To examine the predictive utility of three scales provided in the released database of the Third International Mathematics and Science Study (TIMSS) (international plausible values, standardized percent correct score, and national Rasch score), information was obtained on the performance in state examinations in mathematics and science in 1996 (2,969 Grade 8 students) and in 1997 (2,898 Grade 7 students) of students in the Republic of Ireland who had participated in TIMSS in 1995. Performance on TIMSS was related to later performance in the state examinations using normal and nonparametric maximum likelihood (NPML) random effects models. In every case, standardized percent correct scores were found to be the best predictors of later performance, followed by national Rasch scores, and lastly, by international plausible values. The estimates for normal mixing distributions are close to those estimated by the NPML approach, lending support to the validity of estimates.