Analysis of mixed correlated bivariate zero-inflated count and (<i>k</i>, <i>l</i>)-inflated beta responses with application to social network datasets

This paper presents a new model that monitors the basic network formation mechanisms via the attributes through time. It considers the issue of joint modeling of longitudinal inflated (0, 1)-support continuous and inflated count response variables. For joint model of mentioned response variables, a correlated generalized linear mixed model is studied. The fraction response is inflated in two points <i>k</i> and <i>l</i> (<i>k</i> &lt; <i>l</i>) and a <i>k</i> and <i>l</i> inflated beta distribution is introduced to use as its distribution. Also, the count response is inflated in zero and we use some members of zero-inflated power series distributions, hurdle-at-zero, members of zero-inflated double power series distributions and zero-inflated generalized Poisson distribution as our count response distribution. A full likelihood-based approach is used to yield maximum likelihood estimates of the model parameters and the model is applied to a real social network obtained from an observational study where the rate of the <i>i</i>th node’s responsiveness to the <i>j</i>th node and the number of arrows or edges with some specific characteristics from the <i>i</i>th node to the <i>j</i>th node are the correlated inflated (0, 1)-support continuous and inflated count response variables, respectively. The effect of the sender and receiver positions in an office environment on the responses are investigated simultaneously.