Structural Topic Modeling (STM) is a method for analyzing textual data that allows you to estimate topics while accounting for document-level covariates. The stm package in R is widely used for conducting STM analysis. Here’s an example of how to perform STM using the stm package in R:
The first step is to load data into R. The stm package represents a text corpus in three parts:
a documents list containing word indices and their associated counts,
a vocab character vector containing the words associated with the word indices,
a metadata matrix containing document covariates.
The stm package provides a simple tool to quickly get started for a common use case:
Get data: The researcher has stored text data alongside covariates related to the text in a spreadsheet, such as a .csv file that contains textual data and associated metadata.
Read data: If the researcher reads this data into a R data frame,
Convert and Process data: then the stm package’s function textProcessor can conveniently convert and processes the data to make it ready for analysis in the stm package.
Note: The model does not permit estimation when there are variables used in the model that have missing values. As such, it can be helpful to subset data to observations that do not have missing values for metadata that will be used in the stm model.
To illustrate how to use the stm package, a collection of blogposts about American politics that were written in 2008, from the CMU 2008 Political Blog Corpus (Eisenstein and Xing 2010) wil be used. The blogposts were gathered from six different blogs: American Thinker, Digby, Hot Air, Michelle Malkin, Think Progress, and Talking Points Memo. Each blog has its own particular political bent. The day within 2008 when each blog was written was also recorded. Thus for each blogpost, there is metadata available on the day it was written and the political ideology of the blog for which it was written. In this case, each blog post is a row in a .csv file, with the text contained in a variable called documents.
# Link spreadsheet:
# http://scholar.princeton.edu/sites/default/files/bstewart/files/poliblogs2008.csv
library(stm)stm v1.3.6 successfully loaded. See ?stm for help.
Papers, resources, and other materials at structuraltopicmodel.comdata <- read.csv("poliblogs2008.csv")It is often useful to engage in some processing of the text data before modeling it. The most common processing steps are stemming (reducing words to their root form), dropping punctuation and stop word removal (e.g., the, is, at). The textProcessor function implements each of these steps across multiple languages by using the stm package.
processed <- textProcessor(data$documents, metadata = data) Building corpus...
Converting to Lower Case...
Removing punctuation...
Removing stopwords...
Removing numbers...
Stemming...
Creating Output... out <- prepDocuments(processed$documents, processed$vocab, processed$meta)Removing 83198 of 123990 terms (83198 of 2298953 tokens) due to frequency
Your corpus now has 13246 documents, 40792 terms and 2215755 tokens.docs <- out$documents
vocab <- out$vocab
meta <- out$metaAfter reading in the data, use the utility function prepDocuments to process the loaded data to make sure it is in the right format. prepDocuments also removes infrequent terms depending on the user-set parameter lower.thresh. The utility function plotRemoved will plot the number of words and documents removed for different thresholds.
For example, the user can use the following code to evaluate how many words and documents would be removed from the data set at each word threshold, which is the minimum number of documents a word needs to appear in order for the word to be kept within the vocabulary. Then the user can select their preferred threshold within prepDocuments.
Importantly, prepDocuments will also re-index all metadata/document relationships if any changes occur due to processing. If a document is completely removed due to pre-processing (for example because it contained only rare words), then prepDocuments will drop the corresponding row in the metadata as well. After reading in and processing the text data, it is important to inspect features of the documents and the associated vocabulary list to make sure they have been correctly pre-processed.
plotRemoved(processed$documents, lower.thresh = seq(1, 200, by = 100))
out <- prepDocuments(processed$documents, processed$vocab, processed$meta, lower.thresh = 15)Removing 114230 of 123990 terms (220223 of 2298953 tokens) due to frequency
Your corpus now has 13246 documents, 9760 terms and 2078730 tokens.The data import process will output documents, vocabulary and metadata that can be used for an analysis. In this section, let’s see how to estimate the STM. Next we move to a range of functions to evaluate, understand, and visualize the fitted model object.
The key innovation of the STM is that it incorporates metadata into the topic modeling framework. In STM, metadata can be entered in the topic model in two ways:
topical prevalence: Metadata covariates for topical prevalence allow the observed metadata to affect the frequency with which a topic is discussed.
topical content: Covariates in topical content allow the observed metadata to affect the word rate use within a given topic – that is, how a particular topic is discussed.
Estimation for both topical prevalence and content proceeds via the workhorse stm function.
In this example, let’s use the ratings variable (blog ideology) as a covariate in the topic prevalence portion of the model with the CMU Poliblog data described above. Each document is modeled as a mixture of multiple topics.
Topical prevalence captures how much each topic contributes to a document. Because different documents come from different sources, it is natural to want to allow this prevalence to vary with metadata that we have about document sources.
We will let prevalence be a function of the “rating” variable, which is coded as either “Liberal” or “Conservative,” and the variable “day” which is an integer measure of days running from the first to the last day of 2008. To illustrate, let’s estimate a 20 topic STM model. The user can then pass the output from the model, poliblogPrevFit, through the various functions discussed below (e.g., the plot method for ‘STM’ objects) to inspect the results.
If a user wishes to specify additional prevalence covariates, she would do so using the standard formula notation in R. A feature of the stm function is that “prevalence” can be expressed as a formula that can include multiple covariates and factorial or continuous covariates. For example, by using the formula setup you can enter other covariates additively. Additionally users can include more flexible functional forms of continuous covariates, including standard transforms like log(), as well as ns() or bs() from the splines package.
The stm package also includes a convenience function s(), which selects a fairly flexible b-spline basis. In the current example, the variable day is allowed to be estimated with a spline. Interactions between covariates can also be added using the standard notation for R formulas.
In the example below, we enter in the variables additively, by allowing for the day variable, an integer variable measuring which day the blog was posted, to have a non-linear relationship in the topic estimation stage.
poliblogPrevFit <- stm(documents = out$documents, vocab = out$vocab, K = 20, prevalence = ~rating + s(day), max.em.its = 15, data = out$meta, init.type = "Spectral")Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
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Recovering initialization...
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Initialization complete.
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Completed E-Step (4 seconds).
Completed M-Step.
Completing Iteration 1 (approx. per word bound = -7.677)
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Completing Iteration 2 (approx. per word bound = -7.520, relative change = 2.045e-02)
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Completing Iteration 3 (approx. per word bound = -7.483, relative change = 4.961e-03)
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Completing Iteration 4 (approx. per word bound = -7.467, relative change = 2.095e-03)
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Completing Iteration 5 (approx. per word bound = -7.459, relative change = 1.116e-03)
Topic 1: obama, mccain, poll, voter, democrat
Topic 2: peopl, one, like, think, polit
Topic 3: tax, will, mccain, economi, econom
Topic 4: one, ’re, get, ’ll, like
Topic 5: vote, elect, voter, state, republican
Topic 6: obama, mccain, campaign, barack, john
Topic 7: media, news, stori, time, like
Topic 8: democrat, senat, bill, republican, legisl
Topic 9: will, price, oil, govern, energi
Topic 10: court, law, case, right, will
Topic 11: mccain, campaign, john, million, oil
Topic 12: iran, nuclear, will, iranian, russia
Topic 13: palin, sarah, governor, report, state
Topic 14: israel, terrorist, attack, will, kill
Topic 15: school, obama, will, educ, work
Topic 16: iraq, war, iraqi, troop, militari
Topic 17: global, warm, abort, climat, chang
Topic 18: bush, presid, said, administr, hous
Topic 19: hillari, clinton, democrat, obama, will
Topic 20: will, allah, muslim, say, muhammad
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Completed E-Step (3 seconds).
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Completing Iteration 6 (approx. per word bound = -7.454, relative change = 6.643e-04)
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Completing Iteration 10 (approx. per word bound = -7.446, relative change = 1.550e-04)
Topic 1: obama, mccain, poll, voter, democrat
Topic 2: peopl, like, think, polit, one
Topic 3: tax, will, economi, econom, plan
Topic 4: one, ’re, get, don’t, like
Topic 5: vote, elect, voter, republican, state
Topic 6: obama, mccain, campaign, barack, john
Topic 7: media, news, stori, time, report
Topic 8: democrat, senat, republican, bill, vote
Topic 9: will, oil, energi, price, govern
Topic 10: court, law, case, right, rule
Topic 11: mccain, campaign, million, john, report
Topic 12: iran, nuclear, will, iranian, russia
Topic 13: palin, sarah, governor, state, alaska
Topic 14: terrorist, israel, attack, kill, pakistan
Topic 15: school, work, union, educ, obama
Topic 16: iraq, war, iraqi, troop, militari
Topic 17: global, warm, abort, chang, climat
Topic 18: bush, presid, said, administr, hous
Topic 19: hillari, clinton, will, democrat, obama
Topic 20: will, muslim, allah, islam, say
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Completed E-Step (3 seconds).
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Completing Iteration 11 (approx. per word bound = -7.445, relative change = 1.198e-04)
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Completing Iteration 12 (approx. per word bound = -7.444, relative change = 9.612e-05)
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Completing Iteration 14 (approx. per word bound = -7.443, relative change = 6.582e-05)
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Completed E-Step (3 seconds).
Completed M-Step.
Model Terminated Before Convergence Reached The model is set to run for a maximum of 75 EM iterations (controlled by max.em.its). Convergence is monitored by the change in the approximate variational lower bound. Once the bound has a small enough change between iterations, the model is considered converged.
As with all mixed-membership topic models, the posterior is intractable and non-convex, which creates a multi-modal estimation problem that can be sensitive to initialization. Put differently, the answers the estimation procedure comes up with may depend on starting values of the parameters (e.g., the distribution over words for a particular topic).
There are two approaches to dealing with this that the stm package facilitates.
The first is to use an initialization based on the method of moments, which is deterministic and globally consistent under reasonable conditions (Arora et al. 2013; Roberts et al. 2016a). This is known as a spectral initialization because it uses a spectral decomposition (non-negative matrix factorization) of the word co-occurrence matrix. In practice, this initialization is very helpful. This can be chosen by setting init.type = "Spectral" in the stm function. This option is used in the above example. This means that no matter the seed that is set, the same results will be generated. When the vocabulary is larger than 10,000 words, the function will temporarily subset the vocabulary size for the duration of the initialization.
The second approach is to initialize the model with a short run of a collapsed Gibbs sampler for LDA. For completeness researchers can also initialize the model randomly, but this is generally not recommended. In practice, the spectral initialization is generally recommended as it has been found that it to produce the best results consistently (Roberts et al. 2016a).
When not using the spectral initialization, the analyst should estimate many models, each from different initializations, and then evaluate each model according to some separate standard (several are provided below).
The function selectModel automates this process to facilitate finding a model with desirable properties. Users specify the number of “runs,” which in the example below is set to 20. selectModel first casts a net where “run” (below 10) models are run for two EM steps, and then models with low likelihoods are discarded.
Next, the default returns the 20% of models with the highest likelihoods, which are then run until convergence or the EM iteration maximum is reached. Notice that options for the stm function can be passed to selectModel, such as max.em.its. If users would like to select a larger number of models to be run completely, this can also be set with an option specified in the help file for this function.
poliblogSelect <- selectModel(out$documents, out$vocab, K = 20, prevalence = ~rating + s(day), max.em.its = 15, data = out$meta, runs = 20, seed = 8458159)Casting net
1 models in net
2 models in net
3 models in net
4 models in net
5 models in net
6 models in net
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8 models in net
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10 models in net
11 models in net
12 models in net
13 models in net
14 models in net
15 models in net
16 models in net
17 models in net
18 models in net
19 models in net
20 models in net
Running select models
1 select model run
Beginning LDA Initialization
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Completed E-Step (5 seconds).
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Completing Iteration 1 (approx. per word bound = -7.568)
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Completing Iteration 5 (approx. per word bound = -7.554, relative change = 3.087e-04)
Topic 1: will, tax, american, economi, plan
Topic 2: poll, state, voter, new, race
Topic 3: will, year, energi, price, global
Topic 4: hous, money, million, financi, crisi
Topic 5: mccain, john, said, sen, mccain’
Topic 6: obama, barack, polit, report, media
Topic 7: think, like, peopl, know, dont
Topic 8: will, clinton, democrat, hillari, obama
Topic 9: show, get, like, one, post
Topic 10: report, time, stori, new, one
Topic 11: iran, group, israel, polici, state
Topic 12: american, america, countri, peopl, will
Topic 13: ’re, don’t, question, think, say
Topic 14: one, day, will, man, men
Topic 15: attack, govern, terrorist, forc, nuclear
Topic 16: vote, republican, democrat, senat, elect
Topic 17: iraq, bush, war, militari, iraqi
Topic 18: law, said, hous, legisl, administr
Topic 19: palin, women, sarah, like, experi
Topic 20: obama, mccain, campaign, barack, john
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Completed E-Step (4 seconds).
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Completing Iteration 6 (approx. per word bound = -7.551, relative change = 3.760e-04)
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Completing Iteration 7 (approx. per word bound = -7.548, relative change = 4.394e-04)
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Completing Iteration 9 (approx. per word bound = -7.541, relative change = 5.066e-04)
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Completing Iteration 10 (approx. per word bound = -7.537, relative change = 4.976e-04)
Topic 1: will, tax, american, plan, economi
Topic 2: poll, state, voter, race, new
Topic 3: will, energi, year, price, global
Topic 4: money, hous, million, financi, crisi
Topic 5: mccain, john, said, sen, mccain’
Topic 6: obama, barack, polit, media, report
Topic 7: think, like, peopl, know, just
Topic 8: will, clinton, democrat, hillari, parti
Topic 9: show, get, post, like, one
Topic 10: time, report, stori, new, one
Topic 11: iran, group, israel, polici, state
Topic 12: american, america, countri, will, peopl
Topic 13: ’re, don’t, question, say, want
Topic 14: one, will, day, man, men
Topic 15: attack, govern, terrorist, nuclear, forc
Topic 16: vote, republican, democrat, senat, elect
Topic 17: iraq, bush, war, militari, iraqi
Topic 18: law, said, hous, legisl, administr
Topic 19: palin, women, sarah, experi, run
Topic 20: obama, mccain, campaign, barack, john
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Completed E-Step (4 seconds).
Completed M-Step.
Completing Iteration 11 (approx. per word bound = -7.533, relative change = 4.892e-04)
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Completing Iteration 12 (approx. per word bound = -7.530, relative change = 4.780e-04)
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Completing Iteration 13 (approx. per word bound = -7.526, relative change = 4.640e-04)
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Completing Iteration 14 (approx. per word bound = -7.523, relative change = 4.530e-04)
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Completed E-Step (4 seconds).
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Model Terminated Before Convergence Reached
2 select model run
Beginning LDA Initialization
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Completed E-Step (7 seconds).
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Completing Iteration 1 (approx. per word bound = -7.567)
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Completing Iteration 5 (approx. per word bound = -7.555, relative change = 2.733e-04)
Topic 1: think, peopl, like, polit, dont
Topic 2: one, women, life, word, man
Topic 3: democrat, republican, senat, bill, vote
Topic 4: mccain, obama, campaign, john, said
Topic 5: oil, energi, compani, financi, price
Topic 6: obama, palin, barack, polit, campaign
Topic 7: nation, will, secur, foreign, polici
Topic 8: school, use, famili, peopl, get
Topic 9: said, report, today, former, meet
Topic 10: state, group, work, organ, public
Topic 11: ’re, get, don’t, think, question
Topic 12: iraq, war, militari, iran, iraqi
Topic 13: bush, presid, administr, said, white
Topic 14: media, time, stori, one, news
Topic 15: law, court, rule, state, case
Topic 16: will, can, america, countri, presid
Topic 17: will, world, one, nuclear, even
Topic 18: tax, plan, econom, economi, will
Topic 19: new, time, last, two, day
Topic 20: obama, clinton, hillari, democrat, voter
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Completed E-Step (4 seconds).
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Completing Iteration 6 (approx. per word bound = -7.553, relative change = 3.265e-04)
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Completing Iteration 10 (approx. per word bound = -7.539, relative change = 4.721e-04)
Topic 1: think, peopl, like, polit, dont
Topic 2: women, one, life, man, word
Topic 3: democrat, republican, senat, bill, vote
Topic 4: mccain, campaign, john, obama, said
Topic 5: oil, energi, compani, financi, price
Topic 6: obama, barack, palin, polit, campaign
Topic 7: nation, will, polici, foreign, secur
Topic 8: school, use, famili, peopl, said
Topic 9: said, report, today, former, meet
Topic 10: state, group, work, organ, public
Topic 11: get, ’re, don’t, think, question
Topic 12: iraq, war, militari, iran, iraqi
Topic 13: bush, presid, administr, said, white
Topic 14: media, time, stori, news, one
Topic 15: law, court, rule, case, state
Topic 16: will, can, america, presid, countri
Topic 17: will, world, nuclear, one, also
Topic 18: tax, plan, econom, economi, will
Topic 19: new, last, time, day, two
Topic 20: obama, clinton, hillari, democrat, voter
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Completed E-Step (4 seconds).
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Completing Iteration 11 (approx. per word bound = -7.536, relative change = 4.576e-04)
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Completing Iteration 14 (approx. per word bound = -7.527, relative change = 3.754e-04)
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Completed E-Step (4 seconds).
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Model Terminated Before Convergence Reached
3 select model run
Beginning LDA Initialization
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Completing Iteration 1 (approx. per word bound = -7.571)
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Completing Iteration 5 (approx. per word bound = -7.557, relative change = 3.266e-04)
Topic 1: one, will, man, peopl, love
Topic 2: tax, will, plan, american, econom
Topic 3: mccain, republican, will, john, conserv
Topic 4: said, report, citi, offici, new
Topic 5: iraq, war, militari, forc, secur
Topic 6: govern, hous, crisi, financi, market
Topic 7: bush, presid, said, hous, administr
Topic 8: iran, terrorist, israel, foreign, polici
Topic 9: obama, barack, campaign, polit, obama’
Topic 10: law, court, case, rule, justic
Topic 11: palin, media, news, report, press
Topic 12: question, ’re, get, don’t, say
Topic 13: clinton, hillari, democrat, obama, will
Topic 14: vote, elect, democrat, state, republican
Topic 15: peopl, think, know, dont, just
Topic 16: year, like, one, even, legisl
Topic 17: right, issu, can, peopl, will
Topic 18: mccain, john, campaign, obama, new
Topic 19: will, oil, energi, new, nation
Topic 20: time, report, public, new, york
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Completed E-Step (4 seconds).
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Completing Iteration 6 (approx. per word bound = -7.554, relative change = 3.904e-04)
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Completing Iteration 10 (approx. per word bound = -7.538, relative change = 5.577e-04)
Topic 1: will, one, man, peopl, love
Topic 2: tax, plan, will, american, econom
Topic 3: republican, mccain, will, conserv, john
Topic 4: said, report, citi, offici, new
Topic 5: iraq, war, militari, secur, iraqi
Topic 6: govern, hous, crisi, financi, market
Topic 7: bush, presid, said, hous, administr
Topic 8: iran, terrorist, israel, foreign, state
Topic 9: obama, barack, campaign, polit, obama’
Topic 10: law, court, case, investig, justic
Topic 11: palin, media, news, report, press
Topic 12: question, get, ’re, say, don’t
Topic 13: clinton, hillari, democrat, obama, will
Topic 14: vote, elect, democrat, state, republican
Topic 15: peopl, think, know, just, like
Topic 16: year, like, one, even, legisl
Topic 17: right, issu, can, will, bill
Topic 18: mccain, john, campaign, new, poll
Topic 19: will, oil, energi, nation, new
Topic 20: time, report, public, new, york
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Completed E-Step (4 seconds).
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Completing Iteration 11 (approx. per word bound = -7.534, relative change = 5.434e-04)
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Completing Iteration 14 (approx. per word bound = -7.523, relative change = 4.580e-04)
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Completed E-Step (4 seconds).
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Model Terminated Before Convergence Reached
4 select model run
Beginning LDA Initialization
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Topic 1: poll, obama, state, mccain, among
Topic 2: time, report, use, new, said
Topic 3: bush, hous, oil, bill, energi
Topic 4: legisl, will, one, say, ayer
Topic 5: palin, new, state, sarah, rep
Topic 6: obama, clinton, hillari, will, win
Topic 7: say, think, want, talk, obama
Topic 8: iraq, war, militari, iraqi, troop
Topic 9: tax, econom, economi, govern, money
Topic 10: polit, obama, black, one, wright
Topic 11: american, will, countri, america, peopl
Topic 12: law, report, state, offici, investig
Topic 13: mccain, said, say, news, report
Topic 14: iran, terrorist, attack, israel, foreign
Topic 15: will, can, right, rule, court
Topic 16: like, know, think, just, thing
Topic 17: chicago, time, one, two, citi
Topic 18: obama, mccain, campaign, john, barack
Topic 19: democrat, republican, vote, elect, parti
Topic 20: get, even, one, like, want
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Completing Iteration 10 (approx. per word bound = -7.540, relative change = 4.788e-04)
Topic 1: poll, state, among, percent, obama
Topic 2: report, time, new, use, said
Topic 3: bush, hous, bill, oil, congress
Topic 4: legisl, will, say, one, ayer
Topic 5: palin, new, sarah, state, rep
Topic 6: obama, clinton, hillari, will, win
Topic 7: say, think, want, talk, get
Topic 8: iraq, war, militari, iraqi, troop
Topic 9: tax, econom, economi, govern, money
Topic 10: polit, black, obama, wright, one
Topic 11: american, will, countri, america, peopl
Topic 12: law, report, state, offici, investig
Topic 13: said, mccain, say, sen, mccain’
Topic 14: iran, terrorist, attack, israel, foreign
Topic 15: will, right, rule, can, court
Topic 16: like, know, just, think, thing
Topic 17: chicago, citi, time, stori, two
Topic 18: obama, mccain, campaign, john, barack
Topic 19: democrat, republican, vote, elect, parti
Topic 20: get, even, one, want, like
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Model Terminated Before Convergence Reached In order to select a model for further investigation, users must choose one of the candidate models’ outputs from selectModel. To do this, plotModels can be used to plot two scores: semantic coherence and exclusivity for each model and topic. Each of these criteria are calculated for each topic within a model run.
The plotModels function calculates the average across all topics for each run of the model and plots these by labeling the model run with a numeral. Often users will select a model with desirable properties in both dimensions (i.e., models with average scores towards the upper right side of the plot).
plotModels(poliblogSelect, pch = c(1, 2, 3, 4), legend.position = "bottomright")
As shown in the Figure , the plotModels function also plots each topic’s values, which helps give a sense of the variation in these parameters. For a given model, the user can plot the semantic coherence and exclusivity scores with the topicQuality function.
Next the user would want to select one of these models to work with. For example, the third model could be extracted from the object that is outputted by selectModel.
selectedmodel <- poliblogSelect$runout[[3]]STM assumes a fixed user-specified number of topics. There is not a "right" answer to the number of topics that are appropriate for a given corpus (Grimmer and Stewart 2013), 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 including calculating the held-out log-likelihood (Wallach, Murray, Salakhutdinov, and Mimno 2009) and performing a residual analysis (Taddy 2012).
For example, one could estimate a STM model for 7 and 10 topics and compare the results along each of the criteria. The default initialization is the spectral initialization due to its stability.
This function will also calculate a range of quantities of interest, including the average exclusivity and semantic coherence.
storage <- searchK(out$documents, out$vocab, K = c(7, 10), prevalence = ~rating + s(day), data = meta)Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
.......
Recovering initialization...
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Initialization complete.
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Completed E-Step (2 seconds).
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Completing Iteration 5 (approx. per word bound = -7.584, relative change = 1.013e-03)
Topic 1: obama, democrat, campaign, hillari, clinton
Topic 2: mccain, john, palin, campaign, said
Topic 3: peopl, will, one, american, can
Topic 4: one, like, get, time, just
Topic 5: will, hous, tax, govern, american
Topic 6: state, vote, elect, will, court
Topic 7: iraq, war, will, militari, bush
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Completing Iteration 6 (approx. per word bound = -7.580, relative change = 6.297e-04)
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Completing Iteration 10 (approx. per word bound = -7.572, relative change = 1.471e-04)
Topic 1: obama, democrat, campaign, will, clinton
Topic 2: mccain, john, palin, said, campaign
Topic 3: peopl, will, one, american, can
Topic 4: one, like, get, time, just
Topic 5: will, tax, hous, govern, year
Topic 6: state, vote, senat, elect, court
Topic 7: iraq, war, will, bush, militari
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Completing Iteration 15 (approx. per word bound = -7.569, relative change = 5.247e-05)
Topic 1: obama, democrat, campaign, will, clinton
Topic 2: mccain, john, said, palin, campaign
Topic 3: peopl, one, will, american, can
Topic 4: one, like, time, get, just
Topic 5: will, tax, year, govern, american
Topic 6: state, senat, law, vote, court
Topic 7: iraq, war, will, militari, bush
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Completing Iteration 16 (approx. per word bound = -7.568, relative change = 4.681e-05)
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Completing Iteration 20 (approx. per word bound = -7.567, relative change = 3.379e-05)
Topic 1: obama, democrat, campaign, will, clinton
Topic 2: mccain, said, john, palin, campaign
Topic 3: peopl, will, one, american, can
Topic 4: one, like, time, get, media
Topic 5: will, tax, year, govern, american
Topic 6: state, senat, law, hous, report
Topic 7: iraq, war, will, militari, bush
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Completing Iteration 25 (approx. per word bound = -7.566, relative change = 1.966e-05)
Topic 1: obama, democrat, campaign, will, clinton
Topic 2: mccain, said, john, palin, campaign
Topic 3: peopl, will, one, american, think
Topic 4: one, like, time, get, media
Topic 5: will, tax, year, govern, american
Topic 6: state, hous, senat, law, report
Topic 7: iraq, war, will, militari, american
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Model Converged
Beginning Spectral Initialization
Calculating the gram matrix...
Finding anchor words...
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Recovering initialization...
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Initialization complete.
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Completed E-Step (2 seconds).
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Completing Iteration 5 (approx. per word bound = -7.543, relative change = 9.099e-04)
Topic 1: obama, hillari, democrat, clinton, campaign
Topic 2: mccain, obama, campaign, john, palin
Topic 3: peopl, will, one, american, can
Topic 4: one, like, get, ’re, ’ll
Topic 5: hous, bush, presid, senat, bill
Topic 6: state, vote, elect, republican, court
Topic 7: iraq, war, said, militari, iraqi
Topic 8: will, tax, american, year, govern
Topic 9: media, time, stori, report, news
Topic 10: will, nation, govern, israel, world
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Topic 1: obama, democrat, hillari, will, clinton
Topic 2: mccain, obama, john, campaign, palin
Topic 3: peopl, will, american, one, can
Topic 4: one, get, like, ’re, ’ll
Topic 5: bush, hous, presid, senat, administr
Topic 6: state, vote, elect, republican, court
Topic 7: iraq, war, militari, iraqi, said
Topic 8: will, tax, american, year, govern
Topic 9: media, time, like, stori, report
Topic 10: will, israel, iran, nation, world
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Completing Iteration 15 (approx. per word bound = -7.529, relative change = 4.717e-05)
Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, obama, campaign, palin
Topic 3: peopl, will, american, one, can
Topic 4: one, get, like, ’re, ’ll
Topic 5: bush, hous, presid, administr, senat
Topic 6: state, vote, elect, republican, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, american, govern
Topic 9: media, time, like, think, know
Topic 10: will, iran, israel, nuclear, world
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Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, campaign, obama, palin
Topic 3: peopl, american, will, one, america
Topic 4: one, get, like, ’re, don’t
Topic 5: bush, hous, presid, administr, said
Topic 6: state, vote, elect, republican, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, govern, american
Topic 9: think, media, like, time, know
Topic 10: iran, will, israel, nuclear, world
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Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, campaign, palin, obama
Topic 3: peopl, american, will, one, america
Topic 4: one, get, like, ’re, don’t
Topic 5: bush, hous, presid, administr, said
Topic 6: state, vote, elect, campaign, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, govern, american
Topic 9: think, like, media, know, say
Topic 10: iran, will, israel, world, nuclear
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Completing Iteration 30 (approx. per word bound = -7.527, relative change = 1.534e-05)
Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, campaign, palin, obama
Topic 3: american, will, peopl, one, america
Topic 4: one, get, like, ’re, don’t
Topic 5: bush, hous, presid, administr, said
Topic 6: state, vote, elect, campaign, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, govern, american
Topic 9: think, like, know, peopl, say
Topic 10: iran, will, israel, world, nuclear
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Completing Iteration 35 (approx. per word bound = -7.526, relative change = 1.200e-05)
Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, campaign, palin, obama
Topic 3: american, will, peopl, one, america
Topic 4: one, get, like, ’re, ’ll
Topic 5: bush, hous, presid, administr, said
Topic 6: state, vote, elect, campaign, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, govern, american
Topic 9: think, like, peopl, know, say
Topic 10: iran, will, israel, world, nuclear
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Completing Iteration 40 (approx. per word bound = -7.526, relative change = 1.045e-05)
Topic 1: obama, democrat, will, hillari, clinton
Topic 2: mccain, john, campaign, palin, said
Topic 3: will, american, peopl, one, america
Topic 4: one, get, like, ’re, ’ll
Topic 5: bush, hous, presid, administr, said
Topic 6: state, vote, elect, campaign, senat
Topic 7: iraq, war, militari, iraqi, troop
Topic 8: will, tax, year, govern, american
Topic 9: think, like, peopl, know, say
Topic 10: iran, will, israel, world, nuclear
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Model Converged There is another more preliminary selection strategy based on work by Lee and Mimno (2014). When initialization type is set to “Spectral” the user can specify K=0 to use the algorithm of Lee and Mimno (2014) to select the number of topics. The core idea of the spectral initialization is to approximately find the vertices of the convex hull of the word co-occurrences.
The algorithm of Lee and Mimno (2014) projects the matrix into a low dimensional space using t-distributed stochastic neighbor embedding (Van der Maaten 2014) and then exactly solves for the convex hull. This has the advantage of automatically selecting the number of topics. The added randomness from the projection means that the algorithm is not deterministic like the standard “Spectral” initialization type. Running it with a different seed can result in not only different results but a different number of topics. This procedure has no particular statistical guarantees and should not be seen as estimating the "true" number of topics. However it can be useful to start and has the computational advantage that it only needs to be run once.
Interpreting the STM by plotting and inspecting results
After choosing a model, the user must next interpret the model results. There are many ways to investigate the output, such as inspecting the words associated with topics or the relationship between metadata and topics. To investigate the output of the model, the stm package provides a number of options.
Displaying words associated with topics (labelTopics, plot method for 'STM' objects with argument type = "labels", sageLabels, plot method for 'STM' objects with argument type = "perspectives") or documents highly associated with particular topics (findThoughts, plotQuote).
Estimating relationships between metadata and topics as well as topical content (estimateEffect).
Calculating topic correlations (topicCorr)
Two approaches are describe for users to explore the topics that have been estimated. The first approach is to look at collections of words that are associated with topics. The second approach is to examine actual documents that are estimated to be highly associated with each topic. Both of these approaches should be used. Below, the 20 topic model estimated with the spectral initialization is used.
To explore the words associated with each topic, the labelTopics function can be used. For models where a content covariate is included sageLabels can also be used. Both these functions will print words associated with each topic to the console. The function by default prints several different types of word profiles, including highest probability words and FREX words.
FREX weights words by their overall frequency and how exclusive they are to the topic (calculated as given in Equation 6).13 Lift weights words by dividing by their frequency in other topics, therefore giving higher weight to words that appear less frequently in other topics. For more information on lift, see Taddy (2013).
Similar to lift, score divides the log frequency of the word in the topic by the log frequency of the word in other topics. For more information on score, see the lda R package. In order to translate these results to a format that can easily be used within a paper, the plot method for 'STM' objects with argument type = "labels" will print topic words to a graphic device. Notice that in this case, the labels option is specified as the plot method for 'STM' objects has several functionalities that is described below (the options for “perspectives” and “summary”).
labelTopics(poliblogPrevFit, c(6, 13, 18))Topic 6 Top Words:
Highest Prob: obama, mccain, campaign, barack, john, said, say
FREX: obama, barack, mccain, obama’, debat, wright, joe
Lift: oct, goolsbe, schieffer, town-hal, bayh, austan, robocal
Score: obama, mccain, oct, campaign, barack, biden, wright
Topic 13 Top Words:
Highest Prob: palin, sarah, governor, state, polit, alaska, blagojevich
FREX: blagojevich, palin, sarah, palin’, rezko, alaska, governor
Lift: monegan, blagojevich, wasilla, juneau, rezko’, blago, “palin
Score: palin, sarah, monegan, blagojevich, palin’, alaska, governor
Topic 18 Top Words:
Highest Prob: bush, presid, said, administr, hous, white, report
FREX: cheney, bush’, rove, cia, perino, tortur, interrog
Lift: addington, torture”, fratto, cia’, mcclellan, ashcroft, waterboard
Score: addington, bush, tortur, perino, cia, rove, presid Estimating the relationship between metadata and topics is a core feature of the stm package. These relationships can also play a key role in validating the topic model's usefulness (Grimmer 2010; Grimmer and Stewart 2013). While stm estimates the relationship for the (K − 1) simplex, the workhorse function for extracting the relationships and associated uncertainty on all K topics is estimateEffect. This function simulates a set of parameters which can then be plotted.
Typically, users will pass the same model of topical prevalence used in estimating the STM to the estimateEffect function. The syntax of the estimateEffect function is designed so users specify the set of topics they wish to use for estimation, and then a formula for metadata of interest. Different estimation strategies and standard plot design features can be used by calling the plot method for 'estimateEffect' objects.
estimateEffect can calculate uncertainty in several ways. The default is “Global”, which will incorporate estimation uncertainty of the topic proportions into the uncertainty estimates using the method of composition. If users do not propagate the full amount of uncertainty, e.g., in order to speed up computational time, they can choose uncertainty = "None", which will generally result in narrower confidence intervals because it will not include the additional estimation uncertainty. Calling summary on the 'estimateEffect' object will generate a regression table.
out$meta$rating <- as.factor(out$meta$rating)
prep <- estimateEffect(1:20 ~ rating + s(day), poliblogPrevFit, meta = out$meta, uncertainty = "Global")
summary(prep, topics = 1)
Call:
estimateEffect(formula = 1:20 ~ rating + s(day), stmobj = poliblogPrevFit,
metadata = out$meta, uncertainty = "Global")
Topic 1:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0672878 0.0116892 5.756 8.78e-09 ***
ratingLiberal -0.0040968 0.0029685 -1.380 0.1676
s(day)1 -0.0055655 0.0225761 -0.247 0.8053
s(day)2 -0.0332943 0.0137225 -2.426 0.0153 *
s(day)3 0.0016440 0.0161324 0.102 0.9188
s(day)4 -0.0298897 0.0138301 -2.161 0.0307 *
s(day)5 -0.0210947 0.0147670 -1.429 0.1532
s(day)6 -0.0062131 0.0147803 -0.420 0.6742
s(day)7 0.0009988 0.0142191 0.070 0.9440
s(day)8 0.0440837 0.0176700 2.495 0.0126 *
s(day)9 -0.1014548 0.0176449 -5.750 9.13e-09 ***
s(day)10 -0.0217291 0.0167761 -1.295 0.1953
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The functions described previously to understand STM results can be leveraged to visualize results for formal presentation. In this section let’s focus on several of these visualization tools.
Corpus level visualization can be done in several different ways. The first relates to the expected proportion of the corpus that belongs to each topic. This can be plotted using the plot method for 'STM' objects with argument type = "summary". An example from the political blogs data is given in next figure. We see, for example, that the Sarah Palin/vice president Topic 13 is actually a relatively minor proportion of the discourse. The most common topic is a general topic full of words that bloggers commonly use, and therefore is not very interpretable. The words listed in the figure are the top three words associated with the topic.
plot(poliblogPrevFit, type = "summary", xlim = c(0, 0.3))
In order to plot features of topics in greater detail, there are a number of options in the plot method for 'STM' objects, such as plotting larger sets of words highly associated with a topic or words that are exclusive to the topic. Furthermore, the cloud function will plot a standard word cloud of words in a topic16 and the plotQuote function provides an easy to use graphical wrapper such that complete examples of specific documents can easily be included in the presentation of results.
Now let’s discuss plotting metadata/topic relationships, as the ability to estimate these relationships is a core advantage of the STM model. The core plotting function is the plot method for 'estimateEffect' objects, which handles the output of estimateEffect.
First, users must specify the variable that they wish to use for calculating an effect. If there are multiple variables specified in estimateEffect, then all other variables are held at their sample median. These parameters include the expected proportion of a document that belongs to a topic as a function of a covariate, or a first difference type estimate, where topic prevalence for a particular topic is contrasted for two groups (e.g., liberal versus conservative). estimateEffect should be run and the output saved before plotting when it is time intensive to calculate uncertainty estimates and/or because users might wish to plot different quantities of interest using the same simulated parameters from estimateEffect. The output can then be plotted.
When the covariate of interest is binary, or users are interested in a particular contrast, the method = "difference" option will plot the change in topic proportion shifting from one specific value to another. Figure 6 gives an example. For factor variables, users may wish to plot the marginal topic proportion for each of the levels (“pointestimate”).
plot(prep, covariate = "rating", topics = c(6, 13, 18), model = poliblogPrevFit, method = "difference", cov.value1 = "Liberal", cov.value2 = "Conservative", xlab = "More Conservative ... More Liberal", main = "Effect of Liberal vs. Conservative", xlim = c(-0.1, 0.1), labeltype = "custom", custom.labels = c("Obama/McCain", "Sarah Palin", "Bush Presidency"))
We see Topic 6 is strongly used slightly more by liberals as compared to conservatives, while Topic 13 is close to the middle but still conservative-leaning. Topic 18, the discussion of Bush, was largely associated with liberal writers, which is in line with the observed trend of conservatives distancing from Bush after his presidency.
Notice how the function makes use of standard labeling options available in the native plot() function. This allows the user to customize labels and other features of their plots. Note that in the package, generics are leverage for the plot functions. As such, one can simply use plot and rely on method dispatch.
When users have variables that they want to treat continuously, users can choose between assuming a linear fit or using splines. In the previous example, the day variable is allowed to have a non-linear relationship in the topic estimation stage. Then plot its effect on topics. In Figure 7, the relationship between time and the vice president topic, Topic 13, is plotted. The topic peaks when Sarah Palin became John McCain's running mate at the end of August in 2008.
plot(prep, "day", method = "continuous", topics = 13, model = z, printlegend = FALSE, xaxt = "n", xlab = "Time (2008)")
monthseq <- seq(from = as.Date("2008-01-01"), to = as.Date("2008-12-01"), by = "month")
monthnames <- months(monthseq)
axis(1,at = as.numeric(monthseq) - min(as.numeric(monthseq)), labels = monthnames)
Another modification that is possible in this framework is to allow for interactions between covariates such that one variable may "moderate" the effect of another variable. In this example, the STM is re-estimated to allow for an interaction between day (entered linearly) and rating. Then in estimateEffect() the same interaction is included. This allows us in the plot method for 'estimateEffect' objects to have this interaction plotted. The results are displayed in Figure 10 for Topic 20 (Bush administration). You can observe that conservatives never wrote much about this topic, whereas liberals discussed this topic a great deal, but over time the topic diminished in salience.
poliblogInteraction <- stm(out$documents, out$vocab, K = 20, prevalence =~ rating * day, max.em.its = 75, data = out$meta, init.type = "Spectral")Beginning Spectral Initialization
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Topic 1: obama, mccain, poll, voter, democrat
Topic 2: peopl, one, like, think, polit
Topic 3: tax, will, mccain, economi, econom
Topic 4: one, ’re, get, ’ll, like
Topic 5: vote, elect, voter, state, republican
Topic 6: obama, mccain, campaign, barack, john
Topic 7: media, news, stori, time, like
Topic 8: democrat, senat, bill, republican, legisl
Topic 9: will, price, oil, govern, energi
Topic 10: court, law, case, right, will
Topic 11: mccain, campaign, john, million, report
Topic 12: iran, nuclear, will, iranian, russia
Topic 13: palin, sarah, governor, report, state
Topic 14: israel, terrorist, attack, will, kill
Topic 15: school, obama, educ, will, work
Topic 16: iraq, war, iraqi, troop, militari
Topic 17: global, warm, abort, climat, chang
Topic 18: bush, presid, said, administr, hous
Topic 19: hillari, clinton, democrat, obama, will
Topic 20: will, allah, muslim, say, muhammad
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Topic 2: peopl, like, think, polit, one
Topic 3: tax, will, economi, econom, plan
Topic 4: one, ’re, get, don’t, like
Topic 5: vote, elect, voter, republican, state
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Topic 9: will, oil, energi, price, govern
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Topic 12: iran, nuclear, will, iranian, russia
Topic 13: palin, sarah, governor, state, alaska
Topic 14: terrorist, israel, attack, kill, pakistan
Topic 15: school, work, union, educ, year
Topic 16: iraq, war, iraqi, troop, militari
Topic 17: global, warm, abort, climat, chang
Topic 18: bush, presid, said, administr, hous
Topic 19: hillari, clinton, will, democrat, obama
Topic 20: will, muslim, allah, islam, say
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Topic 12: iran, nuclear, will, world, iranian
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Topic 15: school, work, union, educ, famili
Topic 16: iraq, war, iraqi, troop, militari
Topic 17: global, warm, abort, gay, chang
Topic 18: bush, presid, said, administr, hous
Topic 19: hillari, clinton, will, democrat, obama
Topic 20: will, muslim, allah, christian, god
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Topic 17: global, warm, abort, gay, chang
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Topic 19: clinton, hillari, will, democrat, primari
Topic 20: will, muslim, christian, god, allah
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Topic 20: church, will, muslim, christian, god
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Topic 17: global, warm, abort, gay, chang
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Topic 20: church, will, muslim, christian, god
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Topic 17: global, warm, abort, gay, chang
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Topic 17: global, warm, abort, gay, chang
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Model Converged