An exploratory threshold regression model of the relationship between student performance and attendance

It is widely believed that attendance has a positive effect on student performance in terms of grades achieved. While the empirical evidence generally supports this belief, some studies do not, and the size of the effect varies across disciplines. Interestingly, Durden and Ellis (1995) find that attendance (absence) only has a positive (negative) and significant impact on student performance below (above) a certain threshold using intercept shift dummies. Gendron and Pieper (2005) as well as Westerman et al (2011) have confirmed a similar non-linear relationship using a quadratic function of attendance and logistic regressions based on 3 different quartiles of performance, respectively. We apply Threshold Regression (TR) to a level 5 quantitative economics module to consider an alternative non-linear specification. As far as we are aware there have only been a few papers considering non-linear effects of attendance on student performance and no previous applications of the TR form of non-linearity to model the relationship between attendance and student performance. Our TR method extends the literature by testing whether there are thresholds for continuous variables, such as attendance, that define values of the threshold variable where the model’s coefficients change. If there are thresholds, the method identifies how many and estimates the values where they occur. Our favoured model is a TR specification that has higher explanatory power (47.5%) than all linear and cubic models that we consider. This favoured TR model has one significant threshold, using attendance as the threshold variable, and includes the intercept and the prerequisite module’s grade as variables. Both these variables’ coefficients shift when the threshold level of attendance is 50%. Although there is some ambiguity over which TR model to favour in terms of model fit, our favoured model is the best fitting specification that does not make any impossible predictions of student grades.