A significant amount of data is not attended to clinically in routine sleep studies. Measures of sleep physiology not obvious to the human eye may provide important clues to disease states, and responses to therapy. For example, it has been noted that eye movements change significantly in patients exposed to antidepressant medications. This paper describes how eye movements were different in depressed patients who used antidepressant medications, compared to those who did not. Groups 1 and 2 included five patients each who used citalopram and venlafaxine respectively compared to five patients not taking any antidepressants. Autoregressive (AR) coefficients of eye movements recorded during sleep have been derived. These coefficients represent the shape of the sleep eye movements of all three groups and were classified using discriminant analysis. In this paper, an improved methodology has been used for this classification. This method includes eye movement detection with improved eye movement detection software and evaluation of AR coefficients with fixed segments. The AIC method has been used for determination of an appropriate model order of 27. AR coefficients are then derived on the basis of this optimized value and are then classified with a linear discriminant function. The overall average of the regular method accuracies were 76.4%, and 78.7% for groups 1 and 2 respectively. The overall average of the leave-one-out method accuracies were 75.5% and 77.5% for Groups 1 and 2. The results demonstrate that eye movements can be quantified and characterized with this approach. This methodology will allow the development of new metrics that may assist in disease classification, and response to treatment in a variety of neuropsychiatric conditions.