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I was learning PGM recently and wondering if all linear models can be put into the framework of PGM. We know that the linear model is the most important tool in statistical analysis. It can be generalized to model many different scenarios. If the dependent variable is non-continuous, we have logistic regression, Poisson regression, Cox PH model... If independent variables are non-continuous, we have ANOVA, ANCOVA... If observations are not independent (e.g., multiple levels), we have a Hierarchical Linear Model, Mixed effect model, Variance components model... It seems all these models have a corresponding PGM, so is it true that PGM covers all these models? Can anyone let me know if there is any situation the linear model is applicable, but PGM is not? Also, I wonder what restricts the wide application of PGMs.

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