Comment: Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

Comment on ``Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data'' [arXiv:0804.2958]Comment: Published in at http://dx.doi.org/10.1214/07-STS227C the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Analysis of rolling group therapy data using conditionally autoregressive priors

Group therapy is a central treatment modality for behavioral health disorders such as alcohol and other drug use (AOD) and depression. Group therapy is often delivered under a rolling (or open) admissions policy, where new clients are continuously enrolled into a group as space permits. Rolling admissions policies result in a complex correlation structure among client outcomes. Despite the ubiquity of rolling admissions in practice, little guidance on the analysis of such data is available. We discuss the limitations of previously proposed approaches in the context of a study that delivered group cognitive behavioral therapy for depression to clients in residential substance abuse treatment. We improve upon previous rolling group analytic approaches by fully modeling the interrelatedness of client depressive symptom scores using a hierarchical Bayesian model that assumes a conditionally autoregressive prior for session-level random effects. We demonstrate improved performance using our method for estimating the variance of model parameters and the enhanced ability to learn about the complex correlation structure among participants in rolling therapy groups. Our approach broadly applies to any group therapy setting where groups have changing client composition. It will lead to more efficient analyses of client-level data and improve the group therapy research community's ability to understand how the dynamics of rolling groups lead to client outcomes.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS434 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Grizzly bears in Yellowstone National Park

AbstractThe problem we solved is based on the population of grizzly bears at Yellowstone National Park. Since this population is currently declining, our specific problem centered around a seed group of 52 grizzlies, transported from Yellowstone to another area in the Northwestern United States, similar in climate and availability of proper food. The total land area available for the bears is 1.5 million acres, enough land for 100 bears to thrive. Our problem was to find a harvesting policy to sustain the maximum number of grizzlies on this land.Using the matrix equation Lxi=xi+1 we determined tha this seed population would exceed the level the land area can maintain after 14 years. At this point we began to implement our harvesting procedures. Assuming the bears would be harvested at random, producing a uniform harvesting rate for each age group, we used the matrix equation Lx−HLx=x to solve for a total of 3 percent harvesting yearly after the fourteenth year. Test results confirmed the accuracy of our matrix values

Relationship between Exposureto Class Size Reductionand Student Achievementin California

The CSR Research Consortium has been evaluating the implementation of the Class Size Reduction initiative in California since 1998. Initial reports documented the implementation of the program and its impact on the teacher workforce, the teaching of mathematics and Language Arts, parental involvement and student achievement. This study examines the relationship between student achievement and the number of years students have been exposed to CSR in grades K-3. The analysis was conducted at the grade level within schools using student achievement data collected in 1998-2001. Archival data collected by the state were used to establish CSR participation by grade for each school in the state. Most students had one of two patterns of exposure to CSR, which differed by only one year during grade K-3. The analysis found no strong association between achievement and exposure to CSR for these groups, after controlling for pre-existing differences in the groups