Controlling for individual heterogeneity in longitudinal models, with applications to student achievement

Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a ``bias compression'' property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.Comment: Published at http://dx.doi.org/10.1214/07-EJS057 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Relationship Between Prior Experiences in Mathematics and Pharmacy School Success

Objective. To assess students’ pre-pharmacy math experiences, confidence in math ability, and relationship between experiences, confidence, and grades in math-based pharmacy courses. Methods. A cross-sectional survey of first year to third year pharmacy students was conducted. Students reported type of pre-pharmacy math courses taken, when they were taken [high school (HS) vs. college] and year of HS and college graduation. Students rated their confidence in math ability using the previously validated 11-item Fogerty Math Confidence Scale (Cronbach alpha=0.92). Math grade point average (GPA), Pharmacy College Admission Test quantitative (PCAT quant) scores, and grades (calculations and kinetics) were obtained from transcripts and school records. Spearman correlation and multivariate linear regression were used to compare math experiences, confidence, and grades. Results. There were 198 students who reported taking math courses 7.1 years since HS graduation and 2.9 years since their last schooling prior to pharmacy school. Students who took math courses with more time since HS/last schooling had lower calculations and kinetics grades. Students reporting having taken more HS math courses had better calculations grades. Students with higher math GPA, and PCAT quant scores also had higher calculations and kinetics grades. Greater confidence in math ability was associated with higher calculations grades. In multivariate regressions, PCAT quant scores and years since HS independently predicted calculations grades, and PCAT quant scores independently predicted kinetics grades. Conclusion. The number of pre-pharmacy math courses and time elapsed since they were taken are important factors to consider when predicting a pharmacy student’s success in math-based pharmacy school courses

Specific SPS construction studies: Construction tasks, construction base

A concept for building the 5000 MW reference solar power satellite in Earth orbit is discussed. The system uses silicon solar cells. The GEO base has contiguous facilities for concurrent assembly and subsequent mating of the satellite energy conversion system and its power transmission antenna. The end builder construction system uses 10 synchronized beam machines to automatically fabricate continuous longitudinal beams for the energy conversion system

Cooperation after War: International Development in Bosnia, 1995 to 1999

This paper discusses how predispositions, incentives, the number and heterogeneity of participants, and leadership (Faerman et al. 2001) jointly influenced the international effort to develop Bosnia and Herzegovina. International coalitions, task forces, and advisory groups are increasingly charged with implementing reforms following civil conflict. This requires a complex web of interorganizational relationships among NGOS, donors and host nations at both global and ‘ground’ levels. To better understand development assistance, attention must be paid to the relationships between these varied players. We find that four factors influenced relationships between policy, donor, and implementing organizations; and those strained relationships, in turn, affected development success. The paper draws on interviews, conducted in Bosnia, with 43 development professionals, observation of development meetings in Tuzla and Sarajevo, and review of related documents from international development programs.international development, interorganizational relationships and cooperation

Missing data in value-added modeling of teacher effects

The increasing availability of longitudinal student achievement data has heightened interest among researchers, educators and policy makers in using these data to evaluate educational inputs, as well as for school and possibly teacher accountability. Researchers have developed elaborate "value-added models" of these longitudinal data to estimate the effects of educational inputs (e.g., teachers or schools) on student achievement while using prior achievement to adjust for nonrandom assignment of students to schools and classes. A challenge to such modeling efforts is the extensive numbers of students with incomplete records and the tendency for those students to be lower achieving. These conditions create the potential for results to be sensitive to violations of the assumption that data are missing at random, which is commonly used when estimating model parameters. The current study extends recent value-added modeling approaches for longitudinal student achievement data Lockwood et al. [J. Educ. Behav. Statist. 32 (2007) 125--150] to allow data to be missing not at random via random effects selection and pattern mixture models, and applies those methods to data from a large urban school district to estimate effects of elementary school mathematics teachers. We find that allowing the data to be missing not at random has little impact on estimated teacher effects. The robustness of estimated teacher effects to the missing data assumptions appears to result from both the relatively small impact of model specification on estimated student effects compared with the large variability in teacher effects and the downweighting of scores from students with incomplete data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS405 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Cooperation after war

This paper discusses how predispositions, incentives, the number and heterogeneity of participants, and leadership (Faerman et al. 2001) jointly influenced the international effort to develop Bosnia and Herzegovina. International coalitions, task forces, and advisory groups are increasingly charged with implementing reforms following civil conflict. This requires a complex web of interorganizational relationships among NGOS, donors and host nations at both global and "ground" levels. To better understand development assistance, attention must be paid to the relationships between these varied players. We find that four factors influenced relationships between policy, donor, and implementing organizationsand those strained relationships, in turn, affected development success. The paper draws on interviews, conducted in Bosnia, with 43 development professionals, observation of development meetings in Tuzla and Sarajevo, and review of related documents from international development programs

An application of principal stratification to control for institutionalization at follow-up in studies of substance abuse treatment programs

Participants in longitudinal studies on the effects of drug treatment and criminal justice system interventions are at high risk for institutionalization (e.g., spending time in an environment where their freedom to use drugs, commit crimes, or engage in risky behavior may be circumscribed). Methods used for estimating treatment effects in the presence of institutionalization during follow-up can be highly sensitive to assumptions that are unlikely to be met in applications and thus likely to yield misleading inferences. In this paper we consider the use of principal stratification to control for institutionalization at follow-up. Principal stratification has been suggested for similar problems where outcomes are unobservable for samples of study participants because of dropout, death or other forms of censoring. The method identifies principal strata within which causal effects are well defined and potentially estimable. We extend the method of principal stratification to model institutionalization at follow-up and estimate the effect of residential substance abuse treatment versus outpatient services in a large scale study of adolescent substance abuse treatment programs. Additionally, we discuss practical issues in applying the principal stratification model to data. We show via simulation studies that the model can only recover true effects provided the data meet strenuous demands and that there must be caution taken when implementing principal stratification as a technique to control for post-treatment confounders such as institutionalization.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS179 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org