Stephen Michael Ponisciak
Research Associate, Alliance of Catholic EducationUniversity of Notre Dame
Bayesian Analysis of Teacher Effectiveness
The quality of schools and teachers has become an popular issue in recent years. Several authors have discussed the propriety of using students' scores on state or national tests to evaluate individual students' performance, teachers' performance, and schools' performance. More recently, others (among them Sanders and Horn (1998)) have advocated a ``value-added'' approach, in which a teacher's performance is evaluated using his or her students' gains on the norm-referenced sections of a statewide exam. However, standardized tests bring with them a long and arduous history of controversy. Seeking to avoid these arguments (and to create new ones), we have developed a system to evaluate teacher performance based on students' grades in subsequent courses, rather than test scores. Using five years of data from high schools in one school district, we evaluate the quality of teachers based on students' course grades by treating the teacher and student as random effects in an ordinal probit model with latent variables (as in Johnson (1997) and Johnson and Albert (1999)). Our analysis includes only those courses of study that are clearly consecutive, such as mathematics and foreign languages. We evaluate whether student-level variables, such as the student's average grade in other courses and demographic variables, should be included in the model, and we assess the fit of the model by examining sorted latent residuals and determining how many of the pairwise comparisons are correctly evaluated. We conclude that a teacher effect can be detected (when it exists), and that teachers have a measurable effect on students' subsequent achievement. Such effects appear to decay differently in different subjects, and are affected by student-level covariates.