On the Pervasiveness of Long Range Memory Processes in Daily High School Attendance Rates

Few educational researchers or practitioners would question that high school attendance is an important mediator in the causal network that is used to explain academic achievement, yet attendance remains under-researched. The New York City Department of Education (NYCDOE) has created an opportunity to examine the longitudinal trends and dependencies in daily attendance rates as it created a repository of daily attendance rates for all its schools, starting in 2004. The present analysis examines the dynamical patterns in daily attendance rates over a ten-year period (Sept. 2004 - June 2014) in six small high schools and ten large ones. As was done in previous work, this analysis systematically distinguishes short range, seasonal and long range dependencies in the data using time series analysis. Seasonal cycles are predictable (here, fluctuation by days of the week), the long range dependencies indicate cycles that are unpredictable, suggestive of more complex dynamical processes, such as self-similarity, self-organized criticality and scale invariance, features that are difficult to detect by school building personnel, but are important aspects of the systems' behavior. Seasonal cycles were found in three of the nine large schools and in all six small ones. Significant long range dependencies (Hurst exponent) were found in all large schools and all but one of the small ones. The pervasiveness of the long range processes over and above the seasonal cycles is striking, and may suggest an adaptability of these systems to fluctuations in the exogenous processes that find their expression in daily attendance behavior (e.g., parental involvement). However, this latter interpretation is in need of further empirical support.