Stable Specification Search in Structural Equation Models with Latent Variables

Abstract

In our previous study, we introduced stable specification search for cross-sectional data (S3C). It is an exploratory causal method that combines stability selection concept and multi-objective optimization to search for stable and parsimonious causal structures across the entire range of model complexities. In this study, we extended S3C to S3C-Latent, to model causal relations between latent variables. We evaluated S3C-Latent on simulated data and compared the results to those of PC-MIMBuild, an extension of the PC algorithm, the state-of-the-art causal discovery method. The comparison showed that S3C-Latent achieved better performance. We also applied S3C-Latent to real-world data of children with attention deficit/hyperactivity disorder and data about measuring mental abilities among pupils. The results are consistent with those of previous studies.

Causal Relationships of Sexual Dysfunction Factors in Women Using S3C-Latent

“…S3C is structured to model a causal relationship between observed variables, while S3C-Latent is structured to model the causal relationship between latent variables [24]. Latent variables are variables that cannot be [25]. Specifically, S3C uses the Structural Equation Modeling (SEM) representation of latent variables.…”

“…Specifically, S3C uses the Structural Equation Modeling (SEM) representation of latent variables. SEM of latent variables consists of two models, namely structural models and measurement models [24][25][26][27]. The structural model is a model that shows the relationship between factors .…”

“…Next is the estimation (parameter). These parameters are then converted into a covariance matrix with the implied covariance matrix model [24,25]. is a parameter set that is used to find the best parameter.…”

“…is the covariance matrix of the indicators written as a function of the parameters , is the coverage matrix of indicators and , and is the covariance matrix of the indicator. Figure 2 is an example of SEM with three variables [24,25] ξ1 (with , , and as indicators), ξ2 (with , , and as indicators), and (with , , and as indicators). SEM parameters can only be estimated when the so-called identification conditions are fulfilled.…”

“…SEM parameters can only be estimated when the so-called identification conditions are fulfilled. The conditions for SEM with latent variables that we consider are There are at least three or more indicators per latent variable, Each row of and has only one nonzero element, Each latent variable is scaled, and is diagonal [24,25]. The first condition will be added if there are latent variables that have indicators of less than three.…”