Abstract

The mover-stayer model is a model to study social change over time in heterogeneous population. Also known as “split population model” or as “cure model” in the medical field, the mover-stayer model extends standard survival analysis models by allowing for the existence of a subgroup of individuals called “stayers” that with probability 1, will never experience the event.
In the classical setting, the probability of being a stayer in a given state is the same for all individuals and is equal to the proportion of stayers in that state. Extensions in which this probability depends on fixed-time covariates have already been proposed but the inclusion of time-varying covariates remains challenging.
When subjects are assessed periodically over a time period, exact transition times are usually not observed, and only the state occupied at each assessment, together with the measurements of risk factors, is available. Such data are often called panel data.
This type of data is common in many fields and requires discrete-time methods, which are advantageous for incorporating time-varying explanatory variables.
In this paper, we propose a new dynamic version of the discrete mover-stayer model that is specified by a multinomial logistic regression and incorporates time-varying covariates.
We develop a maximum likelihood estimation procedure for this problem, based on the joint modeling of the multinomial response of interest and the cure status. We investigate the identifiability of the resulting model. Then, we conduct a simulation study to investigate its finite-sample behavior and its performance with respect to other common models used in the literature.
Our paper is motivated by the analysis of student mobility data.
In particular, we want to model the probability for master’s degree students to be movers depending on time-varying covariates such as the bachelor’s degree and the ranking of the university in which they are enrolled, considering that part of the population will never experience the moving event.