 115.0 | 200.0 | 410.0 |  |
|
| 3.0 | 116 | 0 | 198.1 | 13.0 | 45.0 | 200.0 | 458.0 |  |
6 Data preparation
- restrict to a single reef (Agincourt Reef No.1)
- declare categorical variables as factors (this includes REPORT_YEAR)
- declare random effects as factors
- create unit names for sites and transects
7 Exploratory Data Analysis
ltmp_sub |>
ggplot(aes(y = HC, x = REPORT_YEAR)) +
geom_line(aes(group = REEF_SITE_TRANSECT, colour = REEF_SITE), alpha = 1) +
geom_point()
give.n <- function(val, ypos) {
return(data.frame(y = ypos, label = round(mean(val), 1)))
}
ltmp_sub |>
ggplot(aes(y = HC, x = factor(REPORT_YEAR))) +
geom_violin(fill = "orange") +
geom_line(aes(group = REEF_SITE_TRANSECT), alpha = 0.2) +
geom_point() +
stat_summary(
geom = "text",
aes(y = total.points, ymax = HC),
fun.data = give.n,
fun.args = list(ypos = 0)
)Warning in stat_summary(geom = "text", aes(y = total.points, ymax = HC), :
Ignoring unknown aesthetics: ymax
Based on this, it might be better to use the most recent year as the reference…
8 Fit the model
In brms, the default priors are designed to be weakly informative. They are chosen to provide moderate regularisation (to help prevent over fitting) and help stabilise the computations.
Unlike rstanarm, brms models must be compiled before they start sampling. For most models, the compilation of the stan code takes around 45 seconds.
ltmp_sub.form <- bf(
n.points | trials(total.points) ~ fREPORT_YEAR +
(1 | REEF_SITE) + (1 | REEF_SITE_TRANSECT),
family = binomial(link = "logit")
)
options(width=150)
ltmp_sub.form %>% get_prior(data = ltmp_sub) prior class coef group resp dpar nlpar lb ub source
(flat) b default
(flat) b fREPORT_YEAR1995 (vectorized)
(flat) b fREPORT_YEAR1996 (vectorized)
(flat) b fREPORT_YEAR1997 (vectorized)
(flat) b fREPORT_YEAR1998 (vectorized)
(flat) b fREPORT_YEAR1999 (vectorized)
(flat) b fREPORT_YEAR2000 (vectorized)
(flat) b fREPORT_YEAR2001 (vectorized)
(flat) b fREPORT_YEAR2002 (vectorized)
(flat) b fREPORT_YEAR2003 (vectorized)
(flat) b fREPORT_YEAR2004 (vectorized)
(flat) b fREPORT_YEAR2005 (vectorized)
(flat) b fREPORT_YEAR2006 (vectorized)
(flat) b fREPORT_YEAR2007 (vectorized)
(flat) b fREPORT_YEAR2008 (vectorized)
(flat) b fREPORT_YEAR2009 (vectorized)
(flat) b fREPORT_YEAR2010 (vectorized)
(flat) b fREPORT_YEAR2011 (vectorized)
(flat) b fREPORT_YEAR2012 (vectorized)
(flat) b fREPORT_YEAR2013 (vectorized)
(flat) b fREPORT_YEAR2014 (vectorized)
(flat) b fREPORT_YEAR2015 (vectorized)
(flat) b fREPORT_YEAR2016 (vectorized)
(flat) b fREPORT_YEAR2017 (vectorized)
(flat) b fREPORT_YEAR2018 (vectorized)
(flat) b fREPORT_YEAR2019 (vectorized)
(flat) b fREPORT_YEAR2020 (vectorized)
(flat) b fREPORT_YEAR2021 (vectorized)
student_t(3, 0, 2.5) Intercept default
student_t(3, 0, 2.5) sd 0 default
student_t(3, 0, 2.5) sd REEF_SITE 0 (vectorized)
student_t(3, 0, 2.5) sd Intercept REEF_SITE 0 (vectorized)
student_t(3, 0, 2.5) sd REEF_SITE_TRANSECT 0 (vectorized)
student_t(3, 0, 2.5) sd Intercept REEF_SITE_TRANSECT 0 (vectorized)The following link provides some guidance about defining priors. [https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations]
When defining our own priors, we typically do not want them to be scaled.
If we wanted to define our own priors that were less vague, yet still not likely to bias the outcomes, we could try the following priors (mainly plucked out of thin air):
- \(\beta_0\): normal centred at 84 with a standard deviation of 5.9
- mean of 84: since
median(starling$MASS) - sd of 5.9: since
mad(starling$MASS)
- mean of 84: since
- \(\beta_1\): normal centred at 0 with a standard deviation of 13
- sd of 13: since
sd(starling$MASS) / apply(model.matrix(~MONTH*SITUATION, starling)[, -1], 2, sd)
- sd of 13: since
- \(\beta_{2-4}\): normal centred at 0 with a standard deviation of 15
- sd of 15: since
sd(starling$MASS) / apply(model.matrix(~MONTH*SITUATION, starling)[, -1], 2, sd)
- sd of 15: since
- \(\beta_{5-7}\): normal centred at 0 with a standard deviation of 20
- sd of 20: since
sd(starling$MASS) / apply(model.matrix(~MONTH*SITUATION, starling)[, -1], 2, sd)
- sd of 20: since
- \(\sigma\): gamma with shape parameters 6.5 and 1
- 6.5: since
sd(starling$MASS)
- 6.5: since
- \(\sigma_j\): half-cauchy with parameters 0 and 2.5.
- 2.: since
sqrt(sd(starling$MASS))
- 2.: since
- \(\Sigma\): decov with:
- regularisation: the exponent for a LKJ prior on the correlation matrix. A value of 1 (default) implies a joint uniform prior
- concentration: the concentration parameter for a symmetric Dirichlet distribution. A value of 1 (default) implies a joint uniform distribution
- shape and scale: the shape and scale parameters for a gamma prior on the scale and scale parameters of the decov prior. A value of 1 for both (default) simplifies the gamma prior to a unit-exponential distribution.
Note, for hierarchical models, the model will tend to want to have a large \(sigma\) in order to fit the data better. It is a good idea to regularise this tendency by applying a prior that has most mass around zero. Suitable candidates include:
- half-t: as the degrees of freedom approach infinity, this will approach a half-normal
- half-cauchy: this is essentially a half-t with 1 degree of freedom
- exponential
I will also overlay the raw data for comparison.
ltmp_sub |>
group_by(fREPORT_YEAR) |>
summarise(
Median = median(qlogis(n.points / total.points)),
MAD = mad(qlogis(n.points / total.points)),
N = mean(total.points)
)# A tibble: 28 × 4
fREPORT_YEAR Median MAD N
<fct> <dbl> <dbl> <dbl>
1 2023 -0.758 0.303 202.
2 2021 -1.19 0.284 201.
3 2020 -1.30 0.291 201.
4 2019 -1.63 0.236 201.
5 2018 -1.99 0.263 200
6 2017 -2.09 0.242 200
7 2016 -1.15 0.246 200.
8 2015 -1.42 0.352 200
9 2014 -1.66 0.295 200
10 2013 -1.90 0.360 200
# ℹ 18 more rowspriors <- prior(normal(-0.7, 0.3), class = "Intercept") +
prior(normal(0, 2), class = "b") +
prior(student_t(3, 0, 0.5), class = "sd")
ltmp_sub.form <- bf(
n.points | trials(total.points) ~ fREPORT_YEAR +
(1 | REEF_SITE) + (1 | REEF_SITE_TRANSECT),
family = binomial(link = "logit")
)
ltmp_sub.brm2 <- brm(ltmp_sub.form,
data = ltmp_sub,
prior = priors,
sample_prior = "only",
iter = 10000,
warmup = 5000,
chains = 3, cores = 3,
thin = 10,
refresh = 0,
control = list(adapt_delta = 0.99, max_treedepth = 20),
backend = "rstan"
)Compiling Stan program...Start samplingSetting all 'trials' variables to 1 by default if not specified otherwise.
ltmp_sub.brm2 |>
conditional_effects(conditions = data.frame(total.points = 200)) |>
plot(points = TRUE)
The above seem sufficiently wide whilst at the same time not providing any encouragement for the sampler to wander off into very unsupported areas.
The following takes approx 500 seconds
ltmp_sub.brm3 <- update(ltmp_sub.brm2,
sample_prior = "yes",
chains = 3, cores = 3,
control = list(adapt_delta = 0.99, max_treedepth = 20),
thin = 10, iter = 10000, warmup = 5000,
refresh = 100
)The desired updates require recompiling the modelCompiling Stan program...Start samplingWarning: There were 3 divergent transitions after warmup. See
https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
to find out why this is a problem and how to eliminate them.Warning: Examine the pairs() plot to diagnose sampling problems
[1] "b_Intercept"
[2] "b_fREPORT_YEAR2021"
[3] "b_fREPORT_YEAR2020"
[4] "b_fREPORT_YEAR2019"
[5] "b_fREPORT_YEAR2018"
[6] "b_fREPORT_YEAR2017"
[7] "b_fREPORT_YEAR2016"
[8] "b_fREPORT_YEAR2015"
[9] "b_fREPORT_YEAR2014"
[10] "b_fREPORT_YEAR2013"
[11] "b_fREPORT_YEAR2012"
[12] "b_fREPORT_YEAR2011"
[13] "b_fREPORT_YEAR2010"
[14] "b_fREPORT_YEAR2009"
[15] "b_fREPORT_YEAR2008"
[16] "b_fREPORT_YEAR2007"
[17] "b_fREPORT_YEAR2006"
[18] "b_fREPORT_YEAR2005"
[19] "b_fREPORT_YEAR2004"
[20] "b_fREPORT_YEAR2003"
[21] "b_fREPORT_YEAR2002"
[22] "b_fREPORT_YEAR2001"
[23] "b_fREPORT_YEAR2000"
[24] "b_fREPORT_YEAR1999"
[25] "b_fREPORT_YEAR1998"
[26] "b_fREPORT_YEAR1997"
[27] "b_fREPORT_YEAR1996"
[28] "b_fREPORT_YEAR1995"
[29] "sd_REEF_SITE__Intercept"
[30] "sd_REEF_SITE_TRANSECT__Intercept"
[31] "Intercept"
[32] "r_REEF_SITE[Agincourt.Reef.No.1.1,Intercept]"
[33] "r_REEF_SITE[Agincourt.Reef.No.1.2,Intercept]"
[34] "r_REEF_SITE[Agincourt.Reef.No.1.3,Intercept]"
[35] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.1.1,Intercept]"
[36] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.1.2,Intercept]"
[37] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.1.3,Intercept]"
[38] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.1.4,Intercept]"
[39] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.1.5,Intercept]"
[40] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.2.1,Intercept]"
[41] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.2.2,Intercept]"
[42] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.2.3,Intercept]"
[43] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.2.4,Intercept]"
[44] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.2.5,Intercept]"
[45] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.3.1,Intercept]"
[46] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.3.2,Intercept]"
[47] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.3.3,Intercept]"
[48] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.3.4,Intercept]"
[49] "r_REEF_SITE_TRANSECT[Agincourt.Reef.No.1.3.5,Intercept]"
[50] "prior_Intercept"
[51] "prior_b"
[52] "prior_sd_REEF_SITE"
[53] "prior_sd_REEF_SITE_TRANSECT"
[54] "lprior"
[55] "lp__"
[56] "accept_stat__"
[57] "stepsize__"
[58] "treedepth__"
[59] "n_leapfrog__"
[60] "divergent__"
[61] "energy__" 
9 MCMC sampling diagnostics
The bayesplot package offers a range of MCMC diagnostics as well as Posterior Probability Checks (PPC), all of which have a convenient plot() interface. Lets start with the MCMC diagnostics.
See list of available diagnostics by name
bayesplot MCMC module:
mcmc_acf
mcmc_acf_bar
mcmc_areas
mcmc_areas_ridges
mcmc_combo
mcmc_dens
mcmc_dens_chains
mcmc_dens_overlay
mcmc_hex
mcmc_hist
mcmc_hist_by_chain
mcmc_intervals
mcmc_neff
mcmc_neff_hist
mcmc_nuts_acceptance
mcmc_nuts_divergence
mcmc_nuts_energy
mcmc_nuts_stepsize
mcmc_nuts_treedepth
mcmc_pairs
mcmc_parcoord
mcmc_rank_ecdf
mcmc_rank_hist
mcmc_rank_overlay
mcmc_recover_hist
mcmc_recover_intervals
mcmc_recover_scatter
mcmc_rhat
mcmc_rhat_hist
mcmc_scatter
mcmc_trace
mcmc_trace_highlight
mcmc_violinOf these, we will focus on:
- trace: this plots the estimates of each parameter over the post-warmup length of each MCMC chain. Each chain is plotted in a different shade of blue, with each parameter in its own facet. Ideally, each trace should just look like noise without any discernible drift and each of the traces for a specific parameter should look the same (i.e, should not be displaced above or below any other trace for that parameter).
[1] "b_Intercept" "b_fREPORT_YEAR2021"
[3] "b_fREPORT_YEAR2020" "b_fREPORT_YEAR2019"
[5] "b_fREPORT_YEAR2018" "b_fREPORT_YEAR2017"
[7] "b_fREPORT_YEAR2016" "b_fREPORT_YEAR2015"
[9] "b_fREPORT_YEAR2014" "b_fREPORT_YEAR2013"
[11] "b_fREPORT_YEAR2012" "b_fREPORT_YEAR2011"
[13] "b_fREPORT_YEAR2010" "b_fREPORT_YEAR2009"
[15] "b_fREPORT_YEAR2008" "b_fREPORT_YEAR2007"
[17] "b_fREPORT_YEAR2006" "b_fREPORT_YEAR2005"
[19] "b_fREPORT_YEAR2004" "b_fREPORT_YEAR2003"
[21] "b_fREPORT_YEAR2002" "b_fREPORT_YEAR2001"
[23] "b_fREPORT_YEAR2000" "b_fREPORT_YEAR1999"
[25] "b_fREPORT_YEAR1998" "b_fREPORT_YEAR1997"
[27] "b_fREPORT_YEAR1996" "b_fREPORT_YEAR1995"
[29] "sd_REEF_SITE__Intercept" "sd_REEF_SITE_TRANSECT__Intercept"
The chains appear well mixed and very similar
- acf_bar (autocorrelation function): plots the autocorrelation between successive MCMC sample lags for each parameter and each chain
There is no evidence of auto-correlation in the MCMC samples
- rhat_hist: Rhat is a scale reduction factor measure of convergence between the chains. The closer the values are to 1, the more the chains have converged. Values greater than 1.05 indicate a lack of convergence. There will be an Rhat value for each parameter estimated.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
All Rhat values are below 1.05, suggesting the chains have converged.
neff_hist (number of effective samples): the ratio of the number of effective samples (those not rejected by the sampler) to the number of samples provides an indication of the effectiveness (and efficiency) of the MCMC sampler. Ratios that are less than 0.5 for a parameter suggest that the sampler spent considerable time in difficult areas of the sampling domain and rejected more than half of the samples (replacing them with the previous effective sample).
If the ratios are low, tightening the priors may help.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Ratios all very high.
The rstan package offers a range of MCMC diagnostics. Lets start with the MCMC diagnostics.
Of these, we will focus on:
- stan_trace: this plots the estimates of each parameter over the post-warmup length of each MCMC chain. Each chain is plotted in a different colour, with each parameter in its own facet. Ideally, each trace should just look like noise without any discernible drift and each of the traces for a specific parameter should look the same (i.e, should not be displaced above or below any other trace for that parameter).
[1] "b_Intercept" "b_fREPORT_YEAR2021"
[3] "b_fREPORT_YEAR2020" "b_fREPORT_YEAR2019"
[5] "b_fREPORT_YEAR2018" "b_fREPORT_YEAR2017"
[7] "b_fREPORT_YEAR2016" "b_fREPORT_YEAR2015"
[9] "b_fREPORT_YEAR2014" "b_fREPORT_YEAR2013"
[11] "b_fREPORT_YEAR2012" "b_fREPORT_YEAR2011"
[13] "b_fREPORT_YEAR2010" "b_fREPORT_YEAR2009"
[15] "b_fREPORT_YEAR2008" "b_fREPORT_YEAR2007"
[17] "b_fREPORT_YEAR2006" "b_fREPORT_YEAR2005"
[19] "b_fREPORT_YEAR2004" "b_fREPORT_YEAR2003"
[21] "b_fREPORT_YEAR2002" "b_fREPORT_YEAR2001"
[23] "b_fREPORT_YEAR2000" "b_fREPORT_YEAR1999"
[25] "b_fREPORT_YEAR1998" "b_fREPORT_YEAR1997"
[27] "b_fREPORT_YEAR1996" "b_fREPORT_YEAR1995"
[29] "sd_REEF_SITE__Intercept" "sd_REEF_SITE_TRANSECT__Intercept"
The chains appear well mixed and very similar
- stan_acf (auto-correlation function): plots the auto-correlation between successive MCMC sample lags for each parameter and each chain
There is no evidence of auto-correlation in the MCMC samples
- stan_rhat: Rhat is a scale reduction factor measure of convergence between the chains. The closer the values are to 1, the more the chains have converged. Values greater than 1.05 indicate a lack of convergence. There will be an Rhat value for each parameter estimated.
All Rhat values are below 1.05, suggesting the chains have converged.
stan_ess (number of effective samples): the ratio of the number of effective samples (those not rejected by the sampler) to the number of samples provides an indication of the effectiveness (and efficiency) of the MCMC sampler. Ratios that are less than 0.5 for a parameter suggest that the sampler spent considerable time in difficult areas of the sampling domain and rejected more than half of the samples (replacing them with the previous effective sample).
If the ratios are low, tightening the priors may help.
Ratios all very high.
10 Model validation
Post predictive checks provide additional diagnostics about the fit of the model. Specifically, they provide a comparison between predictions drawn from the model and the observed data used to train the model.
See list of available diagnostics by name
bayesplot PPC module:
ppc_bars
ppc_bars_grouped
ppc_boxplot
ppc_dens
ppc_dens_overlay
ppc_dens_overlay_grouped
ppc_dots
ppc_ecdf_overlay
ppc_ecdf_overlay_grouped
ppc_error_binned
ppc_error_hist
ppc_error_hist_grouped
ppc_error_scatter
ppc_error_scatter_avg
ppc_error_scatter_avg_grouped
ppc_error_scatter_avg_vs_x
ppc_freqpoly
ppc_freqpoly_grouped
ppc_hist
ppc_intervals
ppc_intervals_grouped
ppc_km_overlay
ppc_km_overlay_grouped
ppc_loo_intervals
ppc_loo_pit_ecdf
ppc_loo_pit_overlay
ppc_loo_pit_qq
ppc_loo_ribbon
ppc_pit_ecdf
ppc_pit_ecdf_grouped
ppc_ribbon
ppc_ribbon_grouped
ppc_rootogram
ppc_scatter
ppc_scatter_avg
ppc_scatter_avg_grouped
ppc_stat
ppc_stat_2d
ppc_stat_freqpoly
ppc_stat_freqpoly_grouped
ppc_stat_grouped
ppc_violin_grouped- dens_overlay: plots the density distribution of the observed data (black line) overlayed on top of 50 density distributions generated from draws from the model (light blue). Ideally, the 50 realisations should be roughly consistent with the observed data.
The model draws appear to be consistent with the observed data.
- error_scatter_avg: this plots the observed values against the average residuals. Similar to a residual plot, we do not want to see any patterns in this plot. Note, this is not really that useful for models that involve a binomial response
This is not really interpretable
- intervals: plots the observed data overlayed on top of posterior predictions associated with each level of the predictor. Ideally, the observed data should all fall within the predictive intervals.
Using all posterior draws for ppc type 'intervals' by default.
The shinystan package allows the full suite of MCMC diagnostics and posterior predictive checks to be accessed via a web interface.
DHARMa residuals provide very useful diagnostics. Unfortunately, we cannot directly use the simulateResiduals() function to generate the simulated residuals. However, if we are willing to calculate some of the components yourself, we can still obtain the simulated residuals from the fitted stan model.
We need to supply:
- simulated (predicted) responses associated with each observation.
- observed values
- fitted (predicted) responses (averaged) associated with each observation
ltmp_sub.resids <- make_brms_dharma_res(ltmp_sub.brm3, integerResponse = TRUE)
wrap_elements(~ testUniformity(ltmp_sub.resids)) +
wrap_elements(~ plotResiduals(ltmp_sub.resids, form = factor(rep(1, nrow(ltmp_sub))))) +
wrap_elements(~ plotResiduals(ltmp_sub.resids, quantreg = TRUE)) +
wrap_elements(~ testDispersion(ltmp_sub.resids))
resids2 <- recalculateResiduals(ltmp_sub.resids, group = unique(ltmp_sub$fREPORT_YEAR))
testTemporalAutocorrelation(resids2, time = unique(ltmp_sub$fREPORT_YEAR))
Durbin-Watson test
data: simulationOutput$scaledResiduals ~ 1
DW = 1.8473, p-value = 0.6824
alternative hypothesis: true autocorrelation is not 0Warning: no DISPLAY variable so Tk is not available--------------------------------------------------------------
Analysis of Geostatistical Data
For an Introduction to geoR go to http://www.leg.ufpr.br/geoR
geoR version 1.9-6 (built on 2025-08-29) is now loaded
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variog: co-locatted data found, adding one bin at the originUsing as id variablesWarning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.`geom_smooth()` using formula = 'y ~ x'
11 Model investigation
The summary() method generates simple summaries (mean, standard deviation as well as 10, 50 and 90 percentiles).
Warning: There were 3 divergent transitions after warmup. Increasing
adapt_delta above 0.99 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup Family: binomial
Links: mu = logit
Formula: n.points | trials(total.points) ~ fREPORT_YEAR + (1 | REEF_SITE) + (1 | REEF_SITE_TRANSECT)
Data: ltmp_sub (Number of observations: 418)
Draws: 3 chains, each with iter = 10000; warmup = 5000; thin = 10;
total post-warmup draws = 1500
Multilevel Hyperparameters:
~REEF_SITE (Number of levels: 3)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.12 0.14 0.00 0.50 1.00 1576 1584
~REEF_SITE_TRANSECT (Number of levels: 15)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.20 0.05 0.14 0.31 1.00 1382 1419
Regression Coefficients:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -0.69 0.11 -0.87 -0.38 1.00 1196 1271
fREPORT_YEAR2021 -0.51 0.06 -0.63 -0.39 1.00 1417 1297
fREPORT_YEAR2020 -0.52 0.06 -0.63 -0.41 1.00 1337 1346
fREPORT_YEAR2019 -0.89 0.06 -1.01 -0.77 1.00 1336 1281
fREPORT_YEAR2018 -1.27 0.07 -1.40 -1.13 1.00 1327 1509
fREPORT_YEAR2017 -1.32 0.07 -1.46 -1.19 1.00 1522 1349
fREPORT_YEAR2016 -0.38 0.06 -0.49 -0.27 1.00 1248 1457
fREPORT_YEAR2015 -0.71 0.06 -0.82 -0.59 1.00 1370 1383
fREPORT_YEAR2014 -1.01 0.07 -1.15 -0.88 1.00 1232 1361
fREPORT_YEAR2013 -1.13 0.07 -1.25 -1.01 1.00 1269 1339
fREPORT_YEAR2012 -1.41 0.07 -1.55 -1.27 1.00 1343 1417
fREPORT_YEAR2011 -0.33 0.05 -0.44 -0.23 1.00 1247 1130
fREPORT_YEAR2010 -0.03 0.06 -0.14 0.08 1.00 1368 1348
fREPORT_YEAR2009 -0.10 0.06 -0.20 0.01 1.00 1342 1457
fREPORT_YEAR2008 -0.34 0.06 -0.46 -0.23 1.00 1237 1330
fREPORT_YEAR2007 -0.45 0.06 -0.56 -0.33 1.00 1394 1501
fREPORT_YEAR2006 -0.29 0.06 -0.40 -0.18 1.00 1147 1328
fREPORT_YEAR2005 0.19 0.05 0.08 0.30 1.00 1209 1251
fREPORT_YEAR2004 0.07 0.05 -0.03 0.18 1.00 1139 1280
fREPORT_YEAR2003 0.14 0.05 0.04 0.25 1.00 1153 1128
fREPORT_YEAR2002 0.24 0.05 0.14 0.35 1.00 1345 1282
fREPORT_YEAR2001 0.16 0.05 0.06 0.27 1.00 1214 1384
fREPORT_YEAR2000 0.09 0.05 -0.01 0.20 1.00 1373 1349
fREPORT_YEAR1999 0.09 0.05 -0.02 0.19 1.00 1186 1416
fREPORT_YEAR1998 -0.14 0.06 -0.25 -0.03 1.00 1153 1405
fREPORT_YEAR1997 -0.38 0.06 -0.50 -0.27 1.00 1211 1501
fREPORT_YEAR1996 -0.38 0.06 -0.48 -0.27 1.00 1355 1312
fREPORT_YEAR1995 -0.58 0.06 -0.71 -0.45 1.00 1328 1461
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).Warning: There were 3 divergent transitions after warmup. Increasing
adapt_delta above 0.99 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup# A draws_df: 500 iterations, 3 chains, and 55 variables
b_Intercept b_fREPORT_YEAR2021 b_fREPORT_YEAR2020 b_fREPORT_YEAR2019
1 -0.71 -0.58 -0.60 -0.91
2 -0.70 -0.50 -0.51 -1.00
3 -0.58 -0.59 -0.56 -0.97
4 -0.82 -0.53 -0.48 -1.03
5 -0.81 -0.50 -0.43 -0.82
6 -0.65 -0.52 -0.48 -0.94
7 -0.70 -0.60 -0.53 -0.80
8 -0.76 -0.53 -0.53 -0.96
9 -0.78 -0.55 -0.46 -0.82
10 -0.67 -0.41 -0.45 -0.93
b_fREPORT_YEAR2018 b_fREPORT_YEAR2017 b_fREPORT_YEAR2016 b_fREPORT_YEAR2015
1 -1.4 -1.3 -0.42 -0.75
2 -1.2 -1.2 -0.34 -0.74
3 -1.3 -1.4 -0.58 -0.78
4 -1.3 -1.4 -0.42 -0.69
5 -1.2 -1.3 -0.40 -0.71
6 -1.4 -1.3 -0.36 -0.70
7 -1.2 -1.4 -0.41 -0.72
8 -1.2 -1.3 -0.46 -0.61
9 -1.2 -1.2 -0.31 -0.65
10 -1.2 -1.3 -0.43 -0.61
# ... with 1490 more draws, and 47 more variables
# ... hidden reserved variables {'.chain', '.iteration', '.draw'}ltmp_sub.brm3 |>
as_draws_df() |>
dplyr::select(matches("^b_.*|^sd_.*")) |>
mutate(across(matches("b_.*"), plogis)) |>
summarise_draws(
median,
HDInterval::hdi,
Pl = ~ mean(.x < 1),
Pg = ~ mean(.x > 1),
rhat,
ess_bulk
)Warning: Dropping 'draws_df' class as required metadata was removed.# A tibble: 30 × 8
variable median lower upper Pl Pg rhat ess_bulk
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 b_Intercept 0.330 0.286 0.382 1 0 1.00 1136.
2 b_fREPORT_YEAR2021 0.376 0.348 0.403 1 0 1.00 1416.
3 b_fREPORT_YEAR2020 0.374 0.349 0.401 1 0 1.00 1325.
4 b_fREPORT_YEAR2019 0.290 0.267 0.316 1 0 1.000 1327.
5 b_fREPORT_YEAR2018 0.220 0.198 0.243 1 0 1.000 1326.
6 b_fREPORT_YEAR2017 0.211 0.189 0.234 1 0 0.999 1512.
7 b_fREPORT_YEAR2016 0.406 0.381 0.434 1 0 1.00 1229.
8 b_fREPORT_YEAR2015 0.331 0.305 0.357 1 0 1.00 1350.
9 b_fREPORT_YEAR2014 0.267 0.241 0.292 1 0 1.00 1195.
10 b_fREPORT_YEAR2013 0.244 0.222 0.268 1 0 0.999 1263.
# ℹ 20 more rows y ymin ymax .width .point .interval
1 0.6750637 0.6364879 0.7171351 0.95 median hdci y ymin ymax .width .point .interval
1 0.6696107 0.6418767 0.6946751 0.95 median hdciltmp_sub.brm3 |>
bayes_R2(re.form = ~ (1 | REEF_SITE) + (1 | REEF_SITE_TRANSECT), summary = FALSE) |>
median_hdci() y ymin ymax .width .point .interval
1 0.7688076 0.7560056 0.7790249 0.95 median hdci12 Further investigations
Lets start by calculating the cell means
ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR, type = "response") |>
as.data.frame() |>
mutate(
fREPORT_YEAR = factor(fREPORT_YEAR, levels = rev(levels(fREPORT_YEAR))),
REPORT_YEAR = as.numeric(as.character(fREPORT_YEAR))
) |>
ggplot(aes(y = prob, x = REPORT_YEAR)) +
geom_ribbon(aes(ymin = lower.HPD, ymax = upper.HPD), fill = "orange", alpha = 0.3) +
geom_line() +
geom_point() +
theme_classic() +
scale_y_continuous("Live hard coral cover", label = scales::percent_format())Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead.
newdata <- list(fREPORT_YEAR = c(2011, 2012))
ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR,
at = newdata,
type = "response"
)Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead. fREPORT_YEAR prob lower.HPD upper.HPD
2011 0.261 0.2252 0.311
2012 0.108 0.0866 0.134
Point estimate displayed: median
Results are back-transformed from the logit scale
HPD interval probability: 0.95 Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead. contrast odds.ratio lower.HPD upper.HPD
fREPORT_YEAR2012 / fREPORT_YEAR2011 0.343 0.296 0.389
Point estimate displayed: median
Results are back-transformed from the log odds ratio scale
HPD interval probability: 0.95 newdata <- list(fREPORT_YEAR = c(2000:2005, 2012:2013))
cmat <- cbind(c(rep(1 / 6, 6), rep(-1 / 2, 2)))
ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR,
at = newdata,
type = "response"
) |>
regrid() |>
contrast(method = list(fREPORT_YEAR = cmat))Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead. contrast estimate lower.HPD upper.HPD
fREPORT_YEAR 0.242 0.219 0.272
Point estimate displayed: median
HPD interval probability: 0.95 ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR,
at = list(fREPORT_YEAR = c(2011, 2012)),
type = "link"
) |>
pairs(reverse = TRUE) |>
tidy_draws() |>
exp() |>
summarise_draws(
median,
HDInterval::hdi,
Pl = ~ mean(.x < 1),
Pg = ~ mean(.x > 1)
)Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead.# A tibble: 1 × 6
variable median lower upper Pl Pg
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 contrast fREPORT_YEAR2012 - fREPORT_YEAR2011 0.343 0.296 0.389 1 0cmat <- cbind(c(rep(-1 / 7, 7), 1))
ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR,
at = list(fREPORT_YEAR = c(1999:2005, 2012)),
type = "response"
) |>
contrast(method = list(fREPORT_YEAR = cmat))Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead. contrast odds.ratio lower.HPD upper.HPD
fREPORT_YEAR 0.213 0.188 0.238
Point estimate displayed: median
Results are back-transformed from the log odds ratio scale
HPD interval probability: 0.95 ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR,
at = list(fREPORT_YEAR = c(1999:2005, 2012)),
type = "response"
) |>
regrid() |>
contrast(method = list(fREPORT_YEAR = cmat))Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead. contrast estimate lower.HPD upper.HPD
fREPORT_YEAR -0.255 -0.286 -0.229
Point estimate displayed: median
HPD interval probability: 0.95 ltmp.form <- bf(
n.points | trials(total.points) ~ s(REPORT_YEAR) +
(1 | REEF_SITE) + (1 | REEF_SITE_TRANSECT),
family = binomial(link = "log")
)
get_prior(ltmp.form, data = ltmp_sub) prior class coef group resp dpar
(flat) b
(flat) b sREPORT_YEAR_1
student_t(3, 3.9, 2.5) Intercept
student_t(3, 0, 2.5) sd
student_t(3, 0, 2.5) sd REEF_SITE
student_t(3, 0, 2.5) sd Intercept REEF_SITE
student_t(3, 0, 2.5) sd REEF_SITE_TRANSECT
student_t(3, 0, 2.5) sd Intercept REEF_SITE_TRANSECT
student_t(3, 0, 2.5) sds
student_t(3, 0, 2.5) sds s(REPORT_YEAR)
nlpar lb ub source
default
(vectorized)
default
0 default
0 (vectorized)
0 (vectorized)
0 (vectorized)
0 (vectorized)
0 default
0 (vectorized)ltmp_sub |>
summarise(
Median = median(qlogis(HC / 100)),
MAD = mad(qlogis(HC / 100)),
N = mean(total.points)
)# A tibble: 1 × 3
Median MAD N
<dbl> <dbl> <dbl>
1 -1.10 0.579 198.priors <- prior(normal(-1.1, 0.8), class = "Intercept") +
prior(normal(0, 1), class = "b") +
prior(student_t(3, 0, 1), class = "sd") +
prior(student_t(3, 0, 10), class = "sds")
ltmp_sub.brm4 <- brm(ltmp.form,
data = ltmp_sub,
prior = priors,
sample_prior = "yes",
iter = 5000,
warmup = 2000,
chains = 3, cores = 3,
thin = 10,
refresh = 100,
control = list(adapt_delta = 0.99, max_treedepth = 20),
backend = "rstan"
)Compiling Stan program...Start sampling##
ltmp_sub.brm4 |>
conditional_effects(conditions = data.frame(total.points = 200)) |>
plot(points = TRUE)
X1 X2 X3 X4 X5 X6 X7 X8 X9
1 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
2 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
3 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
4 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
5 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
6 1.613482 0.7174855 1.797952 0.9553312 -1.98971 -1.168654 2.144241 1.38704 1
X10
1 -1.660199
2 -1.660199
3 -1.660199
4 -1.660199
5 -1.660199
6 -1.660199
og probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[3] is 3.34124, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 649.427, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 7.24472, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 85.5486, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[6] is 3.47279, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[2] is 1.09665, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 5.88037, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 2.79872, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 1.69481, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[6] is 1.89914, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[185] is 1.0044, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 4.91291, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[12] is 1.19554, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[1] is 844.801, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[13] is 1.34318, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3: Rejecting initial value:
Chain 3: Error evaluating the log probability at the initial value.
Chain 3: Exception: binomial_lpmf: Probability parameter[182] is 1.03449, but must be in the interval [0, 1] (in 'anon_model', line 74, column 4 to column 44)
Chain 3:
Chain 3: Gradient evaluation took 0.000429 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 4.29 seconds.
Chain 3: Adjust your expectations accordingly!
Chain 3:
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Chain 1: ## data.frame(mgcv::smoothCon(s(REPORT_YEAR, k=3), data=ltmp_sub)[[1]]$REPORT_YEAR) |>
## bind_cols(ltmp_sub)
gratia::basis(s(REPORT_YEAR), data = ltmp_sub) |> gratia::draw()
ltmp_glmm <- ltmp_sub.brm3 |>
emmeans(~fREPORT_YEAR, type = "response") |>
as.data.frame() |>
mutate(
fREPORT_YEAR = factor(fREPORT_YEAR, levels = rev(levels(fREPORT_YEAR))),
REPORT_YEAR = as.numeric(as.character(fREPORT_YEAR))
)Warning: Method 'parse_bf' is deprecated. Please use 'brmsterms' instead.ltmp_sub.brm4 |>
conditional_effects() |>
plot() |>
_[[1]] +
geom_line(
data = ltmp_glmm, inherit.aes = FALSE,
aes(y = prob, x = REPORT_YEAR), colour = "blue"
) +
geom_ribbon(
data = ltmp_glmm, inherit.aes = FALSE,
aes(
y = prob, x = REPORT_YEAR,
min = lower.HPD, ymax = upper.HPD
), fill = "orange", alpha = 0.3
) +
theme_classic() +
scale_y_continuous("Live hard coral cover", label = scales::percent_format())Setting all 'trials' variables to 1 by default if not specified otherwise.
