Hands-on Tutorials (Day Two)

Topic modeling

Install the required packages for this tutorial.

# Package names
packages <- c(
  "tidyverse",
  "tidytext",
  "quanteda",
  "textstem",
  "topicmodels",
  "ldatuning",
  "topicdoc",
  "stm",
  "udpipe",
  "parallel",
  "doParallel",
  "seededlda"
)

# Install packages not yet installed
installed_packages <- packages %in% rownames(installed.packages())
if (any(installed_packages == FALSE)) {
  install.packages(packages[!installed_packages])
}

library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.4.0     ✔ purrr   1.0.1
✔ tibble  3.1.8     ✔ dplyr   1.1.0
✔ tidyr   1.3.0     ✔ stringr 1.5.0
✔ readr   2.1.3     ✔ forcats 1.0.0
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
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library(tidytext)
library(quanteda)

Package version: 3.2.4
Unicode version: 14.0
ICU version: 70.1
Parallel computing: 8 of 8 threads used.
See https://quanteda.io for tutorials and examples.

library(textstem)

Loading required package: koRpus.lang.en
Loading required package: koRpus
Loading required package: sylly
For information on available language packages for 'koRpus', run

  available.koRpus.lang()

and see ?install.koRpus.lang()


Attaching package: 'koRpus'

The following objects are masked from 'package:quanteda':

    tokens, types

The following object is masked from 'package:readr':

    tokenize

library(topicmodels)
library(ldatuning)
library(topicdoc)
library(stm)

stm v1.3.6 successfully loaded. See ?stm for help. 
 Papers, resources, and other materials at structuraltopicmodel.com

library(udpipe)
library(parallel)
library(doParallel)

Loading required package: foreach

Attaching package: 'foreach'

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library(seededlda)

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The following objects are masked from 'package:topicmodels':

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ukimmig2010 <- data.frame(text = quanteda::data_char_ukimmig2010)
ukimmig2010$party <- names(quanteda::data_char_ukimmig2010)

ukimmig2010 <- ukimmig2010 %>%
  mutate(lemma = tolower(text)) %>%
  mutate(lemma = lemmatize_strings(lemma))

ukimmig2010_corpus <- quanteda::corpus(ukimmig2010,
                                       docid_field = "party",
                                       text_field = "lemma")

ukimmig2010_dfm <- ukimmig2010_corpus %>%
  quanteda::tokens(remove_punct = TRUE,
         remove_symbols = TRUE,
         remove_numbers = TRUE) %>%
  tokens_tolower() %>%
  tokens_remove(stopwords("en")) %>%
  dfm() %>%
  dfm_trim(min_docfreq = 0.5, max_docfreq = 0.99, 
           docfreq_type = "prop") %>%
  dfm_subset(ntoken(.) > 0)

ukimmig2010_dtm <- convert(ukimmig2010_dfm, to = "topicmodels")

The basic function to fit a topic model is LDA:

topicModel <- LDA(ukimmig2010_dtm, 
                  k = 5, 
                  method="Gibbs")

topicmodels::terms(topicModel, 5)

     Topic 1   Topic 2  Topic 3      Topic 4       Topic 5  
[1,] "control" "new"    "uk"         "people"      "asylum" 
[2,] "year"    "border" "british"    "system"      "right"  
[3,] "work"    "must"   "immigrant"  "citizenship" "country"
[4,] "eu"      "can"    "national"   "end"         "much"   
[5,] "student" "live"   "government" "refugee"     "illegal"

Considering the output of the function LDA, the beta matrix includes the information about the distribution of terms by topics.

tidy_model <- tidy(topicModel)

top_terms <- tidy_model %>%
  group_by(topic) %>%
  top_n(10, beta) %>%
  ungroup() %>%
  arrange(topic, -beta)

top_terms %>%
  mutate(term = reorder_within(term, beta, topic)) %>%
  ggplot(aes(term, beta)) +
  geom_bar(stat = "identity") +
  scale_x_reordered() +
  facet_wrap(~ topic, scales = "free_x") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) 

Information about the distribution of topics in each documents is in the matrix gamma.

tidy_model_gamma <- tidy(topicModel, matrix = "gamma")
head(tidy_model_gamma)

# A tibble: 6 × 3
  document     topic gamma
  <chr>        <int> <dbl>
1 BNP              1 0.167
2 Coalition        1 0.258
3 Conservative     1 0.305
4 Greens           1 0.215
5 Labour           1 0.243
6 LibDem           1 0.156

tidy_model_gamma <- tidy_model_gamma %>%
  mutate(document = 
           mgsub::mgsub(string = document,
                        pattern = unique(tidy_model_gamma$document),
                        replacement = names(data_char_ukimmig2010),
                        fixed = TRUE))

ggplot(tidy_model_gamma) +
  geom_col(aes(x = topic, y = gamma)) +
  facet_wrap(~ document, nrow = 3)

You may want to assign the most prevalent topic to each document in the corpus.

docvars(ukimmig2010_corpus, "pred_topic") <- topicmodels::topics(topicModel)
str(docvars(ukimmig2010_corpus))

'data.frame':   9 obs. of  2 variables:
 $ text      : chr  "IMMIGRATION: AN UNPARALLELED CRISIS WHICH ONLY THE BNP CAN SOLVE. \n\n- At current immigration and birth rates,"| __truncated__ "IMMIGRATION. \n\nThe Government believes that immigration has enriched our culture and strengthened our economy"| __truncated__ "Attract the brightest and best to our country.\n\nImmigration has enriched our nation over the years and we wan"| __truncated__ "Immigration.\n\nMigration is a fact of life.  People have always moved from one country to another, and as a pr"| __truncated__ ...
 $ pred_topic: int  3 2 1 1 1 4 5 5 1

Advanced topic modeling methods

Identify the number of topics

There are different algorithms for estimating the optimal number of topics. The ldatuning package provides a function FindTopicsNumber that calculates different metrics to estimate the most preferable number of topics for LDA model.

tn <- FindTopicsNumber(ukimmig2010_dtm, 
                       topics = seq(5, 50, by = 5),
                       metrics = c("Griffiths2004", 
                                   "CaoJuan2009", 
                                   "Arun2010", 
                                   "Deveaud2014"))
FindTopicsNumber_plot(tn)

Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the ldatuning package.
  Please report the issue at <]8;;https://github.com/nikita-moor/ldatuning/issueshttps://github.com/nikita-moor/ldatuning/issues]8;;>.

---

Here, the Griffiths2004 approach is actually based on the log-likelihood maximization and it is described in the related paper¹. It is also the default approach of ldatuning. The Deveaud2014 is also a common choice.

ggplot(tn,
       aes(x = topics, y = Griffiths2004)) +
  geom_point() +
  geom_line() + 
  ggtitle("Griffiths2004")

Based on this indication, we can peraphs fit a model with about 15 topics.

topicModel15 <- LDA(ukimmig2010_dtm, 
                  k = 15, 
                  method="Gibbs")

topicmodels::terms(topicModel15, 5)

     Topic 1  Topic 2       Topic 3     Topic 4   Topic 5      Topic 6 
[1,] "much"   "people"      "limit"     "seeker"  "government" "asylum"
[2,] "uk"     "make"        "can"       "system"  "must"       "right" 
[3,] "eu"     "country"     "eu"        "part"    "child"      "live"  
[4,] "can"    "ensure"      "immigrant" "allow"   "national"   "high"  
[5,] "arrive" "citizenship" "give"      "control" "immigrant"  "allow" 
     Topic 7   Topic 8   Topic 9       Topic 10  Topic 11   Topic 12   
[1,] "end"     "uk"      "migrant"     "system"  "country"  "british"  
[2,] "control" "asylum"  "citizenship" "house"   "year"     "illegal"  
[3,] "support" "control" "detention"   "work"    "national" "immigrant"
[4,] "new"     "citizen" "non"         "uk"      "work"     "right"    
[5,] "people"  "year"    "control"     "british" "apply"    "country"  
     Topic 13  Topic 14  Topic 15 
[1,] "student" "border"  "work"   
[2,] "border"  "point"   "economy"
[3,] "need"    "benefit" "make"   
[4,] "police"  "new"     "future" 
[5,] "ensure"  "take"    "people" 

tidy_model_gamma_15 <- tidy(topicModel15, matrix = "gamma")
tidy_model_gamma_15 <- tidy_model_gamma_15 %>%
  mutate(document = 
           mgsub::mgsub(string = document,
                        pattern = unique(tidy_model_gamma_15$document),
                        replacement = names(data_char_ukimmig2010),
                        fixed = TRUE))

ggplot(tidy_model_gamma_15) +
  geom_col(aes(x = topic, y = gamma)) +
  facet_wrap(~ document, nrow = 3)

Coherence and exclusivity

The package topicdoc provides diagnostic measures for topic models. They can be used to compare different models. Usually, models with a different number of topics are being compared.

topicModel_diag <- topic_diagnostics(topicModel, ukimmig2010_dtm)

A particularly useful and commonly-used metrics are semantic coherence and exclusivity. A good topic model should have coherent topics (i.e., about a single theme and not a mixture of different themes), which also are well distinguishable from each other, without overlaps (exclusivity).

topicModel_diag %>%
  mutate(topic = as_factor(topic_num)) %>%
  ggplot() +
  geom_point(aes(x = topic_coherence, y = topic_exclusivity, color = topic),
             size = 3) +
  ylab(label = "Semantic Coherence") +
  xlab("Exclusivity") +
  ggtitle("A topic model with 5 topics")

Held-out likelihood (perplexity)

Perplexity is a metric for the accuracy of a probability model in predicting a sample and can be used as a measure of a topic model’s ability to predict new data. The lower the perplexity, the better the model.

Topic models with different number of topics can be compared based on perplexity using cross-validation. This involves dividing data into subsets (usually 5), and using one subset as the validation set while using the remaining as the training set. This ensures that each data point has an equal opportunity of being part of the validation and training sets.

This method is useful in evaluating the overall performance of the model on unseen data and in determining optimal values for tuning the number of topics.

cluster <- makeCluster(detectCores(logical = TRUE) - 1) 
registerDoParallel(cluster)

clusterEvalQ(cluster, {
   library(topicmodels)
})

[[1]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[2]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[3]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[4]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[5]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[6]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

[[7]]
[1] "topicmodels" "stats"       "graphics"    "grDevices"   "utils"      
[6] "datasets"    "methods"     "base"       

burnin <- 1000
iter <- 1000
keep <- 50

full_data <- ukimmig2010_dtm
n <- nrow(full_data)
folds <- 5
splitfolds <- sample(1:folds, n, replace = TRUE)
candidate_k <- c(2, 5, 7, 10, 15, 20, 50, 100)

clusterExport(cluster, c("full_data", "burnin", "iter", "keep", "splitfolds", "folds", "candidate_k"))

# we parallelize by the different number of topics.  
# A processor is allocated a value of k, and does the cross-validation serially.  This is because it is assumed there are more candidate values of k than there are cross-validation folds, hence it will be more efficient to parallelise
system.time({
results <- foreach(j = 1:length(candidate_k), .combine = rbind) %dopar%{
   k <- candidate_k[j]
   results_1k <- matrix(0, nrow = folds, ncol = 2)
   colnames(results_1k) <- c("k", "perplexity")
   for(i in 1:folds){
      train_set <- full_data[splitfolds != i , ]
      valid_set <- full_data[splitfolds == i, ]
      
      fitted <- LDA(train_set, k = k, method = "Gibbs",
                    control = list(burnin = burnin, iter = iter, keep = keep) )
      results_1k[i,] <- c(k, perplexity(fitted, newdata = valid_set))
   }
   return(results_1k)
}
})

   user  system elapsed 
  0.018   0.001   3.589 

stopCluster(cluster)

results_df <- as.data.frame(results)

ggplot(results_df, aes(x = k, y = perplexity)) +
   geom_point() +
   geom_smooth(se = FALSE) +
   ggtitle("5-fold cross-validation") +
   labs(x = "Candidate number of topics", 
        y = "Perplexity when fitting the trained model to the hold-out set")

`geom_smooth()` using method = 'loess' and formula = 'y ~ x'

Structural Topic Models

usa_inaugural_df <- read.csv(file = "data/usa_inaugural_df.csv")

# load the udpipe English model
udpipe_english_model <- udpipe_load_model(file = "./english-ewt-ud-2.5-191206.udpipe")

# annotate the text
usa_inaugural_udpipe <- udpipe_annotate(udpipe_english_model, 
                                  x = usa_inaugural_df$text, 
                                  tagger = "default", 
                                  parser = "none") %>%
                  as.data.frame()

inaug_dfm <- usa_inaugural_df %>%
  corpus() %>%
  quanteda::tokens(remove_punct = TRUE,
         remove_symbols = TRUE,
         remove_numbers = TRUE) %>%
  tokens_tolower() %>%
  tokens_remove(stopwords("en")) %>%
  # lemmatization
  tokens_replace(
    pattern = usa_inaugural_udpipe$token, 
    replacement = usa_inaugural_udpipe$lemma,
    valuetype = "fixed") %>%
    dfm() %>%
    dfm_trim(min_docfreq = 0.5, max_docfreq = 0.99, 
           docfreq_type = "prop") %>%
  dfm_subset(ntoken(.) > 0)

inaug_stm_dfm <- convert(inaug_dfm, to = "stm")

out <- prepDocuments(inaug_stm_dfm$documents, 
                     inaug_stm_dfm$vocab, 
                     inaug_stm_dfm$meta)

Determine the number of topics

There is not a “right” answer to the number of topics that are appropriate for a given corpus, but the function searchK uses a data-driven approach to selecting the number of topics. The function will perform several automated tests to help choose the number of topics.

k_search <- searchK(out$documents, out$vocab, K = c(5, 10, 15, 20),
                    prevalence = ~s(Year) + Party, 
                    data = out$meta, init.type = "Spectral")

Beginning Spectral Initialization 
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Topic 1: shall, now, people, upon, government 
 Topic 2: we, america, world, new, nation 
 Topic 3: government, states, people, power, upon 
 Topic 4: war, nation, every, we, united 
 Topic 5: nation, can, man, must, world 
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Model Converged 
Beginning Spectral Initialization 
     Calculating the gram matrix...
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    .
Initialization complete.
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Topic 1: shall, now, take, office, oath 
 Topic 2: we, america, new, world, freedom 
 Topic 3: government, union, states, power, constitution 
 Topic 4: war, year, without, we, less 
 Topic 5: man, thing, nation, see, life 
 Topic 6: law, upon, can, people, may 
 Topic 7: we, responsibility, government, people, peace 
 Topic 8: government, country, people, great, every 
 Topic 9: nation, country, peace, united, resource 
 Topic 10: must, change, world, can, people 
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Topic 1: shall, now, take, constitution, office 
 Topic 2: we, america, new, world, freedom 
 Topic 3: government, union, power, states, constitution 
 Topic 4: war, year, we, less, force 
 Topic 5: thing, man, nation, see, we 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, responsibility, government, peace, world 
 Topic 8: country, government, great, every, people 
 Topic 9: nation, peace, country, freedom, justice 
 Topic 10: must, change, world, can, make 
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Topic 1: shall, now, constitution, take, office 
 Topic 2: we, america, new, time, world 
 Topic 3: union, government, power, states, constitution 
 Topic 4: war, year, force, we, less 
 Topic 5: thing, man, nation, we, great 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, responsibility, government, peace, world 
 Topic 8: country, government, every, great, people 
 Topic 9: nation, peace, country, freedom, can 
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Completing Iteration 20 (approx. per word bound = -4.898, relative change = 8.672e-05) 
Topic 1: shall, now, constitution, take, office 
 Topic 2: we, america, new, time, together 
 Topic 3: union, government, power, states, constitution 
 Topic 4: war, year, force, we, less 
 Topic 5: thing, man, nation, we, great 
 Topic 6: upon, law, people, government, public 
 Topic 7: we, responsibility, government, peace, world 
 Topic 8: country, every, government, great, united 
 Topic 9: nation, peace, freedom, country, free 
 Topic 10: must, change, can, world, make 
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Completing Iteration 25 (approx. per word bound = -4.896, relative change = 6.256e-05) 
Topic 1: shall, now, take, constitution, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, government, power, states, constitution 
 Topic 4: war, force, year, make, may 
 Topic 5: thing, man, nation, we, great 
 Topic 6: upon, law, people, government, public 
 Topic 7: we, responsibility, peace, government, world 
 Topic 8: country, every, government, great, united 
 Topic 9: nation, peace, freedom, world, country 
 Topic 10: must, can, change, make, world 
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Completing Iteration 30 (approx. per word bound = -4.895, relative change = 4.892e-05) 
Topic 1: shall, now, take, constitution, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, government, power, states, constitution 
 Topic 4: war, force, year, make, great 
 Topic 5: thing, man, nation, we, great 
 Topic 6: upon, law, people, government, public 
 Topic 7: we, responsibility, peace, government, world 
 Topic 8: country, every, government, great, united 
 Topic 9: nation, peace, freedom, world, free 
 Topic 10: must, can, change, make, world 
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Completing Iteration 35 (approx. per word bound = -4.894, relative change = 3.994e-05) 
Topic 1: shall, now, take, constitution, may 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, force, great, make, year 
 Topic 5: thing, man, nation, we, great 
 Topic 6: upon, law, people, government, public 
 Topic 7: we, responsibility, peace, world, government 
 Topic 8: country, every, government, great, united 
 Topic 9: nation, peace, freedom, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 40 (approx. per word bound = -4.893, relative change = 3.230e-05) 
Topic 1: shall, now, take, may, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, great 
 Topic 6: upon, law, people, government, public 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, every, government, great, united 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 45 (approx. per word bound = -4.892, relative change = 2.473e-05) 
Topic 1: shall, now, take, may, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, great 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, every, government, united, public 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 46 (approx. per word bound = -4.892, relative change = 2.380e-05) 
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Completing Iteration 50 (approx. per word bound = -4.892, relative change = 1.948e-05) 
Topic 1: shall, now, may, take, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, great 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, every, government, public, united 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 51 (approx. per word bound = -4.892, relative change = 1.853e-05) 
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Completing Iteration 55 (approx. per word bound = -4.891, relative change = 1.588e-05) 
Topic 1: shall, now, may, upon, office 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, great 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, every, government, public, united 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 60 (approx. per word bound = -4.891, relative change = 1.349e-05) 
Topic 1: shall, now, upon, may, can 
 Topic 2: we, america, time, new, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, great 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, world, responsibility, peace, government 
 Topic 8: country, every, government, public, citizen 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 65 (approx. per word bound = -4.891, relative change = 1.166e-05) 
Topic 1: shall, now, upon, may, can 
 Topic 2: we, america, new, time, people 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, life 
 Topic 6: law, upon, people, government, public 
 Topic 7: we, world, responsibility, peace, government 
 Topic 8: country, every, government, public, citizen 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 70 (approx. per word bound = -4.890, relative change = 1.087e-05) 
Topic 1: shall, now, upon, may, can 
 Topic 2: we, america, new, people, time 
 Topic 3: union, power, government, states, constitution 
 Topic 4: war, great, make, force, peace 
 Topic 5: thing, man, nation, we, life 
 Topic 6: law, people, government, upon, public 
 Topic 7: world, we, responsibility, peace, government 
 Topic 8: country, every, government, public, citizen 
 Topic 9: nation, freedom, peace, world, free 
 Topic 10: must, can, change, make, one 
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Completing Iteration 71 (approx. per word bound = -4.890, relative change = 1.104e-05) 
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Completing Iteration 72 (approx. per word bound = -4.890, relative change = 1.066e-05) 
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Model Converged 
Beginning Spectral Initialization 
     Calculating the gram matrix...
     Finding anchor words...
    ...............
     Recovering initialization...
    .
Initialization complete.
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Completing Iteration 1 (approx. per word bound = -4.941) 
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Completing Iteration 5 (approx. per word bound = -4.892, relative change = 1.029e-03) 
Topic 1: shall, chief, constitution, administration, subject 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, upon 
 Topic 4: war, year, every, part, without 
 Topic 5: thing, man, great, see, life 
 Topic 6: law, upon, people, can, may 
 Topic 7: we, responsibility, people, government, peace 
 Topic 8: country, government, great, people, protect 
 Topic 9: nation, country, resource, peace, justice 
 Topic 10: must, change, world, make, people 
 Topic 11: oath, now, take, shall, require 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, can, nation 
 Topic 14: power, citizen, government, duty, public 
 Topic 15: sense, people, government, find, united 
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Completing Iteration 6 (approx. per word bound = -4.889, relative change = 7.688e-04) 
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Completing Iteration 10 (approx. per word bound = -4.880, relative change = 3.262e-04) 
Topic 1: shall, administration, subject, chief, upon 
 Topic 2: we, america, new, together, nation 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, year, less, force, part 
 Topic 5: thing, man, great, nation, see 
 Topic 6: law, upon, people, can, may 
 Topic 7: we, responsibility, government, peace, world 
 Topic 8: country, great, government, states, people 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: must, change, world, make, can 
 Topic 11: now, oath, take, require, people 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, can, nation 
 Topic 14: power, citizen, may, every, principle 
 Topic 15: people, government, sense, find, states 
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Completing Iteration 11 (approx. per word bound = -4.879, relative change = 2.737e-04) 
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Completing Iteration 12 (approx. per word bound = -4.877, relative change = 2.335e-04) 
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Completing Iteration 13 (approx. per word bound = -4.876, relative change = 1.985e-04) 
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Completing Iteration 14 (approx. per word bound = -4.876, relative change = 1.728e-04) 
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Completing Iteration 15 (approx. per word bound = -4.875, relative change = 1.502e-04) 
Topic 1: shall, administration, subject, upon, chief 
 Topic 2: we, america, new, together, people 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, year, less, may 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, may, can 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: must, change, can, world, make 
 Topic 11: now, oath, take, people, require 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, can, man 
 Topic 14: power, citizen, may, every, principle 
 Topic 15: people, government, sense, states, spirit 
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Completing Iteration 16 (approx. per word bound = -4.874, relative change = 1.322e-04) 
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Completing Iteration 19 (approx. per word bound = -4.873, relative change = 9.702e-05) 
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Completing Iteration 20 (approx. per word bound = -4.872, relative change = 8.994e-05) 
Topic 1: shall, upon, chief, subject, administration 
 Topic 2: we, america, new, together, people 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, year, may, less 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, may, can 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: must, change, can, make, world 
 Topic 11: now, oath, take, people, require 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, can 
 Topic 14: power, citizen, may, every, principle 
 Topic 15: people, government, sense, states, spirit 
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Completing Iteration 21 (approx. per word bound = -4.872, relative change = 8.328e-05) 
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Completing Iteration 22 (approx. per word bound = -4.871, relative change = 7.691e-05) 
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Completing Iteration 23 (approx. per word bound = -4.871, relative change = 7.270e-05) 
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Completing Iteration 24 (approx. per word bound = -4.871, relative change = 6.877e-05) 
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Completing Iteration 25 (approx. per word bound = -4.870, relative change = 6.450e-05) 
Topic 1: shall, chief, upon, office, subject 
 Topic 2: we, america, new, together, people 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, may, year, purpose 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, may, public 
 Topic 7: we, responsibility, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, peace, can, resource 
 Topic 10: must, change, make, can, world 
 Topic 11: now, oath, can, people, take 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, nation 
 Topic 14: power, citizen, may, principle, every 
 Topic 15: people, government, sense, states, spirit 
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Completing Iteration 26 (approx. per word bound = -4.870, relative change = 6.079e-05) 
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Completing Iteration 27 (approx. per word bound = -4.870, relative change = 5.735e-05) 
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Completing Iteration 28 (approx. per word bound = -4.870, relative change = 5.400e-05) 
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Completing Iteration 29 (approx. per word bound = -4.869, relative change = 4.997e-05) 
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Completing Iteration 30 (approx. per word bound = -4.869, relative change = 4.627e-05) 
Topic 1: shall, chief, upon, office, may 
 Topic 2: we, america, new, together, people 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, may, year, make 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, may, public 
 Topic 7: responsibility, we, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, peace, can, resource 
 Topic 10: must, change, make, can, world 
 Topic 11: now, oath, can, people, question 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, nation 
 Topic 14: power, citizen, principle, may, every 
 Topic 15: people, government, sense, states, spirit 
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Completing Iteration 31 (approx. per word bound = -4.869, relative change = 4.234e-05) 
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Completing Iteration 32 (approx. per word bound = -4.869, relative change = 3.971e-05) 
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Completing Iteration 33 (approx. per word bound = -4.869, relative change = 3.604e-05) 
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Completing Iteration 34 (approx. per word bound = -4.868, relative change = 3.322e-05) 
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Completing Iteration 35 (approx. per word bound = -4.868, relative change = 3.030e-05) 
Topic 1: shall, upon, chief, office, may 
 Topic 2: we, america, new, together, people 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, may, make, year 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, public, may 
 Topic 7: responsibility, we, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, can, peace, resource 
 Topic 10: must, change, make, can, world 
 Topic 11: now, can, oath, people, question 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, nation 
 Topic 14: power, citizen, principle, every, may 
 Topic 15: people, government, sense, states, spirit 
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Completing Iteration 36 (approx. per word bound = -4.868, relative change = 2.780e-05) 
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Completing Iteration 37 (approx. per word bound = -4.868, relative change = 2.576e-05) 
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Completing Iteration 38 (approx. per word bound = -4.868, relative change = 2.359e-05) 
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Completing Iteration 39 (approx. per word bound = -4.868, relative change = 2.159e-05) 
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Completing Iteration 40 (approx. per word bound = -4.868, relative change = 2.053e-05) 
Topic 1: shall, upon, may, chief, office 
 Topic 2: we, america, new, people, together 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, make, may, year 
 Topic 5: thing, man, great, nation, life 
 Topic 6: law, upon, people, public, government 
 Topic 7: responsibility, we, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, country, can, peace, resource 
 Topic 10: must, change, make, can, world 
 Topic 11: now, can, oath, one, people 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, nation 
 Topic 14: power, citizen, principle, every, may 
 Topic 15: people, government, sense, spirit, states 
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Completing Iteration 41 (approx. per word bound = -4.868, relative change = 1.859e-05) 
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Completing Iteration 42 (approx. per word bound = -4.868, relative change = 1.745e-05) 
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Completing Iteration 43 (approx. per word bound = -4.867, relative change = 1.626e-05) 
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Completing Iteration 44 (approx. per word bound = -4.867, relative change = 1.544e-05) 
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Completing Iteration 45 (approx. per word bound = -4.867, relative change = 1.496e-05) 
Topic 1: shall, upon, may, office, chief 
 Topic 2: we, america, new, people, together 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, force, make, may, year 
 Topic 5: thing, man, great, nation, life 
 Topic 6: upon, law, people, public, government 
 Topic 7: responsibility, we, world, peace, government 
 Topic 8: country, great, government, states, united 
 Topic 9: nation, can, country, peace, resource 
 Topic 10: must, change, make, can, world 
 Topic 11: now, can, oath, one, question 
 Topic 12: freedom, world, nation, free, know 
 Topic 13: we, let, ask, man, nation 
 Topic 14: power, citizen, every, principle, may 
 Topic 15: people, government, sense, spirit, states 
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Completed E-Step (0 seconds). 
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Completing Iteration 46 (approx. per word bound = -4.867, relative change = 1.324e-05) 
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Completing Iteration 47 (approx. per word bound = -4.867, relative change = 1.200e-05) 
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Completing Iteration 48 (approx. per word bound = -4.867, relative change = 1.219e-05) 
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Completing Iteration 49 (approx. per word bound = -4.867, relative change = 1.077e-05) 
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Model Converged 
Beginning Spectral Initialization 
     Calculating the gram matrix...
     Finding anchor words...
    ....................
     Recovering initialization...
    .
Initialization complete.
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Completed E-Step (0 seconds). 
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Completing Iteration 1 (approx. per word bound = -4.939) 
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Completing Iteration 2 (approx. per word bound = -4.909, relative change = 6.111e-03) 
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Completing Iteration 3 (approx. per word bound = -4.894, relative change = 3.001e-03) 
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Completing Iteration 4 (approx. per word bound = -4.885, relative change = 1.857e-03) 
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Completing Iteration 5 (approx. per word bound = -4.879, relative change = 1.296e-03) 
Topic 1: shall, chief, constitution, president, subject 
 Topic 2: america, new, we, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, year, every, without, just 
 Topic 5: thing, man, see, life, nation 
 Topic 6: people, rule, may, can, law 
 Topic 7: responsibility, we, peace, world, home 
 Topic 8: country, protect, people, every, government 
 Topic 9: nation, country, resource, justice, peace 
 Topic 10: must, change, world, new, old 
 Topic 11: oath, now, shall, take, office 
 Topic 12: freedom, world, nation, know, free 
 Topic 13: we, let, ask, nation, can 
 Topic 14: public, power, duty, citizen, every 
 Topic 15: sense, people, find, government, united 
 Topic 16: upon, law, question, government, country 
 Topic 17: shall, law, can, provide, may 
 Topic 18: power, government, since, great, united 
 Topic 19: much, one, can, people, great 
 Topic 20: people, government, we, must, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 6 (approx. per word bound = -4.874, relative change = 9.809e-04) 
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Completing Iteration 7 (approx. per word bound = -4.870, relative change = 7.775e-04) 
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Completing Iteration 8 (approx. per word bound = -4.867, relative change = 6.324e-04) 
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Completing Iteration 9 (approx. per word bound = -4.864, relative change = 5.200e-04) 
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Completing Iteration 10 (approx. per word bound = -4.862, relative change = 4.308e-04) 
Topic 1: shall, chief, constitution, president, country 
 Topic 2: america, new, we, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, less, year, every, just 
 Topic 5: thing, man, life, see, nation 
 Topic 6: people, rule, may, law, upon 
 Topic 7: responsibility, we, peace, world, home 
 Topic 8: country, protect, every, people, one 
 Topic 9: nation, country, resource, peace, can 
 Topic 10: must, change, world, old, new 
 Topic 11: now, oath, take, shall, office 
 Topic 12: freedom, world, nation, know, free 
 Topic 13: we, ask, let, can, man 
 Topic 14: power, public, duty, citizen, character 
 Topic 15: people, government, sense, find, spirit 
 Topic 16: upon, law, question, government, country 
 Topic 17: shall, law, make, can, provide 
 Topic 18: great, power, united, since, states 
 Topic 19: much, can, one, people, great 
 Topic 20: we, people, must, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 11 (approx. per word bound = -4.860, relative change = 3.566e-04) 
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Completing Iteration 12 (approx. per word bound = -4.859, relative change = 2.963e-04) 
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Completing Iteration 13 (approx. per word bound = -4.858, relative change = 2.484e-04) 
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Completing Iteration 14 (approx. per word bound = -4.857, relative change = 2.098e-04) 
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Completing Iteration 15 (approx. per word bound = -4.856, relative change = 1.767e-04) 
Topic 1: shall, chief, constitution, country, president 
 Topic 2: america, new, we, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, less, every, year, give 
 Topic 5: thing, man, nation, life, great 
 Topic 6: people, rule, may, free, upon 
 Topic 7: responsibility, we, peace, world, home 
 Topic 8: country, every, protect, people, one 
 Topic 9: nation, country, resource, can, peace 
 Topic 10: change, must, old, world, new 
 Topic 11: now, oath, take, shall, office 
 Topic 12: freedom, world, nation, know, free 
 Topic 13: we, ask, let, can, man 
 Topic 14: power, public, duty, citizen, character 
 Topic 15: people, government, sense, spirit, find 
 Topic 16: upon, question, law, government, public 
 Topic 17: law, shall, make, may, provide 
 Topic 18: great, united, since, power, states 
 Topic 19: can, much, one, people, great 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 16 (approx. per word bound = -4.855, relative change = 1.504e-04) 
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Completing Iteration 17 (approx. per word bound = -4.855, relative change = 1.283e-04) 
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Completing Iteration 18 (approx. per word bound = -4.854, relative change = 1.090e-04) 
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Completing Iteration 19 (approx. per word bound = -4.854, relative change = 9.356e-05) 
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Completing Iteration 20 (approx. per word bound = -4.853, relative change = 8.160e-05) 
Topic 1: shall, chief, may, constitution, country 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, less, every, give, year 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, people, may, free, upon 
 Topic 7: responsibility, world, peace, we, home 
 Topic 8: country, every, protect, one, people 
 Topic 9: nation, country, resource, can, peace 
 Topic 10: change, must, old, world, new 
 Topic 11: now, oath, take, people, office 
 Topic 12: freedom, world, nation, know, must 
 Topic 13: we, ask, let, man, can 
 Topic 14: power, public, duty, citizen, character 
 Topic 15: people, government, sense, spirit, find 
 Topic 16: upon, question, law, government, public 
 Topic 17: law, shall, make, may, government 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, right 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 21 (approx. per word bound = -4.853, relative change = 6.842e-05) 
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Completing Iteration 22 (approx. per word bound = -4.853, relative change = 6.054e-05) 
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Completing Iteration 23 (approx. per word bound = -4.852, relative change = 5.349e-05) 
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Completing Iteration 24 (approx. per word bound = -4.852, relative change = 4.630e-05) 
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Completing Iteration 25 (approx. per word bound = -4.852, relative change = 4.200e-05) 
Topic 1: shall, chief, may, country, constitution 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, less, give, every, nation 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, people, may, free, upon 
 Topic 7: responsibility, world, peace, we, home 
 Topic 8: country, every, protect, one, people 
 Topic 9: nation, country, resource, peace, can 
 Topic 10: change, must, old, world, new 
 Topic 11: now, oath, take, people, office 
 Topic 12: freedom, world, nation, must, know 
 Topic 13: we, ask, let, man, can 
 Topic 14: power, public, duty, character, citizen 
 Topic 15: people, government, sense, spirit, find 
 Topic 16: upon, question, law, government, country 
 Topic 17: law, shall, make, may, government 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, right 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 26 (approx. per word bound = -4.852, relative change = 3.823e-05) 
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Completing Iteration 27 (approx. per word bound = -4.852, relative change = 3.372e-05) 
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Completing Iteration 28 (approx. per word bound = -4.851, relative change = 3.084e-05) 
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Completing Iteration 29 (approx. per word bound = -4.851, relative change = 2.797e-05) 
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Completing Iteration 30 (approx. per word bound = -4.851, relative change = 2.635e-05) 
Topic 1: shall, chief, may, country, measure 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, less, give, shall, nation 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, people, free, may, upon 
 Topic 7: responsibility, world, peace, we, home 
 Topic 8: country, every, protect, one, people 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, world, man 
 Topic 11: now, oath, take, people, office 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, man, can 
 Topic 14: power, public, character, duty, citizen 
 Topic 15: people, government, sense, spirit, find 
 Topic 16: upon, question, government, country, law 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 31 (approx. per word bound = -4.851, relative change = 2.304e-05) 
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Completing Iteration 32 (approx. per word bound = -4.851, relative change = 2.241e-05) 
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Completing Iteration 33 (approx. per word bound = -4.851, relative change = 2.080e-05) 
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Completing Iteration 34 (approx. per word bound = -4.851, relative change = 1.974e-05) 
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Completing Iteration 35 (approx. per word bound = -4.851, relative change = 1.778e-05) 
Topic 1: shall, chief, may, measure, present 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, less, give, nation 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, people, may, upon 
 Topic 7: responsibility, world, peace, we, must 
 Topic 8: country, every, protect, one, people 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, man, way 
 Topic 11: now, oath, take, people, office 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, man, peace 
 Topic 14: power, public, character, duty, citizen 
 Topic 15: people, government, sense, spirit, states 
 Topic 16: upon, question, country, government, public 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 36 (approx. per word bound = -4.851, relative change = 1.777e-05) 
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Completing Iteration 37 (approx. per word bound = -4.850, relative change = 1.723e-05) 
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Completing Iteration 38 (approx. per word bound = -4.850, relative change = 1.674e-05) 
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Completing Iteration 39 (approx. per word bound = -4.850, relative change = 1.522e-05) 
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Completing Iteration 40 (approx. per word bound = -4.850, relative change = 1.490e-05) 
Topic 1: shall, chief, may, measure, present 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, give, nation, year 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, people, may, upon 
 Topic 7: responsibility, world, peace, we, must 
 Topic 8: country, every, protect, one, people 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, man, nation 
 Topic 11: now, oath, take, people, office 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, peace, man 
 Topic 14: power, public, character, duty, citizen 
 Topic 15: people, government, sense, upon, public 
 Topic 16: upon, question, country, government, public 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 41 (approx. per word bound = -4.850, relative change = 1.509e-05) 
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Completing Iteration 42 (approx. per word bound = -4.850, relative change = 1.505e-05) 
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Completing Iteration 43 (approx. per word bound = -4.850, relative change = 1.375e-05) 
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Completing Iteration 44 (approx. per word bound = -4.850, relative change = 1.370e-05) 
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Completing Iteration 45 (approx. per word bound = -4.850, relative change = 1.462e-05) 
Topic 1: shall, chief, may, measure, present 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, year, nation, give 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, people, may, peace 
 Topic 7: responsibility, world, peace, we, must 
 Topic 8: country, every, protect, one, citizen 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, man, nation 
 Topic 11: now, oath, people, take, office 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, peace, man 
 Topic 14: power, public, character, duty, citizen 
 Topic 15: people, government, sense, upon, public 
 Topic 16: upon, question, country, government, public 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, people, government, economy 
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Completed E-Step (0 seconds). 
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Completing Iteration 46 (approx. per word bound = -4.850, relative change = 1.445e-05) 
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Completing Iteration 47 (approx. per word bound = -4.850, relative change = 1.441e-05) 
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Completing Iteration 48 (approx. per word bound = -4.850, relative change = 1.392e-05) 
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Completing Iteration 49 (approx. per word bound = -4.850, relative change = 1.300e-05) 
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Completing Iteration 50 (approx. per word bound = -4.850, relative change = 1.428e-05) 
Topic 1: shall, chief, may, measure, day 
 Topic 2: america, we, new, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, year, nation, give 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, people, may, peace 
 Topic 7: responsibility, world, peace, must, we 
 Topic 8: country, every, protect, one, citizen 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, man, nation 
 Topic 11: now, oath, people, take, office 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, peace, man 
 Topic 14: power, public, character, duty, principle 
 Topic 15: people, government, sense, upon, public 
 Topic 16: upon, question, country, government, public 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, people, economy, government 
...........................................................
Completed E-Step (0 seconds). 
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Completing Iteration 51 (approx. per word bound = -4.850, relative change = 1.273e-05) 
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...........................................................
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Completing Iteration 55 (approx. per word bound = -4.849, relative change = 1.145e-05) 
Topic 1: shall, chief, may, measure, day 
 Topic 2: america, new, we, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, year, nation, give 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, may, people, peace 
 Topic 7: responsibility, world, peace, must, we 
 Topic 8: country, every, protect, one, citizen 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, old, man, nation 
 Topic 11: now, oath, people, take, united 
 Topic 12: freedom, world, nation, must, live 
 Topic 13: ask, we, let, peace, man 
 Topic 14: power, public, character, principle, duty 
 Topic 15: people, government, upon, sense, public 
 Topic 16: upon, question, country, government, public 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, make 
 Topic 20: we, must, economy, people, government 
...........................................................
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Completing Iteration 60 (approx. per word bound = -4.849, relative change = 1.123e-05) 
Topic 1: shall, chief, may, measure, day 
 Topic 2: america, new, we, together, world 
 Topic 3: union, government, states, constitution, power 
 Topic 4: war, shall, year, nation, give 
 Topic 5: thing, man, nation, life, great 
 Topic 6: rule, free, may, peace, people 
 Topic 7: responsibility, world, peace, must, we 
 Topic 8: country, every, protect, one, citizen 
 Topic 9: nation, country, peace, resource, can 
 Topic 10: change, must, man, old, nation 
 Topic 11: now, oath, people, take, united 
 Topic 12: freedom, world, nation, live, must 
 Topic 13: ask, we, let, peace, man 
 Topic 14: power, public, character, principle, may 
 Topic 15: people, government, upon, sense, public 
 Topic 16: upon, question, country, public, government 
 Topic 17: law, shall, make, government, may 
 Topic 18: great, since, united, states, power 
 Topic 19: can, much, one, people, great 
 Topic 20: we, must, economy, government, people 
...........................................................
Completed E-Step (0 seconds). 
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Model Converged 

plot.searchK(k_search)

k_search

$results
   K   exclus    semcoh   heldout residual     bound    lbound em.its
1  5 8.782945 -7.944008 -4.960393 1.624187   -117078 -117073.2     48
2 10 9.285102 -11.98722 -4.967642 1.532483 -116254.2 -116239.1     73
3 15  9.29123 -11.69239 -5.034053 1.615663 -115704.1 -115676.2     50
4 20 9.328248 -12.40123  -5.00695 1.760186 -115273.8 -115231.5     61

$call
searchK(documents = out$documents, vocab = out$vocab, K = c(5, 
    10, 15, 20), init.type = "Spectral", prevalence = ~s(Year) + 
    Party, data = out$meta)

attr(,"class")
[1] "searchK"

k_search$results %>%
  select(K, exclus, semcoh) %>%
  mutate(K = unlist(K),
         exclus = unlist(exclus),
         semcoh = unlist(semcoh)) %>%
  mutate(K = as_factor(K)) %>%
  ggplot() +
  geom_point(aes(x = exclus, y = semcoh, color = K), size = 5) +
  ggtitle("Semantic Coherence vs Exclusivity") +
  ylab("Semantic Coherence") +
  xlab("Exclusivity")

If init.type="Spectral" you can also set K=0 to use the algorithm of Lee and Mimno (2014) to set the number of topics

inaug_stm_fit <- stm(documents = out$documents, 
                     vocab = out$vocab,
                     data = out$meta,
                     K = 9, 
                     prevalence = ~s(Year) + Party, 
                     init.type = "Spectral")

Beginning Spectral Initialization 
     Calculating the gram matrix...
     Finding anchor words...
    .........
     Recovering initialization...
    .
Initialization complete.
...........................................................
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Completing Iteration 1 (approx. per word bound = -4.944) 
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Completing Iteration 5 (approx. per word bound = -4.912, relative change = 5.865e-04) 
Topic 1: shall, now, upon, oath, may 
 Topic 2: we, america, new, let, together 
 Topic 3: government, country, public, states, people 
 Topic 4: war, nation, year, without, force 
 Topic 5: thing, man, great, nation, upon 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: we, responsibility, government, people, can 
 Topic 8: must, change, make, can, people 
 Topic 9: union, government, states, power, constitution 
...........................................................
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Completing Iteration 10 (approx. per word bound = -4.904, relative change = 2.227e-04) 
Topic 1: shall, upon, now, people, oath 
 Topic 2: we, america, new, let, world 
 Topic 3: government, country, public, states, people 
 Topic 4: war, nation, year, force, we 
 Topic 5: thing, man, nation, great, see 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: we, government, responsibility, people, peace 
 Topic 8: must, change, make, can, world 
 Topic 9: union, government, power, states, constitution 
...........................................................
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Completing Iteration 15 (approx. per word bound = -4.900, relative change = 1.362e-04) 
Topic 1: shall, upon, law, now, people 
 Topic 2: we, america, new, let, time 
 Topic 3: government, country, public, states, people 
 Topic 4: war, nation, year, force, united 
 Topic 5: thing, man, nation, see, great 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, people, peace 
 Topic 8: must, can, change, make, world 
 Topic 9: union, power, government, states, constitution 
...........................................................
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Completing Iteration 19 (approx. per word bound = -4.898, relative change = 8.397e-05) 
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Completing Iteration 20 (approx. per word bound = -4.898, relative change = 7.453e-05) 
Topic 1: shall, upon, law, people, now 
 Topic 2: we, america, new, let, time 
 Topic 3: government, country, public, states, people 
 Topic 4: war, great, nation, force, year 
 Topic 5: thing, man, nation, see, life 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, people 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, states, constitution 
...........................................................
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Completing Iteration 21 (approx. per word bound = -4.898, relative change = 6.636e-05) 
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Completing Iteration 25 (approx. per word bound = -4.897, relative change = 4.497e-05) 
Topic 1: shall, upon, law, people, now 
 Topic 2: we, america, new, time, let 
 Topic 3: government, country, public, states, every 
 Topic 4: war, great, nation, force, united 
 Topic 5: thing, man, nation, see, life 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, must 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 26 (approx. per word bound = -4.896, relative change = 4.137e-05) 
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Completing Iteration 30 (approx. per word bound = -4.896, relative change = 3.169e-05) 
Topic 1: upon, shall, law, people, now 
 Topic 2: we, america, new, time, let 
 Topic 3: government, country, public, every, states 
 Topic 4: war, great, nation, make, united 
 Topic 5: thing, man, nation, see, life 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, world 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 35 (approx. per word bound = -4.895, relative change = 2.348e-05) 
Topic 1: upon, shall, law, people, now 
 Topic 2: we, america, new, time, world 
 Topic 3: government, country, public, every, people 
 Topic 4: war, great, make, united, force 
 Topic 5: thing, man, nation, see, life 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, world 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 40 (approx. per word bound = -4.895, relative change = 1.779e-05) 
Topic 1: upon, shall, law, people, now 
 Topic 2: we, america, new, time, world 
 Topic 3: government, country, public, every, citizen 
 Topic 4: war, great, make, united, force 
 Topic 5: thing, man, nation, life, see 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, world 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 45 (approx. per word bound = -4.894, relative change = 1.342e-05) 
Topic 1: upon, law, shall, people, now 
 Topic 2: we, america, new, time, world 
 Topic 3: country, government, public, every, citizen 
 Topic 4: war, great, make, united, force 
 Topic 5: thing, man, nation, life, see 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, world 
 Topic 8: must, can, change, make, one 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 50 (approx. per word bound = -4.894, relative change = 1.062e-05) 
Topic 1: upon, law, shall, people, now 
 Topic 2: we, america, new, time, world 
 Topic 3: country, government, public, every, citizen 
 Topic 4: war, great, make, united, force 
 Topic 5: thing, man, nation, see, life 
 Topic 6: freedom, nation, world, free, peace 
 Topic 7: government, we, responsibility, peace, world 
 Topic 8: must, can, change, make, government 
 Topic 9: union, power, government, constitution, states 
...........................................................
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Completing Iteration 51 (approx. per word bound = -4.894, relative change = 1.035e-05) 
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Completing Iteration 52 (approx. per word bound = -4.894, relative change = 1.016e-05) 
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Completed E-Step (0 seconds). 
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Model Converged 

Estimate effects

It is then possible to analyze the results. In this case, by checking the variation in topic prevalence over time, and by party.

estimate_inaug <- estimateEffect(1:9 ~ s(Year) + Party,
                                 inaug_stm_fit,
                                 meta = out$meta,
                                 uncertainty = "Global")
# summary(year_topic, topics = 1)

par(mfrow=c(3,3))
for(i in 1:9){
  plot(
  estimate_inaug,
  covariate = "Year",
  method = "continuous",
  topics = i,
  model = inaug_stm_fit,
  printlegend = FALSE,
  xlab = "Time")
}

---

par(mfrow = c(3, 3))
for(i in 1:9){
  plot.estimateEffect(
  estimate_inaug,
  covariate = "Party",
  method = "difference",
  cov.value1 = "Democratic",
  cov.value2 = "Republican",
  topics = i,
  model = inaug_stm_fit,
  printlegend = FALSE,
  xlab = "← Republican     Democratic →",
  main = "Democratic vs Republican (D-R)",
  xlim = c(-0.2, 0.2),
  cex = 0.5,
  labeltype = "custom",
  custom.labels = c("", "")
)
}

Estimates

The result can be read as a regression model.

summary(estimate_inaug)

Call:
estimateEffect(formula = 1:9 ~ s(Year) + Party, stmobj = inaug_stm_fit, 
    metadata = out$meta, uncertainty = "Global")


Topic 1:

Coefficients:
                             Estimate Std. Error t value Pr(>|t|)   
(Intercept)                -0.6560642  0.2999152  -2.187  0.03419 * 
s(Year)1                    0.9657122  0.3717516   2.598  0.01280 * 
s(Year)2                    0.6685440  0.3153818   2.120  0.03983 * 
s(Year)3                    0.7169954  0.3254208   2.203  0.03298 * 
s(Year)4                    1.0737266  0.3139968   3.420  0.00138 **
s(Year)5                    0.8424747  0.3212461   2.623  0.01203 * 
s(Year)6                    0.6791383  0.3041562   2.233  0.03082 * 
s(Year)7                    0.7288687  0.3114955   2.340  0.02400 * 
s(Year)8                    0.6185376  0.3128653   1.977  0.05448 . 
s(Year)9                    0.7332742  0.3126560   2.345  0.02370 * 
s(Year)10                   0.6863272  0.3074015   2.233  0.03083 * 
PartyDemocratic-Republican -0.0778787  0.0994000  -0.783  0.43763   
PartyFederalist             0.1195849  0.1499224   0.798  0.42946   
Partynone                   0.7672243  0.2803215   2.737  0.00898 **
PartyRepublican             0.0006405  0.0281950   0.023  0.98198   
PartyWhig                   0.0247918  0.0642640   0.386  0.70156   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Topic 2:

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)  
(Intercept)                 0.159194   0.275049   0.579   0.5658  
s(Year)1                   -0.092249   0.310864  -0.297   0.7681  
s(Year)2                   -0.164481   0.273439  -0.602   0.5506  
s(Year)3                   -0.122783   0.312284  -0.393   0.6961  
s(Year)4                   -0.098119   0.281270  -0.349   0.7289  
s(Year)5                   -0.073466   0.290830  -0.253   0.8018  
s(Year)6                   -0.060987   0.282222  -0.216   0.8299  
s(Year)7                    0.057262   0.296491   0.193   0.8478  
s(Year)8                    0.594031   0.304308   1.952   0.0575 .
s(Year)9                    0.046384   0.301654   0.154   0.8785  
s(Year)10                   0.518333   0.287353   1.804   0.0783 .
PartyDemocratic-Republican -0.008223   0.100854  -0.082   0.9354  
PartyFederalist            -0.068284   0.162362  -0.421   0.6762  
Partynone                  -0.120181   0.235861  -0.510   0.6130  
PartyRepublican            -0.070150   0.036009  -1.948   0.0579 .
PartyWhig                  -0.025729   0.065478  -0.393   0.6963  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Topic 3:

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)  
(Intercept)                 0.89739    0.50796   1.767   0.0844 .
s(Year)1                   -0.57591    0.58753  -0.980   0.3325  
s(Year)2                    0.07553    0.52506   0.144   0.8863  
s(Year)3                   -0.97702    0.56196  -1.739   0.0893 .
s(Year)4                   -0.44988    0.51076  -0.881   0.3833  
s(Year)5                   -0.78101    0.52481  -1.488   0.1440  
s(Year)6                   -0.80381    0.51485  -1.561   0.1258  
s(Year)7                   -0.88691    0.52150  -1.701   0.0962 .
s(Year)8                   -0.86330    0.52334  -1.650   0.1063  
s(Year)9                   -0.71904    0.52677  -1.365   0.1794  
s(Year)10                  -0.83511    0.52123  -1.602   0.1164  
PartyDemocratic-Republican -0.18159    0.18610  -0.976   0.3346  
PartyFederalist             0.01745    0.30671   0.057   0.9549  
Partynone                  -0.37717    0.41122  -0.917   0.3642  
PartyRepublican            -0.02725    0.04284  -0.636   0.5282  
PartyWhig                   0.08192    0.11245   0.728   0.4703  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Topic 4:

Coefficients:
                           Estimate Std. Error t value Pr(>|t|)  
(Intercept)                -0.41019    0.33566  -1.222   0.2283  
s(Year)1                    0.13105    0.38345   0.342   0.7342  
s(Year)2                    0.47780    0.33686   1.418   0.1633  
s(Year)3                    0.46778    0.37991   1.231   0.2249  
s(Year)4                    0.56383    0.34830   1.619   0.1128  
s(Year)5                    0.39631    0.35063   1.130   0.2646  
s(Year)6                    0.46536    0.34506   1.349   0.1845  
s(Year)7                    0.44604    0.35054   1.272   0.2101  
s(Year)8                    0.42641    0.35410   1.204   0.2351  
s(Year)9                    0.41181    0.35459   1.161   0.2519  
s(Year)10                   0.47667    0.34950   1.364   0.1797  
PartyDemocratic-Republican  0.29777    0.13150   2.264   0.0286 *
PartyFederalist             0.30649    0.20591   1.488   0.1439  
Partynone                   0.40160    0.28898   1.390   0.1718  
PartyRepublican             0.02766    0.03288   0.841   0.4048  
PartyWhig                  -0.04556    0.08050  -0.566   0.5743  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


Topic 5:

Coefficients:
                             Estimate Std. Error t value Pr(>|t|)
(Intercept)                 0.3374745  0.4975994   0.678    0.501
s(Year)1                   -0.1323070  0.5492672  -0.241    0.811
s(Year)2                   -0.4817526  0.4983039  -0.967    0.339
s(Year)3                   -0.0744738  0.5670069  -0.131    0.896
s(Year)4                   -0.3888787  0.5040379  -0.772    0.445
s(Year)5                   -0.0006305  0.5321625  -0.001    0.999
s(Year)6                   -0.0066862  0.5116620  -0.013    0.990
s(Year)7                   -0.2903559  0.5197831  -0.559    0.579
s(Year)8                   -0.1463314  0.5268193  -0.278    0.783
s(Year)9                   -0.2777969  0.5277732  -0.526    0.601
s(Year)10                  -0.1956399  0.5140284  -0.381    0.705
PartyDemocratic-Republican -0.0118565  0.1774551  -0.067    0.947
PartyFederalist            -0.1412754  0.2999661  -0.471    0.640
Partynone                  -0.2698651  0.4269787  -0.632    0.531
PartyRepublican            -0.0726179  0.0497082  -1.461    0.151
PartyWhig                  -0.0924995  0.1172027  -0.789    0.434


Topic 6:

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                 0.186685   0.418899   0.446    0.658
s(Year)1                   -0.003462   0.471555  -0.007    0.994
s(Year)2                   -0.190691   0.421232  -0.453    0.653
s(Year)3                   -0.159271   0.474074  -0.336    0.739
s(Year)4                   -0.220197   0.426641  -0.516    0.608
s(Year)5                   -0.241876   0.440493  -0.549    0.586
s(Year)6                   -0.065019   0.429880  -0.151    0.880
s(Year)7                    0.398757   0.442540   0.901    0.373
s(Year)8                   -0.572770   0.447366  -1.280    0.207
s(Year)9                    0.407283   0.455279   0.895    0.376
s(Year)10                  -0.289771   0.432293  -0.670    0.506
PartyDemocratic-Republican -0.008977   0.151854  -0.059    0.953
PartyFederalist            -0.075178   0.254177  -0.296    0.769
Partynone                  -0.168644   0.359689  -0.469    0.642
PartyRepublican             0.068664   0.043387   1.583    0.121
PartyWhig                   0.010496   0.098449   0.107    0.916


Topic 7:

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                 0.096747   0.379711   0.255    0.800
s(Year)1                    0.018962   0.429947   0.044    0.965
s(Year)2                   -0.046506   0.378933  -0.123    0.903
s(Year)3                    0.010050   0.438249   0.023    0.982
s(Year)4                   -0.107207   0.390743  -0.274    0.785
s(Year)5                    0.107546   0.404945   0.266    0.792
s(Year)6                   -0.072010   0.393124  -0.183    0.856
s(Year)7                   -0.042701   0.398436  -0.107    0.915
s(Year)8                    0.174676   0.407118   0.429    0.670
s(Year)9                   -0.236162   0.404217  -0.584    0.562
s(Year)10                  -0.042249   0.391550  -0.108    0.915
PartyDemocratic-Republican -0.045572   0.147148  -0.310    0.758
PartyFederalist            -0.078189   0.226204  -0.346    0.731
Partynone                  -0.081952   0.325836  -0.252    0.803
PartyRepublican             0.033166   0.040568   0.818    0.418
PartyWhig                  -0.003141   0.094894  -0.033    0.974


Topic 8:

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                 0.058007   0.346890   0.167    0.868
s(Year)1                   -0.054100   0.398536  -0.136    0.893
s(Year)2                   -0.110797   0.345581  -0.321    0.750
s(Year)3                    0.074318   0.395220   0.188    0.852
s(Year)4                   -0.109914   0.354446  -0.310    0.758
s(Year)5                    0.096857   0.367451   0.264    0.793
s(Year)6                    0.199124   0.356652   0.558    0.580
s(Year)7                   -0.093319   0.361749  -0.258    0.798
s(Year)8                    0.046202   0.373882   0.124    0.902
s(Year)9                   -0.047498   0.369585  -0.129    0.898
s(Year)10                  -0.019955   0.357884  -0.056    0.956
PartyDemocratic-Republican  0.032947   0.127849   0.258    0.798
PartyFederalist            -0.007213   0.202854  -0.036    0.972
Partynone                   0.025119   0.294464   0.085    0.932
PartyRepublican             0.034428   0.035829   0.961    0.342
PartyWhig                  -0.049514   0.082733  -0.598    0.553


Topic 9:

Coefficients:
                            Estimate Std. Error t value Pr(>|t|)
(Intercept)                 0.333138   0.355843   0.936    0.354
s(Year)1                   -0.262287   0.394364  -0.665    0.510
s(Year)2                   -0.227670   0.368189  -0.618    0.540
s(Year)3                    0.058907   0.412951   0.143    0.887
s(Year)4                   -0.266731   0.357028  -0.747    0.459
s(Year)5                   -0.346621   0.370819  -0.935    0.355
s(Year)6                   -0.334761   0.361622  -0.926    0.360
s(Year)7                   -0.319509   0.367711  -0.869    0.390
s(Year)8                   -0.282890   0.371225  -0.762    0.450
s(Year)9                   -0.318967   0.372158  -0.857    0.396
s(Year)10                  -0.301906   0.364843  -0.827    0.413
PartyDemocratic-Republican  0.003670   0.141389   0.026    0.979
PartyFederalist            -0.070476   0.220473  -0.320    0.751
Partynone                  -0.176665   0.301264  -0.586    0.561
PartyRepublican             0.005748   0.031769   0.181    0.857
PartyWhig                   0.098983   0.110352   0.897    0.375

Interpretation

The eight topic looks slightly more prevalent in Democrats than Republican inaugural addresses.

labelTopics(inaug_stm_fit, 8)

Topic 8 Top Words:
     Highest Prob: must, can, change, make, government, one, great 
     FREX: change, must, old, action, order, among, continue 
     Lift: change, old, order, action, hold, continue, maintain 
     Score: change, old, must, america, action, policy, order 

plot(inaug_stm_fit, type = "summary", xlim = c(0, 0.5))

thoughts8 <- findThoughts(inaug_stm_fit,
                          texts = usa_inaugural_df$text,
                          n = 2,
                          topics = 8)$docs[[1]]

plotQuote(thoughts8, width = 30, main = "Topic 6")

inaug_stm_fit_corr <- topicCorr(inaug_stm_fit)
plot(inaug_stm_fit_corr)

Seeded Topic Models

guardian <- read.csv("http://www.luigicurini.com/uploads/6/7/9/8/67985527/guardian.csv")

Create a small dictionary of keywords (seed words) to define the desired topics.

imm_frames <- dictionary(list(securitarian = c("control", "border", 
                                               "police", "detention",
                                               "illegal", "legal"),
                        humanitarian = c("asylum", "child", 
                                         "seeker", "refugee",
                                         "human", "right")))

imm_frames

Dictionary object with 2 key entries.
- [securitarian]:
  - control, border, police, detention, illegal, legal
- [humanitarian]:
  - asylum, child, seeker, refugee, human, right

Fit the model.

set.seed(1234)
slda <- textmodel_seededlda(ukimmig2010_dfm, imm_frames, residual = TRUE)
print(terms(slda, 20))

      securitarian humanitarian  other        
 [1,] "border"     "asylum"      "system"     
 [2,] "control"    "british"     "people"     
 [3,] "country"    "right"       "new"        
 [4,] "illegal"    "immigrant"   "can"        
 [5,] "work"       "much"        "ensure"     
 [6,] "police"     "seeker"      "citizenship"
 [7,] "eu"         "year"        "need"       
 [8,] "detention"  "uk"          "end"        
 [9,] "government" "child"       "make"       
[10,] "student"    "people"      "migrant"    
[11,] "uk"         "refugee"     "point"      
[12,] "national"   "act"         "agency"     
[13,] "must"       "take"        "house"      
[14,] "live"       "allow"       "high"       
[15,] "non"        "national"    "support"    
[16,] "citizen"    "benefit"     "british"    
[17,] "limit"      "arrive"      "give"       
[18,] "ensure"     "citizenship" "thousand"   
[19,] "future"     "high"        "economy"    
[20,] "economic"   "work"        "priority"   

Check which documents are assigned to which topic.

table(topics(slda))

securitarian humanitarian        other 
           3            4            2 

Laboratory with real-world data

Footnotes

1. Griffiths, T. L., & Steyvers, M. (2004). Finding scientific topics. Proceedings of the National academy of Sciences, 101(suppl_1), 5228-5235.