Path Analysis for Recursive Generalized Linear Model Systems

TL;DR: In this paper, the authors proposed a path analysis method for categorical variables based on generalized linear models (GLMs), which is an analogy to the LISREL approach for path analysis of continuous variables.

Abstract: Path analysis is usually carried out in causal systems of continuous variables, i.e. Linear Structural Equation Model (LISREL) (Bentler & Weeks, 1980). In LISREL approach, causal relationships among variables concerned are described by a path diagram, and the relationships are translated into linear equations of the variables. In comparison with path analysis of continuous variables, that of categorical variables is complex, because the causal system under consideration cannot be described by linear regression equations. Hagenaars (1998) made a discussion of path analysis of categorical variables by using a loglinear model approach. Although the approach is an analogy to LISREL, the discussion of the direct and indirect e¤ects was not made. In path analysis with categorical variables, it is a question how the e¤ects are measured. Eshima et al. (2001) proposed a method of path analysis of categorical variables by using logit models. In this approach, the direct and indirect e¤ects of variables are discussed according to log odds ratios and the average e¤ects are de…ned for summarizing them; however the interpretation of the average e¤ects was not provided. Kuha & Goldthorpe (2010) proposed a path analysis method according to log odds ratios; however increasing categories in variables makes the path analysis to be complex. This paper proposes a basic method for path analysis in causal systems with generalized linear models (GLMs). First, the odds ratio in GLMs is discussed and the interpretation in entropy is given. Second, the total, direct and indirect summary e¤ects in GLMs are discussed by using log odds ratios, and to standardize the e¤ects the entropy crenelation coe¢ cient (ECC) or the entropy coe¢ cient of determination in GLMs is employed. A numerical example is given to illustrate the present approach. Finally, discussions and conclusions to this study are provided.