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Applications of Linear Mixed Effect Models: An Analysis of Missouri School Data

Dan Kowal, Department of Mathematics, Washington University in St. Louis

March 22, 2012 - 4:15 pm to 5:15 pm
Location: Cupples I, Room 6 | Host: Prof. Jimin Ding

Undergraduate Senior Honors Thesis Presentation
Abstract: In this report, we analyze standardized mathematics exam scores from a Missouri school district. Using linear mixed effect modeling, we model student exam scores as repeated measurements in order to investigate the influencing factors on student performance. After considering several mixed effect models and comparing them using information criteria (AIC and BIC) and likelihood ratio tests, we settle on two models for the data: (i) a random intercept model that assumes constant variance across exams and equal correlation between exams, and (ii) an extension of this model that allows the variance of exam scores for low-income students to vary across exams. By analyzing fixed effect parameter estimates and random intercept predictions, we find significant stratification within ethnicity and economic status. We further investigate the presence of monotone trends of exam scores in order to identify groups of students whose performance significantly improved or declined relative to the national student population. By combining these results, we can identify student features that predict either strong or weak performance on the standardized mathematics exams.

 

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