In a previous post we recovered the conditional independence structure in a dataset of mixed variables describing different aspects of the life of individuals diagnosed with Autism Spectrum Disorder, using the mgm package. While depicting the independence structure in multivariate data set gives a first overview of the relations between variables, in most applications we interested in the exact parameter estimates. For instance, for interactions between continuous variables, we would like to know the sign and the size of parameters - i.e., if the nodes in the graph are positively or negatively related, and how strong these associations are. In the case of interactions between categorical variables, we are interested in the signs and sizes of the set of parameters that describes the exact non-linear relationship between variables.
Determining conditional independence relationships through undirected graphical models is a key component in the statistical analysis of complex obervational data in a wide variety of disciplines. In many situations one seeks to estimate the underlying graphical model of a dataset that includes variables of different domains.