Causal Clustering for 2-Factor Measurement Models

Abstract

Many scientific research programs aim to learn the causal structure of real world phenomena. This learning problem is made more difficult when the target of study cannot be directly observed. One strategy commonly used by social scientists is to create measurable "indicator" variables that covary with the latent variables of interest. Before leveraging the indicator variables to learn about the latent variables, however, one needs a measurement model of the causal relations between the indicators and their corresponding latents. These measurement models are a special class of Bayesian networks. This paper addresses the problem of reliably inferring measurement models from measured indicators, without prior knowledge of the causal relations or the number of latent variables. We present a provably correct novel algorithm, FindOneFactorClusters (FOFC), for solving this inference problem. Compared to other state of the art algorithms, FOFC is faster, scales to larger sets of indicators, and is more reliable at small sample sizes. We also present the first correctness proofs for this problem that do not assume linearity or acyclicity among the latent variables.

Finding Pure Submodels for Improved Differentiation of Bifactor and Second-Order Models

“…If pure indicators are even rarer, then using the FOFC algorithm is one way of discovering that, which would be an important fact about the limitations of current psychometric models. There is also a second algorithm, Find Two Factor Clusters (Kummerfeld et al 2014), that uses a related set of rank constraints to look for “pure” bi-factor models, which can be employed in place of FOFC. Although these results are encouraging, further research into making the output of FOFC more reliable and more stable is needed, and empirical applications are also needed.…”

“…First we describe an algorithm for finding pure sub–models from data: Find One Factor Clusters or FOFC for short (Kummerfeld & Ramsey forthcoming, Kummerfeld et al 2014). A more detailed description of this algorithm is given in Appendix 2.…”

“…This assumption is called “rank faithfulness” (Kummerfeld et al 2014). Its justification is measure-theoretic.…”

“…Hence we leave it up to the researcher to decide the threshold for “sufficiently many indicators.” If the second–order model is rejected, the algorithm does not specify what to conclude about accepting or rejecting the bi–factor model. One possibility is to use the Find Two Factor Clusters algorithm (Kummerfeld et al 2014) that is analogous to FOFC and can be applied to the same data to draw conclusions about accepting or rejecting the bi–factor model. However, we will leave a full discussion of that for another article.…”

Comparison of strategies for scalable causal discovery of latent variable models from mixed data

“…The FindOneFactorClusters (FOFC) algorithm imposes restrictions on the graphical structure of the true causal model, thereby rendering it unsuitable to the general causal discovery problem [10]. Previously Overcomplete ICA was used to learn a causal ordering amongst the variables which allows an experimenter to learn experimental predictions, however this approach is limited in scale and requires few latent variables relative to sample size [8].…”