Reliability of Topic Modeling (2025)

Abstract: Topic models allow researchers to extract latent factors from text data and use those variables in downstream statistical analyses. However, these methodologies can vary significantly due to initialization differences, randomness in sampling procedures, or noisy data. Reliability of these methods is of particular concern as many researchers treat learned topic models as ground truth for subsequent analyses. In this work, we show that the standard practice for quantifying topic model reliability fails to capture essential aspects of the variation in two widely-used topic models. Drawing from a extensive literature on measurement theory, we provide empirical and theoretical analyses of three other metrics for evaluating the reliability of topic models. On synthetic and real-world data, we show that McDonald’s \omega provides the best encapsulation of reliability. This metric provides an essential tool for validation of topic model methodologies that should be a standard component of any topic model-based research.

## introduction over twenty years after its popularization by @xcite , topic modeling remains a leading methodology for analyzing natural language. researchers use models such as latent dirichlet allocation (lda) and its many variations to uncover latent topics in human language, with applications ranging from mathematics to genomics @xcite @xcite . these methods convert high-dimensional data into low-dimensional topic representations which are more easily used in downstream analyses @xcite . when it comes to human language and similar domains, topic models clearly cannot capture the full complexity of the data, so they instead provide a useful approximation of the data's underlying structure @xcite . lda and many topic models are fit with approximate methods due to their intractable likelihoods; these implementations may be sensitive to random initialization, hyperparameter selection, or small perturbations to the data @xcite . we analyze topic models through the lens of internal consistency reliability, offering insight into the downstream analyses which they enable. internal consistency reliability, a well-established concept in psychometrics, describes how well varying items measure the true underlying construct @xcite . in this setting, reliability measures the extent to which different replications of a topic model consistently capture the underlying thematic structure. while there may be multiple suitable granular structures for different tasks, our focus is on identifying the optimal structure that best represents the underlying organization within a specific dataset. we conceptualize topic modeling as a measurement problem; the lower-dimensional representation produced by a topic model provides an imperfect measure of the data's underlying structure. many analyses relying on topic models do not consider the reliability of these measurements nor the effect that unreliability could have on their analyses. @xcite , for example, train an lda topic model on research abstracts to quantify trends in ai research; if repeated re-trainings of lda produced significant variation in the learned topics, it would undermine any research conclusions drawn from those topics. this is true for many other applications of topic modeling, from analyses of consumer complaints, academic peer review, and twitter posts @xcite @xcite . a better understanding of topic modeling reliability can strengthen our understanding of these papers and many like them. reliability is not a new consideration for the nlp field. inter-annotator agreement (iaa) has been widely studied in analyses of human labelers @xcite @xcite . iaa has also been explored during the interpretation of topic models; @xcite analyzes reliability of annotators' ability to name topics from their most prevalent words. compared to this widespread study of the reliability of annotators, there has been relatively little exploration of the reliability of topic models themselves. @xcite highlights in particular the need for a measure of the internal consistency of such models. the study of internal consistency reliability was first popularized by @xcite but has been widely studied in the statistical literature @xcite @xcite . despite the existence of this statistical theory, the widely-adopted standard practice for measuring topic model reliability is an ad hoc approach @xcite . this approach repeatedly fits a topic model using different random initializations and calculates the proportion of topic matches. here, two topics are said to match if the cosine similarity between their top-word probabilities is above a threshold of 0.7. among the issues with this method is its use of a fixed threshold, which has been criticized in studies of iaa @xcite . in this paper, we show that the lack of theoretical grounding and omission of the document over topics distribution in the standard practice method results in an entirely insufficient reliability quantification. building on the statistical literature, we introduce and evaluate methods that encompass both the reliability of topic models in terms of top words and distribution of documents over topics. foot_0 ## related work most work related to topic model reliability has been focused on topic model quality. coherence, a measure of quality and human interpretability of a topic, has been widely studied @xcite . topic model quality differs fundamentally from topic model reliability. existing methods attempt to quantify topic model reliability or stability either employ variations of similarity measures and/or require domain knowledge. @xcite quantifies the stability of topic models using similarity and domain specific information, differing from our approach both in methodology and in their requirement for domain specific knowledge. given its reliance on domain knowledge, this method is unrelated to our work and not directly comparable. @xcite proposes assessing reliability of the topics and the topic model using varying similarity measures. @xcite proposes the asymptotic average standard deviation of pairwise similarity as a measure of robustness, and argues that robustness is akin to reliability. @xcite proposes a reliability measure comprised of the proportion of top-word cosine similarities above a threshold of 0.7 and is currently the widely accepted standard practice for reliability of topic models. these methods for quantifying reliability are not rooted in statistical practice, an absence shown to be problematic for inter-annotator reliability in @xcite . we emphasize that the similarity measure is not a measure of reliability and showcase the shortcomings of this type of quantification. internal consistency reliability has specifically been called for in embeddings, in scores for llm performance on benchmarks, and in nlp methods at large @xcite @xcite . further nlp literature uses the term reliability, but does not refer to statistical reliability measures @xcite @xcite . ## preliminaries: unidimensional reliability reliability literature focuses heavily on unidimensonal cases @xcite . we first consider unidimensional reliability to investigate assumptions for the multidimensional counterparts. unidimensional reliability is later employed to quantify reliability of a trivial topic model with two topics, as only one topic is necessary for identifiability. ## topic model reliability methods in the context of nontrivial topic modeling, where numerous topics are considered, unidimensional measurements or groups thereof are inadequate representations of the data. we propose three multidimensional counterparts as potential suitable extensions for topic model reliability. to adequately compare topics, topics must be aligned first to determine their counterpart in other replications. we use the standard practice topic matching method defined in @xcite of matching topics with the highest cosine similarity among top-word probabilities. this matching choice is selected purposefully to allow for a direct comparison between the current standard practice reliability measure from @xcite and the reliability measures we introduce below. ## data to demonstrate the reliability of lda in a controlled setting, we conducted experiments using both trivial and nontrivial synthetic datasets, each consisting of 10,000 texts generated using the framework outlined in wood-doughty et al. @xcite . the trivial dataset is a bag-of-words sample with a vocabulary of 16 and a ground truth of 2 topics. the nontrivial dataset is derived from a bagof-words lda model with 200 topics, trained on filtered webtext data @xcite . for the nontrivial data, we considered topic models with a misspecified number of topics (20, 50, and 100), simulating a common scenario in practice as determining the optimal number of topics remains a challenging task @xcite . considering reliability across models with varying numbers of topics remains crucial for applications that interpret topic models, such as @xcite , to provide a measure of the certainty in the research conclusions drawn from interpretations of topics. we also applied our methodology to a realworld dataset of 5,223 consumer complaints about cryptocurrency companies filed with the cfpb, a corpus publicly available on the entity's website @xcite . in this dataset, the true number of topics is unknown, so we investigated reliability variation across 20, 50 and 100 topics. to assess reliability, we generated 100 replications for the application and nontrivial synthetic data and 10 replications for the trivial synthetic data, each with a randomly generated seed. this approach allows evaluation of the consistency of topic model results across various random initializations. for synthetic and application data, topic model replications were generated using the topicmodels package from @xcite and the stm package from @xcite . both packages employed a specified number of topics and their default settings, with gibbs sampling for topicmodels and spectral decomposition (deterministic) for stm. these replications were executed on a cpu. ## results our three proposed reliability measures are compared against the widely accepted and adopted standard practice method outlined in @xcite . while alternative baselines exist, such as those proposed by @xcite and @xcite , these have similar limitations to the standard practice. existing approaches that do not require domain-specific knowledge, including the maier et al. ( 2018 ) method, rely on similarity measures. these similarity measures do not inherently capture true reliability, as detailed in section 2. while we acknowledge the significant influence and widespread adoption of the maier et al. ( 2018 ) method, making it a standard for topic model reliability evaluation, its reliance on similarity measures, which lack a strong statistical foundation, presents a fundamental limitation for accurately assessing true model reliability. this limitation extends to other methods employing similar techniques. methods like @xcite , which rely on domain-specific knowledge or subjective judgments, are not directly comparable to our work and are therefore not considered here. given these considerations, we prioritize the maier et al. ( 2018 ) method as the primary baseline due to its widespread adoption and the shared shortcomings of currently available comparative approaches. the usage of 0.7 as a cutoff within the maier et al. ( 2018 ) methodology (the current standard practice) is likely due to existing literature that argues cronbach's alpha should @xmath0.7 to be considered reliable @xcite . while our results will show the detriment of the current practice metric's incorporation of such a hard cutoff with further investigation provided in appendix a, related reliability literature is useful for interpreting and understanding resulting reliability measures. we use the widely accepted cronbach's alpha rule of thumb, described in ## discussion reliability is a critical factor in topic model analysis, significantly influencing subsequent research. our findings highlight the intricate relationship between topic model complexity, predictive accuracy, and reliability. while increasing the number of topics in an lda model can enhance feature representation for predictive tasks, it can also compromise the model's reliability when used for corpusbased analysis. furthermore, inherent randomness in topic models can introduce significant variability, making results less interpretable and reliable. our reliability method provides a vital tool that should be a standard component of any topic modelbased research, serving as a cornerstone for assessing robustness of topic models and ensuring reliability of subsequent analyses. this method can be extended to alternative topic modeling methods like nmf and bertopic, a planned direction for our future work @xcite . researchers should prioritize reliability as a fundamental component of topic model analysis, akin to the significance of standard errors in statistical modeling. by reporting reliability measures, researchers can present a more comprehensive and accurate understanding of their findings, mitigating the risk of drawing misleading conclusions. ## limitations the work in this paper is limited by the existing reliability measurements. currently, no nonlinear reliability measures exist as all existing measurements rely upon the classical statistical test theory assumptions, of which linearity of errors is included. given that measurement error in topic models is not expected to be linear, such a measure would strengthen this work. while the selected topic matching process facilitates direct comparison to the standard practice method, it simplifies the complex relationship between topics and documents by neglecting document over topic distributions. this simplification, though necessary for comparability, may overlook important aspects of document over topic associations. future research could explore more comprehensive topic matching methods that explicitly consider the distribution of documents over topics and alternative similarity measures that incorporate additional semantic information. it's important to note that the selected topic matching method was primarily driven by comparability with existing standards, and future research could investigate the impact of different topic matching methods on the proposed approach's overall performance. the @xcite method has emerged as the de facto standard for topic model reliability assessment, evidenced by its widespread adoption and significant research attention, serving as a robust and representative benchmark for stability assessment and providing a solid foundation for comparison. we emphasize that similarity measures are not a measure of reliability and are not statistically grounded, a core weakness of the @xcite methodology. following this reasoning, we argue that all related methods employing similarity measures are similarly weakened by the lack of statistical theory to back up the method and assume the limitations accordingly. despite the practical relevance of the standard practice baseline and its robust and representative nature as a benchmark for stability assessment, comparing to a single baseline presents a limitation in scope. future work could investigate the impact of different baselines on our proposed reliability measure and explore the potential benefits of incorporating alternative approaches. the work in this paper is limited to lda topic models, but provides a framework that can be extended to alternative topic modeling methods like nmf and bertopic @xcite . as we note in section 7, this is a planned direction for future work. ## ethics statement no ethical issues are posed by the theory or application discussed in this work. the application data from the cfpb public website is anonymized and contains no unique identifiers, thereby preventing any potential privacy violations. future applications of the methods developed in this paper may pose ethical issues depending on the proprietary nature of future data sets. required privacy regulations should be followed closely by researchers applying these methods to proprietary datasets.