Investigating growth models of academic achievement scores by maximum likelihood and bayes estimations

In this study, the quadratic growth model established with the mathematics achievement scores of the students from preschool to the fifth grade was estimated according to the maximum likelihood and Bayesian methods. In that model, motivation and attention were measured at nine different time points with the math achievement. On the student level, gender, ethnicity, school starting age, socioeconomic level variables, school level, school type, and national school lunch program percentage were selected as predictors. For the analyses, ECLS-K 2011 (Early Childhood Longitudinal Study – Kindergarten) dataset was used. Analyses were conducted after a listwise deletion with a sample size of 2181 from 165 schools. In conclusion, both methods produced similar results, however Bayesian methods produced lower error estimations for small and large sample sizes. From the education perspective, it is found that students' math scores increase over time, and the growth rate decreases. Motivation, attention, school starting age, and socioeconomic status significantly predict math growth, and all of these variables have a positive coefficient. Even though there is no significant difference between male and female students initially, the linear growth of male students is higher. Additionally, male students' growth rate decrease starts earlier than the females. The initial math scores and the linear growth rate of African American and Hispanic students were lower than white and Asian students. The school type variable has only affected the quadratic growth rate.