This document provides a side-by-side comparison of
** LDATS** (version 0.2.7) results with
analysis from Christensen
et al. 2018. Due to the size and duration of model runs, we use
pre-generated model output from the LDATS-replications
repo.

Step | Changes from Christensen et al 2018 to
`LDATS` |
Effect on comparison | Recommendations for future users |
---|---|---|---|

Data | Paper adjusts abundances according to unit effort,
while `LDATS` uses raw capture numbers. |
None: run comparison using adjusted data | Use raw, unweighted abundances. |

LDA model selection | Paper conservatively overestimated the number of
parameters for calculating AIC for model selection. `LDATS`
calculates AIC appropriately. |
Paper LDA selects 4 topics, while `LDATS`
finds 6. Compare all combinations of paper and `LDATS` LDA
models and changepoint models |
Use `LDATS` AIC calculation. |

Changepoint model document weights | Paper weighted all sampling periods equally regardless
of abundance. `LDATS` by default weights the information from
each sampling period according to the number of individuals captured
(i.e. the amount of information gleaned about the underlying community
composition). |
None; use `weights = NULL` to set all
weights equal to 1 for LDATS |
Weight sampling periods according to abundance |

Overall LDA + changepoint results | All combinations of LDA + changepoint model find 4 changepoints at approximately the same time steps | Choice of LDA model has more of an effect than choice of changepoint model | `LDATS` reflects best practices, but the
paper methods will produce qualitatively similar results. |

To obtain the most recent version of
** LDATS**, install the most recent version
from GitHub:

```
install.packages("devtools")
::install_github("weecology/LDATS") devtools
```

Load in the ** LDATS** package.

```
library(LDATS)
set.seed(42)
<- 200
nseeds <- 10000 nit
```

To run the analyses here, you will also need to download
** dplyr**,

`gridExtra`

`multipanel`

`RColorBrewer`

`RCurl`

`reshape2`

`install.packages(c("dplyr", "gridExtra", "multipanel", "RColorBrewer", "RCurl", "reshape2"))`

Because both the Latent Dirichlet Allocation (LDA) and time series
components of the analysis can take a long time to run (especially with
the settings above for the number of seeds and iterations), we will use
pre-generated model outputs and turn off certain code chunks that run
the models using a global `rmarkdown`

parameter,
`run_models = FALSE`

.

To change this functionality, you can re-render this file with:

`::render("paper-comparison.Rmd", params = list(run_models = TRUE)) rmarkdown`

We’re going to download analysis scripts, data files, and model objects, so we use a temporary location for storage:

`<- "." vignette_files `

To replicate the Christensen et al. 2018 analysis, we download some of the original scripts & data files from Extreme-events-LDA repo, as well as some raw data files from the PortalData repo, which are stored in the LDATS-replications repo:

Main Analysis Scripts:

`rodent_LDA_analysis.R`

- main script for analyzing rodent community change using LDA

`rodent_data_for_LDA.R`

- contains a function that creates the rodent data table used in analyses

`AIC_model_selection.R`

- contains functions for calculating AIC for different candidate LDA models

`changepointmodel.r`

- contains change-point model code

`LDA-distance.R`

- function for computing Hellinger distance analyses

Data:

`Rodent_table_dat.csv`

- table of rodent data, created by rodent_data_for_LDA.R

`moon_dates.csv`

- table of census dates (downloaded from the PortalData repository)

`Portal_rodent_trapping.csv`

- table of trapping effort (downloaded from the PortalData repository)

`paper_dat.csv`

- rodent data table from Christensen et al. 2018

`paper_dates.csv`

- dates used in Christensen et al. 2018

`paper_covariates.csv`

- table of dates and covariate data

Figure scripts:

`LDA_figure_scripts.R`

- contains functions for making main plots in manuscript (Fig 1). Called from rodent_LDA_analysis.R

```
<- file.path(vignette_files, "scripts", "rodent_LDA_analysis.r")
test_file
if (!file.exists(test_file)){
# scripts
dir.create(file.path(vignette_files, "scripts"), showWarnings = FALSE)
<- "https://raw.githubusercontent.com/weecology/LDATS-replications/master/scripts/"
github_path <- c("rodent_LDA_analysis.r", "rodent_data_for_LDA.r",
files_to_download "AIC_model_selection.R", "changepointmodel.r",
"LDA-distance.R", "LDA_figure_scripts.R")
for (file in files_to_download) {
download.file(url = paste0(github_path, file),
destfile = file.path(vignette_files, "scripts", file))
}
# data
dir.create(file.path(vignette_files, "data"), showWarnings = FALSE)
<- "https://raw.githubusercontent.com/weecology/LDATS-replications/master/data/"
github_path <- c("moon_dates.csv", "Portal_rodent_trapping.csv",
files_to_download "Rodent_table_dat.csv", "paper_dat.csv",
"paper_dates.csv", "paper_covariates.csv")
for (file in files_to_download) {
download.file(url = paste0(github_path, file),
destfile = file.path(vignette_files, "data", file))
} }
```

We also have pre-generated model outputs that we download from the LDATS-replications repo:

LDA models:

`ldats_ldamodel.RDS`

- the best LDA model as selected by LDATS

`paper_ldamodel.RDS`

- the best LDA model as selected by the Christensen et al. analysis

Changepoint outputs:

`ldats_ldats.RDS`

,`ldats_ldats_cpt.RDS`

,`ldats_ldats_cpt_dates.RDS`

- the posterior distribution, count, and dates of changepoints, using the LDATS LDA model and the LDATS changepoint selection

`ldats_paper.RDS`

,`ldats_paper_cpt.RDS`

, `ldats_paper_cpt_dates.RDS- the posterior distribution, count, and dates of changepoints, using the LDATS LDA model and the paper’s changepoint selection

`paper_ldats.RDS`

,`paper_ldats_cpt.RDS`

, `paper_ldats_cpt_dates.RDS- the posterior distribution, count, and dates of changepoints, using the paper LDA model and the LDATS changepoint selection

`paper_paper.RDS`

,`paper_paper_cpt.RDS`

, `paper_paper_cpt_dates.RDS- the posterior distribution, count, and dates of changepoints, using the paper LDA model and the paper’s changepoint selection

`cpt_dates.RDS`

- summary table of changepoint results across models

Figures

`lda_distances.png`

- figure showing the variance in the topics identified by the paper’s LDA model code

`paper_paper_cpt_plot.png`

- figure showing the time series results for the paper analysis of the paper LDA

`ldats_paper_cpt_plot.png`

- figure showing the time series results for the paper analysis of the LDATS LDA

`annual_hist.RDS`

- function for making histogram of change points over years

```
<- file.path(vignette_files, "output", "ldats_ldamodel.RDS")
test_file
if (!file.exists(test_file)){
dir.create(file.path(vignette_files, "output"), showWarnings = FALSE)
<- "https://raw.githubusercontent.com/weecology/LDATS-replications/master/output/"
github_path <- c("ldats_ldamodel.RDS", "paper_ldamodel.RDS",
files_to_download "ldats_ldats.RDS", "ldats_paper.RDS",
"paper_ldats.RDS", "paper_paper.RDS",
"ldats_rodents_adjusted.RDS", "rodents.RDS",
"ldats_paper_cpt.RDS", "ldats_paper_cpt_dates.RDS",
"ldats_ldats_cpt.RDS", "ldats_ldats_cpt_dates.RDS",
"paper_paper_cpt.RDS", "paper_paper_cpt_dates.RDS",
"paper_ldats_cpt.RDS", "paper_ldats_cpt_dates.RDS",
"annual_hist.RDS", "cpt_dates.RDS",
"lda_distances.png", "paper_paper_cpt_plot.png",
"ldats_paper_cpt_plot.png")
for (file in files_to_download){
download.file(url = paste0(github_path, file),
destfile = file.path(vignette_files, "output", file),
mode = "wb")
} }
```

The dataset of Portal rodents on control plots is included in the LDATS package:

```
data(rodents)
head(rodents[[1]])
#> BA DM DO DS NA. OL OT PB PE PF PH PI PL PM PP RF RM RO SF SH SO
#> 1 0 13 0 2 2 0 0 0 1 1 0 0 0 0 3 0 0 0 0 0 0
#> 2 0 20 1 3 2 0 0 0 0 4 0 0 0 0 2 0 0 0 0 0 0
#> 3 0 21 0 8 4 0 0 0 1 2 0 0 0 0 1 0 0 0 0 0 0
#> 4 0 21 3 12 4 2 3 0 1 1 0 0 0 0 0 0 0 0 0 0 0
#> 5 0 16 1 9 5 2 1 0 0 2 0 0 0 0 0 0 1 0 0 0 0
#> 6 0 17 1 13 5 1 5 0 0 3 0 0 0 0 0 0 0 0 0 0 0
```

We can compare this against the data used in Christensen et al:

```
# parameters for subsetting the full Portal rodents data
<- 1:436
periods <- c(2, 4, 8, 11, 12, 14, 17, 22)
control_plots <- c("BA", "DM", "DO", "DS", "NA", "OL", "OT", "PB", "PE", "PF",
species_list "PH", "PI", "PL", "PM", "PP", "RF", "RM", "RO", "SF", "SH", "SO")
source(file.path(vignette_files, "scripts", "rodent_data_for_LDA.r"))
# assemble `paper_dat`, the data from Christensen et al. 2018
<- create_rodent_table(period_first = min(periods),
paper_dat period_last = max(periods),
selected_plots = control_plots,
selected_species = species_list)
# assemble `paper_covariates`, the associated dates and covariate data
<- read.csv(file.path(vignette_files, "data", "moon_dates.csv"), stringsAsFactors = F)
moondat
<- moondat %>%
paper_dates ::filter(period %>% dplyr::between(min(periods), max(periods))) %>%
dplyr::pull(censusdate) %>%
dplyras.Date()
<- data.frame(
paper_covariates index = seq_along(paper_dates),
date = paper_dates,
year_continuous = lubridate::decimal_date(paper_dates)) %>%
::mutate(
dplyrsin_year = sin(year_continuous * 2 * pi),
cos_year = cos(year_continuous * 2 * pi)
)
```

`LDATS`

```
<- rodents[[1]] == paper_dat
compare
length(which(rowSums(compare) < ncol(compare)))
#> [1] 16
```

There are 16 rows where the data included in LDATS differs from the paper data. This is because the LDATS data is not adjusted to account for trapping effort, while the paper data is, by dividing all census counts by the actual number of plots trapped and multiplying by 8 to account for incompletely-trapped censuses.

To confirm this, refer to lines 36-46 in
`rodent_data_for_LDA.r`

:

```
# retrieve data on number of plots trapped per month
= read.csv('https://raw.githubusercontent.com/weecology/PortalData/master/Rodents/Portal_rodent_trapping.csv')
trap_table = filter(trap_table, plot %in% selected_plots)
trap_table_controls = aggregate(trap_table_controls$sampled,by=list(period = trap_table_controls$period),FUN=sum)
nplots_controls
# adjust species counts by number of plots trapped that month
= as.data.frame.matrix(r_table)
r_table_adjusted for (n in 1:436) {
#divide by number of control plots actually trapped (should be 8) and multiply by 8 to estimate captures as if all plots were trapped
= round(r_table_adjusted[n,]/nplots_controls$x[n]*8)
r_table_adjusted[n,] }
```

We can run the same procedure on the LDATS data to verify that we obtain a data.frame that matches.

```
# get the trapping effort for each sample
<- read.csv(file.path(vignette_files, "data", "Portal_rodent_trapping.csv"))
trap_table <- dplyr::filter(trap_table, plot %in% control_plots)
trap_table_controls <- aggregate(trap_table_controls$sampled,
nplots_controls by = list(period = trap_table_controls$period),
FUN = sum)
# adjust species counts by number of plots trapped that month
# divide by number of control plots actually trapped (should be 8) and
# multiply by 8 to estimate captures as if all plots were trapped
<- as.data.frame.matrix(rodents[[1]])
ldats_rodents_adjusted <- round(ldats_rodents_adjusted[periods, ] / nplots_controls$x[periods] * 8) ldats_rodents_adjusted[periods, ]
```

Now we can compare the adjusted LDATS dataset with both the original ldats dataset and the dataset from the paper:

```
<- rodents[[1]] == ldats_rodents_adjusted
compare_raw length(which(rowSums(compare_raw) < ncol(compare_raw)))
<- ldats_rodents_adjusted == paper_dat
compare_adjusted length(which(rowSums(compare_adjusted) < ncol(compare_adjusted)))
```

Because the LDA procedure weights the information from documents
(census periods) according to the number of words (rodents captured), we
now believe it is most appropriate to run the LDA on *unadjusted*
trapping data, and we recommend that users of LDATS do so. However, to
maintain consistency with Christensen et al 2018, we will proceed using
the *adjusted* rodent table in this vignette.

`1]] <- paper_dat rodents[[`

The LDATS rodent data comes with a
`document_covariate_table`

, which we will use later as the
predictor variables for the changepoint models. In this table, time is
expressed as new moon numbers. Later we will want to be able to
interpret the results in terms of census dates. We will add a column to
the `document_covariate_table`

to convert new moon numbers to
census dates. We will not reference this column in any of the formulas
we pass to the changepoint models, so it will be ignored until we need
it.

```
head(rodents$document_covariate_table)
#> newmoon sin_year cos_year
#> 1 1 -0.2470 -0.9690
#> 2 2 -0.6808 -0.7325
#> 3 3 -0.9537 -0.3008
#> 4 4 -0.9813 0.1925
#> 5 5 -0.7583 0.6519
#> 6 6 -0.3537 0.9354
```

```
<- dplyr::left_join(rodents$document_covariate_table,
new_cov_table ::select(moondat, newmoonnumber, censusdate),
dplyrby = c("newmoon" = "newmoonnumber")) %>%
::rename(date = censusdate)
dplyr
$document_covariate_table <- new_cov_table rodents
```

While LDATS can run start-to-finish with `LDATS::LDA_TS`

,
here we will work through the process function-by-function to isolate
differences with the paper. For a breakdown of the `LDA_TS`

pipeline, see the `codebase`

vignette.

First, we run the LDA models from LDATS to identify the number of topics:

```
<- LDATS::LDA_set(document_term_table = rodents$document_term_table,
ldats_ldas topics = 2:6, nseeds = nseeds)
<- LDATS::select_LDA(LDA_models = ldats_ldas)[[1]]
ldats_ldamodel
saveRDS(ldats_ldamodel, file = file.path(vignette_files, "ldats_ldamodel.RDS"))
```

Second, we run the LDA models from Christensen et al. to do the same task:

```
source(file.path(vignette_files, "scripts", "AIC_model_selection.R"))
source(file.path(vignette_files, "scripts", "LDA-distance.R"))
# Some of the functions require the data to be stored in the `dat` variable
<- paper_dat
dat
# Fit a bunch of LDA models with different seeds
# Only use even numbers for seeds because consecutive seeds give identical results
<- 2 * seq(nseeds)
seeds
# repeat LDA model fit and AIC calculation with a bunch of different seeds to test robustness of the analysis
<- repeat_VEM(paper_dat,
best_ntopic
seeds,topic_min = 2,
topic_max = 6)
hist(best_ntopic$k, breaks = seq(from = 0.5, to = 9.5),
xlab = "best # of topics", main = "")
# 2b. how different is species composition of 4 community-types when LDA is run with different seeds?
# ==================================================================
# get the best 100 seeds where 4 topics was the best LDA model
<- best_ntopic %>%
seeds_4topics filter(k == 4) %>%
arrange(aic) %>%
head(min(100, nseeds)) %>%
pull(SEED)
# choose seed with highest log likelihood for all following analyses
# (also produces plot of community composition for "best" run compared to "worst")
png(file.path(vignette_files, "output", "lda_distances.png"), width = 800, height = 400)
<- paper_dat # calculate_LDA_distance has some required named variables
dat <- calculate_LDA_distance(paper_dat, seeds_4topics)
best_seed dev.off()
<- unlist(best_seed)[2]
mean_dist <- unlist(best_seed)[3]
max_dist
# ==================================================================
# 3. run LDA model
# ==================================================================
<- 4
ntopics <- unlist(best_seed)[1] # For the paper, use seed 206
SEED <- LDA(paper_dat, ntopics, control = list(seed = SEED), method = "VEM")
ldamodel
saveRDS(ldamodel, file = file.path(vignette_files, "paper_ldamodel.RDS"))
```

`::include_graphics(file.path(vignette_files, "output", "lda_distances.png")) knitr`

To visualize the LDA assignment of species to topics, we load in the saved LDA models from previously:

```
<- readRDS(file.path(vignette_files, "output", "paper_ldamodel.RDS"))
ldamodel <- readRDS(file.path(vignette_files, "output", "ldats_ldamodel.RDS")) ldats_ldamodel
```

How the paper LDA model assigns species to topics:

`plot(ldamodel, cols = NULL, option = "D")`

How the LDATS LDA model assigns species to topics:

`plot(ldats_ldamodel, cols = NULL, option = "D")`

The paper method finds 4 topics and LDATS finds 6. This is because of an update to the model selection procedure. The paper conservatively overestimates the number of parameters (by counting all of the variational parameters) and therefore overpenalizes the AIC for models with more topics. Comparatively, the LDATS method now uses the number of parameters remaining after the variational approximation, as returned by the LDA object. For this vignette, we will compare the results from using both LDA models.

We will compare four combinations of LDA + changepoint models:

- LDATS LDA + LDATS changepoint
- LDATS LDA + paper changepoint
- Paper LDA + LDATS changepoint
- Paper LDA + paper changepoint

Having divided the data to generate catch-per-effort, the paper
changepoint model weighted all sample periods equally. In comparison,
LDATS does not force an equal weighting, but assumes that as default,
and can weight sample periods according to how many individuals were
captured (controlled by the `weights`

argument to
`LDA_TS`

, and easily calculated for a document-term matrix
using `document_term_weights`

. We now believe it is more
appropriate to weight periods proportional to captures in the time
series (despite the LDA function returning only proportions of each
topic), and this is what we recommend for LDATS users. For the purposes
of comparison, however, we will continue set all weights = 1 for both
changepoint models. For an example of LDATS run with proportional
weights, see the rodents
vignette.

We define a few helper functions for running the changepoints model of Christensen et al. and processing the output to obtain the dates:

```
#### Run changepoint ####
source(file.path(vignette_files, "scripts", "changepointmodel.r"))
<- function(lda_model, paper_covariates, n_changepoints = 1:6){
find_changepoints # set up parameters for model
<- dplyr::select(paper_covariates,
x
year_continuous,
sin_year,
cos_year)
# run models with 1, 2, 3, 4, 5, 6 changepoints
<- data.frame(n_changepoints = n_changepoints)
cpt_results $cpt_model <- lapply(cpt_results$n_changepoints,
cpt_resultsfunction(n_changepoints){
changepoint_model(lda_model, x, n_changepoints, maxit = nit,
weights = rep(1, NROW(x)))
})return(cpt_results)
}
# Among a selection of models with different # of changepoints,
# - compute AIC
# - select the model with the best AIC
# - get the posterior distributions for the changepoints
<- function(cpt_results, ntopics){
select_cpt_model # compute log likelihood as the mean deviance
$mean_deviances <- vapply(cpt_results$cpt_model,
cpt_resultsfunction(cpt_model) {mean(cpt_model$saved_lls)},
0)
# compute AIC = ( -2 * log likelihood) + 2 * (#parameters)
$AIC <- cpt_results$mean_deviances * -2 +
cpt_results2 * (3 * (ntopics - 1) * (cpt_results$n_changepoints + 1) +
$n_changepoints))
(cpt_results
# select the best model
<- cpt_results$cpt_model[[which.min(cpt_results$AIC)]]
cpt return(cpt)
}
# transform the output from `compute_cpt` and match up the time indices with
# dates from the original data
<- function(cpt, covariates = paper_covariates){
get_dates $saved[,1,] %>%
cptt() %>%
as.data.frame() %>%
::melt() %>%
reshape::left_join(covariates, by = c("value" = "index"))
dplyr }
```

Run the Christensen et al. time series model to identify changepoints on the LDA topics selected by LDATS:

```
<- find_changepoints(ldats_ldamodel, paper_covariates)
ldats_paper_results
saveRDS(ldats_paper_results, file = file.path(vignette_files, "output", "ldats_paper.RDS"))
```

Extract the dates of the changepoints:

```
<- readRDS(file.path(vignette_files, "output", "ldats_paper.RDS"))
ldats_paper_results
<- select_cpt_model(ldats_paper_results,
ldats_paper_cpt ntopics = ldats_ldamodel@k)
<- get_dates(ldats_paper_cpt) ldats_paper_cpt_dates
```

Run the Christensen et al. time series model to identify changepoints on the LDA topics selected by Christensen et al.:

```
<- find_changepoints(ldamodel, paper_covariates)
paper_paper_results
saveRDS(paper_paper_results, file = file.path(vignette_files, "paper_paper.RDS"))
```

Extract the dates of the changepoints:

```
<- readRDS(file.path(vignette_files, "output", "paper_paper.RDS"))
paper_paper_results
<- select_cpt_model(paper_paper_results,
paper_paper_cpt ntopics = ldamodel@k)
<- get_dates(ldats_paper_cpt) paper_paper_cpt_dates
```

Run the LDATS time series model to identify changepoints on the LDA topics selected by LDATS:

```
<- TS_on_LDA(LDA_models = ldats_ldamodel,
ldats_ldats_results document_covariate_table = rodents$document_covariate_table,
formulas = ~ sin_year + cos_year,
nchangepoints = 1:6,
timename = "newmoon",
weights = NULL,
control = list(nit = nit))
saveRDS(ldats_ldats_results, file = file.path(vignette_files, "output", "ldats_ldats.RDS"))
```

Unlike the paper changepoint model, LDATS can recognize that sampling periods may not be equidistant, and can place changepoint estimates at new moons if they fall between nonconsecutive sampling periods. We can estimate the dates corresponding to those new moons, extrapolating from the census dates for adjacent census periods.

```
# make the full sequence of possible newmoon values
<- seq(min(rodents$document_covariate_table$newmoon),
full_index max(rodents$document_covariate_table$newmoon))
# generate a lookup table with dates for the newmoons, using `approx` to
# linearly interpolate the missing values
<- approx(rodents$document_covariate_table$newmoon,
ldats_dates as.Date(rodents$document_covariate_table$date),
%>%
full_index) as.data.frame() %>%
mutate(index = x,
date = as.Date(y, origin = "1970-01-01")) %>%
select(index, date)
```

Select the best time series model and extract the dates of the changepoints:

```
<- readRDS(file.path(vignette_files, "output", "ldats_ldats.RDS"))
ldats_ldats_results
<- select_TS(ldats_ldats_results)
ldats_ldats_cpt
<- ldats_ldats_cpt$rhos %>%
ldats_ldats_cpt_dates as.data.frame() %>%
::melt() %>%
reshape::left_join(ldats_dates, by = c("value" = "index")) dplyr
```

Run the LDATS time series model to identify changepoints on the LDA topics selected by Christensen et al.:

```
<- TS_on_LDA(LDA_models = ldamodel,
paper_ldats_results document_covariate_table = rodents$document_covariate_table,
formulas = ~ sin_year + cos_year,
nchangepoints = 1:6,
timename = "newmoon",
weights = NULL,
control = list(nit = nit))
saveRDS(paper_ldats_results, file = file.path(vignette_files, "output", "paper_ldats.RDS"))
```

Select the best time series model and extract the dates of the changepoints:

```
<- readRDS(file.path(vignette_files, "output", "paper_ldats.RDS"))
paper_ldats_results
<- select_TS(paper_ldats_results)
paper_ldats_cpt
<- paper_ldats_cpt$rhos %>%
paper_ldats_cpt_dates as.data.frame() %>%
::melt() %>%
reshape::left_join(ldats_dates, by = c("value" = "index")) dplyr
```

```
nlevels(ldats_paper_cpt_dates$variable)
#> [1] 4
nlevels(paper_paper_cpt_dates$variable)
#> [1] 4
nlevels(ldats_ldats_cpt_dates$variable)
#> [1] 4
nlevels(paper_ldats_cpt_dates$variable)
#> [1] 4
```

All of the models find four changepoints.

`plot(paper_ldats_cpt)`

`plot(ldats_ldats_cpt)`

`<- readRDS(file.path(vignette_files, "output", "annual_hist.RDS")) annual_hist `

```
<- find_changepoint_location(paper_paper_cpt)
paper_cpts <- ldamodel@k
ntopics
png(file.path(vignette_files, "output", "paper_paper_cpt_plot.png"), width = 800, height = 600)
get_ll_non_memoized_plot(ldamodel, paper_covariates, paper_cpts, make_plot = TRUE,
weights = rep(1, NROW(paper_covariates)))
dev.off()
```

`<- annual_hist(paper_paper_cpt, paper_covariates$year_continuous) paper_paper_hist `

`::include_graphics(file.path(vignette_files, "output", "paper_paper_cpt_plot.png")) knitr`

```
<- find_changepoint_location(ldats_paper_cpt)
ldats_cpts <- ldats_ldamodel@k
ntopics
png(file.path(vignette_files, "output", "ldats_paper_cpt_plot.png"), width = 800, height = 600)
get_ll_non_memoized_plot(ldats_ldamodel, paper_covariates, ldats_cpts, make_plot = TRUE,
weights = rep(1, NROW(paper_covariates)))
dev.off()
```

`<- annual_hist(ldats_paper_cpt, paper_covariates$year_continuous) ldats_paper_hist `

`::include_graphics(file.path(vignette_files, "output", "ldats_paper_cpt_plot.png")) knitr`

The results of the changepoint model appear robust to both choice of LDA model and choice of changepoint model.

`::kable(cpt_dates) knitr`

changepoint | ldatsLDA_ldatsCPT | ldatsLDA_paperCPT | paperLDA_ldatsCPT | paperLDA_paperCPT |
---|---|---|---|---|

V1 | 1984-01-30 | 1984-01-11 | 1984-04-27 | 1984-01-11 |

V2 | 1991-05-30 | 1991-05-29 | 1993-04-19 | 1991-05-29 |

V3 | 1999-01-25 | 1998-12-21 | 1999-07-07 | 1998-12-21 |

V4 | 2009-11-15 | 2009-09-29 | 2010-01-20 | 2009-09-29 |

The choice of LDA has more influence on the changepoint locations than the choice of changepoint model - probably because the LDATS LDA has 6 topics, and the paper LDA has 4. However, all of the models agree to within 6 months in most cases, and a year for the broader early 1990s changepoint.