Incomplete ordinal panel responses with initial condition and skew-normal random effect

This paper presents a model for the ordinal categorical panel data with skew-normal random effects, endogenous initial condition, and non ignorable (NI) non monotone missing data. We assumed three separate models for the initial condition, subsequent responses, and missing procedure. The baseline or initial response variable and subsequent response variables are modeled as ordinal logistic, whereas the logistic binary model is considered for the missing process where the maximum likelihood estimates are obtained using Monte Carlo methods. The results show that in the presence of missing data, the skew-normal random effects produce better results compared to the normal one, and considering the endogenous initial conditions is effective in modeling the results of the observed and missing responses such that the patients whose severity of schizophrenia is higher at the beginning of the process have a higher chance of missing on the subsequence times. In this research, schizophrenia data and then simulation studies have been used to check the performance of the proposed model. The results show that the skew-normal random effect using the NI non monotone missing mechanism by increasing the skewness value produces better results in the analysis of simulation studies.