298 research outputs found
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
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