An estimation of causal structure based on Latent LiNGAM for mixed data

• Published in: Behaviormetrika Vol. 47; no. 1; pp. 105 - 121
• Main Authors: Yamayoshi, Mako, Tsuchida, Jun, Yadohisa, Hiroshi
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 2020; Springer Nature B.V
• Subjects: Algorithms; Chemistry and Earth Sciences; Computer Science; Economics; Expected values; Finance; Generalized linear models; Insurance; Management; Mathematics and Statistics; Methods; Original Paper; Physics; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Variables; Latent variable; Link function; Generalized linear model; SEM; Causal structure
• ISSN: 0385-7417; 1349-6964
• DOI: 10.1007/s41237-019-00095-3

The linear non-gaussian acyclic model (LiNGAM) has been proposed as a method for estimating causal structures using structural equation modeling (SEM). LiNGAM is useful as an exploratory estimation method for a causal structure. However, the assumptions that all observed variables in LiNGAM are continuous is not applicable in case of mixed data (i.e., when discrete variables are also included in the dataset). Therefore, we propose the Latent LiNGAM (L-LiNGAM), where each variable corresponds to a continuous latent variable and is observed as data through transformation via a link function. In the numerical study, when mixing discrete variables, the estimation of causal structure using L-LiNGAM is proven useful in terms of sum of squared error and path recovery. Moreover, from real-world data applications, the causal structure estimated by L-LiNGAM is shown to be the best for evaluation under SEM. The model fit is also superior to that of existing methods.