Causal clustering for 2-factor measurement models

Many social scientists are interested in inferring causal relations between "latent" variables that they cannot directly measure. One strategy commonly used to make such inferences is to use the values of variables that can be measured directly that are thought to be "indicators" of the latent variables of interest, together with a hypothesized causal graph relating the latent variables to their indicators. To use the data on the indicators to draw inferences about the causal relations between the latent variables (known as the structural model), it is necessary to hypothesize causal relations between the indicators and the latents that they are intended to indirectly measure, (known as the measurement model). The problem addressed in this paper is how to reliably infer the measurement model given measurements of the indicators, without knowing anything about the structural model, which is ultimately the question of interest. In this paper, we develop the Find- TwoFactorClusters (FTFC) algorithm, a search algorithm that, when compared to existing algorithms based on vanishing tetrad constraints, also works for a more complex class of measurement models, and does not assume that the model describing the causal relations between the latent variables is linear or acyclic.