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Estimating linear causality in the presence of latent variables

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Abstract

Learning causality from data is known as the causal discovery problem, and it is an important and relatively new field. In many applications, there often exist latent variables, if such latent variables are completely ignored, which can lead to the estimation results seriously biased. In this paper, a method of combining exploratory factor analysis and path analysis (EFA-PA) is proposed to infer the causality in the presence of latent variables. Our method expands latent variables as well as their linear causal relationships with observed variables, which enhances the accuracy of causal models. Such model can be thought of as the simplest possible causal models for continuous data. The EFA-PA is very similar to that of structural equation model, but the theoretical model established by the structural equation model needs to be modified in the process of data fitting until the ideal model is established.The model gained by EFA-PA not only avoids subjectivity but also reduces estimation complexity. It is found that the EFA-PA estimation model is superior to the other models. EFA-PA can provides a basis for the correct estimation of the causal relationship between the observed variables in the presence of latent variables. The experiment shows that EFA-PA is better than the structural equation model.

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Acknowledgements

We thank the editor and referees for comments that led to improvements in the manuscript. The research is supported by the National Natural Science Foundation of China (61573266).

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Authors and Affiliations

  1. The School of Mathematics and Statistics, Xidian University, Xinglong Section of Xifeng Road 266, Xi’an, 710126, Shaanxi, China

    Nina Fei & Youlong Yang

Authors
  1. Nina Fei
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  2. Youlong Yang
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Correspondence to Nina Fei.

Appendix

Appendix

1. See Table 5.

Table 5 The specific meaning of the16 observed variables
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2. See Fig. 6.

With a scree plot auxiliary judgment the number of latents

Fig. 6
figure 6

Scree plot is used to help determine the number of latent variables

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3. See Table 6.

Table 6 Factor loading matrix after orthogonal
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Fei, N., Yang, Y. Estimating linear causality in the presence of latent variables. Cluster Comput 20, 1025–1033 (2017). https://doi.org/10.1007/s10586-017-0824-5

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