Variational EM for the Structural Topic Model

Estimation of the Structural Topic Model using semi-collapsed variational EM. The function takes sparse representation of a document-term matrix, an integer number of topics, and covariates and returns fitted model parameters. Covariates can be used in the prior for topic prevalence, in the prior for topical content or both. See an overview of functions in the package here: stm-package

stm(documents, vocab, K, prevalence = NULL, content = NULL, data = NULL,
  init.type = c("Spectral", "LDA", "Random", "Custom"), seed = NULL,
  max.em.its = 500, emtol = 1e-05, verbose = TRUE, reportevery = 5,
  LDAbeta = TRUE, interactions = TRUE, ngroups = 1, model = NULL,
  gamma.prior = c("Pooled", "L1"), sigma.prior = 0, kappa.prior = c("L1",
  "Jeffreys"), control = list())

The document term matrix to be modeled. These can be supplied in the native stm format, a sparse term count matrix with one row per document and one column per term, or a quanteda dfm (document-feature matrix) object. When using the sparse matrix or quanteda format this will include the vocabulary and, for quanteda, optionally the metadata. If using the native list format, the object must be a list of with each element corresponding to a document. Each document is represented as an integer matrix with two rows, and columns equal to the number of unique vocabulary words in the document. The first row contains the 1-indexed vocabulary entry and the second row contains the number of times that term appears. This is similar to the format in the lda package except that (following R convention) the vocabulary is indexed from one. Corpora can be imported using the reader function and manipulated using the prepDocuments. Raw texts can be ingested using textProcessor. Note that when using quanteda dfm directly there may be higher memory use (because the texts and metadata are stored twice). You can convert from quanteda's format directly to our native format using the quanteda function convert.


Character vector specifying the words in the corpus in the order of the vocab indices in documents. Each term in the vocabulary index must appear at least once in the documents. See prepDocuments for dropping unused items in the vocabulary. If documents is a sparse matrix or quanteda dfm object, then vocab should not (and must not) be supplied. It is contained already inside the column names of the matrix.


Typically a positive integer (of size 2 or greater) representing the desired number of topics. 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 (although unlike the standard spectral initialization this is not deterministic). Additional detail on choosing the number of topics below.


A formula object with no response variable or a matrix containing topic prevalence covariates. Use s, ns or bs to specify smooth terms. See details for more information.


A formula containing a single variable, a factor variable or something which can be coerced to a factor indicating the category of the content variable for each document.


an optional data frame containing the prevalence and/or content covariates. If unspecified the variables are taken from the active environment.


The method of initialization, by default the spectral initialization. Must be either Latent Dirichlet Allocation ("LDA"), "Random", "Spectral" or "Custom". See details for more info. If you want to replicate a previous result, see the argument seed. For "Custom" see the format described below under the custom.beta option of the control parameters.


Seed for the random number generator. stm saves the seed it uses on every run so that any result can be exactly reproduced. When attempting to reproduce a result with that seed, it should be specified here.


The maximum number of EM iterations. If convergence has not been met at this point, a message will be printed. If you set this to 0 it will return the initialization.


Convergence tolerance. EM stops when the relative change in the approximate bound drops below this level. Defaults to .00001. You can set it to 0 to have the algorithm run max.em.its number of steps. See advanced options under control for more options.


A logical flag indicating whether information should be printed to the screen. During the E-step (iteration over documents) a dot will print each time 1% of the documents are completed. At the end of each iteration the approximate bound will also be printed.


An integer determining the intervals at which labels are printed to the screen during fitting. Defaults to every 5 iterations.


a logical that defaults to TRUE when there are no content covariates. When set to FALSE the model performs SAGE style topic updates (sparse deviations from a baseline).


a logical that defaults to TRUE. This automatically includes interactions between content covariates and the latent topics. Setting it to FALSE reduces to a model with no interactive effects.


Number of groups for memoized inference. See details below.


A prefit model object. By passing an stm object to this argument you can restart an existing model. See details for more info.


sets the prior estimation method for the prevalence covariate model. The default Pooled options uses Normal prior distributions with a topic-level pooled variance which is given a moderately regularizing half-cauchy(1,1) prior. The alternative L1 uses glmnet to estimate a grouped penalty between L1-L2. If your code is running slowly immediately after "Completed E-Step" appears, you may want to switch to the L1 option. See details below.


a scalar between 0 and 1 which defaults to 0. This sets the strength of regularization towards a diagonalized covariance matrix. Setting the value above 0 can be useful if topics are becoming too highly correlated.


sets the prior estimation for the content covariate coefficients. The default option is the L1 prior. The second option is Jeffreys which is markedly less computationally efficient but is included for backwards compatability. See details for more information on computation.


a list of additional advanced parameters. See details.


This is the main function for estimating a Structural Topic Model (STM). STM is an admixture with covariates in both mixture components. Users provide a corpus of documents and a number of topics. Each word in a document comes from exactly one topic and each document is represented by the proportion of its words that come from each of the K topics. These proportions are found in the N (number of documents) by K (user specified number of topics) theta matrix. Each of the K topics are represented as distributions over words. The K-by-V (number of words in the vocabulary) matrix logbeta contains the natural log of the probability of seeing each word conditional on the topic.

The most important user input in parametric topic models is the number of topics. There is no right answer to the appropriate number of topics. More topics will give more fine-grained representations of the data at the potential cost of being less precisely estimated. The number must be at least 2 which is equivalent to a unidimensional scaling model. For short corpora focused on very specific subject matter (such as survey experiments) 3-10 topics is a useful starting range. For small corpora (a few hundred to a few thousand) 5-50 topics is a good place to start. Beyond these rough guidelines it is application specific. Previous applications in political science with medium sized corpora (10k to 100k documents) have found 60-100 topics to work well. For larger corpora 100 topics is a useful default size. Of course, your mileage may vary.

When init.type="Spectral" and K=0 the number of topics is set using the algorithm in Lee and Mimno (2014). See vignette for details. We emphasize here as we do there that this does not estimate the "true" number of topics and does not necessarily have any particular statistical properties for consistently estimating the number of topics. It can however provide a useful starting point.

The model for topical prevalence includes covariates which the analyst believes may influence the frequency with which a topic is discussed. This is specified as a formula which can contain smooth terms using splines or by using the function s. The response portion of the formula should be left blank. See the examples. These variables can include numeric and factor variables. While including variables of class Dates or other non-numeric, non-factor types will work in stm it may not always work for downstream functions such as estimateEffect.

The topical convent covariates are those which affect the way in which a topic is discussed. As currently implemented this must be a single variable which defines a discrete partition of the dataset (each document is in one and only one group). We may relax this in the future. While including more covariates in topical prevalence will rarely affect the speed of the model, including additional levels of the content covariates can make the model much slower to converge. This is due to the model operating in the much higher dimensional space of words in dictionary (which tend to be in the thousands) as opposed to topics.

In addition to the default priors for prevalence, we also make use of the glmnet package to allow for penalties between the L1 and L2 norm. In these settings we estimate a regularization path and then select the optimal shrinkage parameter using a user-tuneable information criterion. By default selecting the L1 option will apply the L1 penalty selecting the optimal shrinkage parameter using AIC. The defaults have been specifically tuned for the STM but almost all the relevant arguments can be changed through the control structure below. Changing the gamma.enet parameters allow the user to choose a mix between the L1 and L2 norms. When set to 1 (as by default) this is the lasso penalty, when set to 0 its the ridge penalty. Any value in between is a mixture called the elastic net.

The default prior choice for content covariates is now the L1 option. This uses an approximation framework developed in Taddy (2013) called Distributed Multinomial Regression which utilizes a factorized poisson approximation to the multinomial. See Roberts, Stewart and Airoldi (2014) for details on the implementation here. This is dramatically faster than previous versions. The old default setting which uses a Jeffreys prior is also available.

The argument init.type allows the user to specify an intialization method. The default choice, "Spectral", provides a deterministic inialization using the spectral algorithm given in Arora et al 2014. See Roberts, Stewart and Tingley (2016) for details and a comparison of different approaches. Particularly when the number of documents is relatively large we highly recommend the Spectral algorithm which often performs extremely well. Note that the random seed plays no role in the spectral initialization as it is completely deterministic (unless using the K=0 or random projection settings). When the vocab is larger than 10000 terms we use only the most frequent 10000 terms in creating the initialization. This may case the first step of the algorithm to have a very bad value of the objective function but it should quickly stabilize into a good place. You can tweak the exact number where this kicks in with the maxV argument inside control. There appear to be some cases where numerical instability in the Spectral algorithm can cause differences across machines (particularly Windows machines for some reason). It should always give exactly the same answer for a given machine but if you are seeing different answers on different machines, see for a longer explanation. The other option "LDA" which uses a few passes of a Gibbs sampler is perfectly reproducible across machines as long as the seed is set.

Specifying an integer greater than 1 for the argument ngroups causes the corpus to be broken into the specified number of groups. Global updates are then computed after each group in turn. This approach, called memoized variational inference in Hughes and Sudderth (2013), can lead to more rapid convergence when the number of documents is large. Note that the memory requirements scale linearly with the number of groups so this provides a tradeoff between memory efficiency and speed. The claim of speed here is based on the idea that increasing the number of global updates should help the model find a solution in fewer passes through the document set. However, itt is worth noting that for any particular case the model need not converge faster and definitely won't converge to the same location. This functionality should be considered somewhat experimental and we encourage users to let us know what their experiences are like here in practice.

Models can now be restarted by passing an STM object to the argument model. This is particularly useful if you run a model to the maximum iterations and it terminates without converging. Note that all the standard arguments still need to be passed to the object (including any formulas, the number of topics, etc.). Be sure to change the max.em.its argument or it will simply complete one additional iteration and stop.

You can pass a custom initialization of the beta model parameters to stm.

The control argument is a list with named components which can be used to specify numerous additional computational details. Valid components include:


Controls the maximum number of iterations when estimating the prior for content covariates. When the mode is Jeffreys, estimation proceeds by iterating between the kappa vector corresponding to a particular topic and the associated variance tau before moving on to the next parameter vector. this controls the maximum number of iterations. It defaults to NULL effectively enforcing convergence. When the mode is L1 this sets the maximum number of passes in the coordinate descent algorithm and defaults to 1e8.


Sets the convergence tolerance in the optimization for content covariates. When the mode is Jeffreys this sets the convergence tolerance in the iteration between the kappa vector and variances tau and defaults to 1e-5. With L1 it defaults to 1e-6.


When the mode for content covariate estimation is Jeffreys this controls the maximum number of passes through the sequence of kappa vectors. It defaults to 3. It has no role under L1- see tau.maxit option instead.


When the mode for content covariate estimation is Jeffreys this controls the tolerance for convergence (measured by the L1 norm) for the entire M-step. It is set to .01 by default. This has no role under mode L1- see tau.tol option instead.


a logical indicating whether in content covariate models the intercept should be fixed to the background distribution. TRUE by default. This only applies when kappa.prior is set to L1. If FALSE the intercept is estimated from the data without penalty. In practice estimated intercepts often push term probabilities to zero, resulting in topics that look more like those in a Dirichlet model- that is, most terms have approximately zero probability with some terms with high probability.


When using the L1 mode for content covariates this controls the elastic net mixing parameter. See the argument alpha in glmnet. Value must be between 1 and 0 where 1 is the lasso penalty (the default) and 0 is the ridge penalty. The closer the parameter is to zero the less sparse the solution will tend to be.


Controls the elastic net mixing parameter for the prevalence covariates. See above for a description.


For L1 mode prevalence covariates this controls the selection of the regularization parameter. We use a generic information criterion which penalizes complexity by the parameter ic.k. When set to 2 (as by default) this results in AIC. When set to log(n) (where n is the total number of documents in the corpus) this is equivalent to BIC. Larger numbers will express a preference for sparser (simpler) models.


An integer indicating the maximum number of iterations that the prevalence regression variational algorithm can run before erroring out. Defaults to 1000.


Controls the length of the regularization path when using L1 mode for content covariates. Defaults to 500. Note that glmnet relies heavily on warm starts and so a high number will often (counter-intuitively) be less costly than a low number. We have chosen a higher default here than the default in the glmnet package and we don't recommend changing it.


For L1 mode content covariates this controls the explored path of regularization values. This defaults to .0001. Setting higher numbers will result in more sparse solutions. This is here primarily for dealing with convergence issues, if you want to favor selection of sparser solutions see the next argument.


For L1 mode content covariates this controls the selection of the regularization parameter. We use a generic information criterion which penalizes complexity by the parameter ic.k. When set to 2 (as by default) this results in AIC. When set to log(n) (where n is the total number of words in the corpus) this is equivalent to BIC. Larger numbers will express a preference for sparser (simpler) models.


Sets the number of iterations for collapsed gibbs sampling in LDA initializations. Defaults to 50


Sets the burnin for collapsed gibbs sampling in LDA intializations. Defaults to 25


Sets the prevalence hyperparameter in collapsed gibbs sampling in LDA initializations. Defaults to 50/K


Sets the topic-word hyperparameter in collapsed gibbs sampling in LDa intializations. Defaults to .01


A logical indicating whether a standard contrast coding should be used for content covariates. Typically this should remain at the default of FALSE.


Parameter between 0 and 1 controlling the sparsity of random projections for the spectral initailization. Defaults to .05


Dimensionality of the random projections for the spectral initialization. Defaults to 3000.

Controls the size of blocks considered at a time when computing the random projections for the spectral initialization. Defaults to 2000.


A logical which when TRUE turns on the experimental random projections spectral initialization.


For spectral initializations this will set the maximum number of words to be used in the initialization. It uses the most frequent words first and then they are reintroduced following initialization. This allows spectral to be used with a large V.


Set to codeTRUE by default. If set to FALSE will solve the recovery problem in the Spectral algorithm using a downhill simplex method. See for more discussion.


A logical indicating whether the algorithm is allowed to declare convergence when the change in the bound has become negative. Defaults to TRUE. Set to FALSE to keep the algorithm from converging when the bound change is negative. NB: because this is only an approximation to the lower-bound the change can be negative at times. Right now this triggers convergence but the final approximate bound might go higher if you are willing to wait it out. The logic of the default setting is that a negative change in the bound usually means it is barely moving at all.


If init.type="Custom" you can pass your own initialization of the topic-word distributions beta to use as an initialization. Please note that this takes some care to be sure that it is provided in exactly the right format. The number of topics and vocab must match exactly. The vocab must be in the same order. The values must not be pathological (for instance setting the probability of a single word to be 0 under all topics). The beta should be formatted in the same way as the piece of a returned stm model object stmobj$beta$logbeta. It should be a list of length the number of levels of the content covariate. Each element of the list is a K by V matrix containing the logged word probability conditional on the topic. If you use this option we recommend that you use max.em.its=0 with the model initialization set to random, inspect the returned form of stmobj$beta$logbeta and ensure that it matches your format.


The K=0 spectral setting uses tSNE to create a low-dimensional projection of the vocab co-occurence matrix. tSNE starts with a PCA projection as an initialization. We actually do the projection outside the tSNE code so we can use a randomized projection approach. We use the 50 dimensional default of the rtsne package. That can be changed here.


The Rtsne function in the rtsne package uses a perplexity parameter. This defaults to 30 and can throw an error when too high. stm will automatically lower the parameter for you until it works, but it can also be directly set here.


An object of class STM


The corpus mean of topic prevalence and coefficients


Covariance matrix


List containing the log of the word probabilities for each topic.


The settings file. The Seed object will always contain the seed which can be fed as an argument to recover the model.


The vocabulary vector used.


list of convergence elements including the value of the approximate bound on the marginal likelihood at each step.


Number of Documents by Number of Topics matrix of topic proportions.


Matrix of means for the variational distribution of the multivariate normal latent variables used to calculate theta.


The inverse of the sigma matrix.


The time elapsed in seconds


The version number of the package with which the model was estimated.


Roberts, M., Stewart, B., Tingley, D., and Airoldi, E. (2013) "The structural topic model and applied social science." In Advances in Neural Information Processing Systems Workshop on Topic Models: Computation, Application, and Evaluation.

Roberts M., Stewart, B. and Airoldi, E. (2016) "A model of text for experimentation in the social sciences" Journal of the American Statistical Association.

Roberts, M., Stewart, B., Tingley, D., Lucas, C., Leder-Luis, J., Gadarian, S., Albertson, B., et al. (2014). Structural topic models for open ended survey responses. American Journal of Political Science, 58(4), 1064-1082.

Roberts, M., Stewart, B., & Tingley, D. (2016). "Navigating the Local Modes of Big Data: The Case of Topic Models. In Data Analytics in Social Science, Government, and Industry." New York: Cambridge University Press.

See Also

prepDocuments labelTopics estimateEffect

  • stm
# }
#An example using the Gadarian data.  From Raw text to fitted model using 
#textProcessor() which leverages the tm Package
out <- prepDocuments(temp$documents, temp$vocab, temp$meta)
mod.out <- stm(out$documents, out$vocab, 3, 
               prevalence=~treatment + s(pid_rep), data=out$meta)

#The same example using quanteda instead of tm via textProcessor()
#Note this example works with quanteda version 0.9.9-31 and later
gadarian_corpus <- corpus(gadarian, text_field = "open.ended.response")
gadarian_dfm <- dfm(gadarian_corpus, 
                     remove = stopwords("english"),
                     stem = TRUE)
stm_from_dfm <- stm(gadarian_dfm, K = 3, prevalence = ~treatment + s(pid_rep),
                    data = docvars(gadarian_corpus))
#An example of restarting a model
mod.out <- stm(out$documents, out$vocab, 3, prevalence=~treatment + s(pid_rep), 
               data=out$meta, max.em.its=5)
mod.out2 <- stm(out$documents, out$vocab, 3, prevalence=~treatment + s(pid_rep), 
                data=out$meta, model=mod.out, max.em.its=10)
# }
Documentation reproduced from package stm, version 1.3.3, License: MIT + file LICENSE

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