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

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

Protocol for a systematic review of preference-based instruments for measuring care-related outcomes and their suitability for the palliative care setting

Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/ INTRODUCTION: Despite informal caregivers' integral role in supporting people affected by disease or disability, economic evaluations often ignore the costs and benefits experienced by this group, especially in the palliative setting. The purpose of this systematic review is to identify preference-based instruments for measuring care-related outcomes and provide guidance on the selection of instrument in palliative care economic evaluations.METHODS AND ANALYSIS: A comprehensive search of the literature will be conducted from database inception (ASSIA; CINAHL; Cochrane library including DARE, NHS EED, HTA; Econlit; Embase; PsychINFO; PubMed). Published peer-reviewed, English-language articles reporting preference-based instruments for measuring care-related outcomes in any clinical area will be included. One researcher will complete the searches and screen the results for potentially eligible studies. A randomly selected subset of 10% citations will be independently screened by two researchers. Any disagreement will be resolved by consensus among the research team. Subsequently, a supplementary search will identify studies detailing the development, valuation, validation and application of the identified instruments. The degree of suitability of the instruments for palliative economic evaluations will be assessed using criteria in the International Society for Quality of Life Research minimum standards for patient-reported outcome measures, the checklist for reporting valuation studies of multiattribute utility-based instruments and information on the development of the instrument in the palliative setting. A narrative summary of the included studies and instruments will be provided; similarities and differences will be described and possible reasons for variations explored. Recommendations for practice on selection of instruments in palliative care economic analyses will be provided.ETHICS AND DISSEMINATION: This is a planned systematic review of published literature. Therefore, ethics approval to conduct this research is not required. Findings will be presented at leading palliative care and health economic conferences and published in a peer-reviewed journal.TRIAL REGISTRATION NUMBER: CRD42016034188

Slow Slip Events and Time-Dependent Variations in Locking Beneath Lower Cook Inlet of the Alaska-Aleutian Subduction Zone

We identify a series of abrupt changes in GPS site velocities in Lower Cook Inlet, Alaska, in late 2004, early 2010, and late 2011. The site motions during each time period are nearly linear. The surface deformations inferred from GPS for pre-2004 and 2010–2011 are similar to each other, as are 2004–2010 and post-2011. We estimate the slip distribution on the Alaska-Aleutian subduction plate interface accounting for upper plate block rotations and interpret this toggling between two deformation patterns as caused by transient slip. We find that by allowing negative slip deficit rates (i.e., creep rates in excess of relative plate motion), the data in Lower Cook Inlet are fit significantly better during pre-2004 and 2010–2011, suggesting the occurrence of slow slip events (SSEs) there during those time periods. The earlier SSE lasted at least 9 years (observations in that area began in 1995) with Mw ~7.8. The latter SSE had almost the same area as the earlier one and a duration of ~2 years with Mw ~7.2. During 2004–2010 and post-2011, the inversions result in only positive slip deficit rates (i.e., locking) in Lower Cook Inlet. Slip rates are nearly constant during the Lower Cook Inlet SSEs, and the events start and stop abruptly. Both of these properties contrast with observations of SSEs in Upper Cook Inlet and elsewhere. The Lower Cook Inlet SSEs are consistent with previously proposed duration-magnitude scaling laws and demonstrate that slow slip events can last as long as a decade

GNSS Differential Code Bias Determination Using Rao‐Blackwellized Particle Filtering

The Assimilative Canadian High Arctic Ionospheric Model (A-CHAIM) is a near-real-time data assimilation model of the high latitude ionosphere, incorporating measurements from many instruments, including slant Total Electron Content measurements from ground-based Global Navigation Satellite System (GNSS) receivers. These measurements have receiver-specific Differential Code Biases (DCB) which must be resolved to produce an absolute measurement, which are resolved simultaneously with the ionospheric state using Rao-Blackwellized particle filtering. These DCBs are compared to published values and to DCBs determined using eight different Global Ionospheric Maps (GIM), which show small but consistent systematic differences. The potential cause of these systematic biases is investigated using multiple experimental A-CHAIM test runs, including the effect of plasmaspheric electron content. By running tests using the GIM-derived DCBs, it is shown that using A-CHAIM DCBs produces the lowest overall error, and that using GIM DCBs causes an overestimation of the topside electron density which can exceed 100% when compared to in situ measurements from DMSP

Fault Locking, Block Rotation and Crustal Deformation in the Pacific Northwest

We interpret Global Positioning System (GPS) measurements in the northwestern United States and adjacent parts of western Canada to describe relative motions of crustal blocks, locking on faults and permanent deformation associated with convergence between the Juan de Fuca and North American plates. To estimate angular velocities of the oceanic Juan de Fuca and Explorer plates and several continental crustal blocks, we invert the GPS velocities together with seafloor spreading rates, earthquake slip vector azimuths and fault slip azimuths and rates. We also determine the degree to which faults are either creeping aseismically or, alternatively, locked on the block-bounding faults. The Cascadia subduction thrust is locked mainly offshore, except in central Oregon, where locking extends inland. Most of Oregon and southwest Washington rotate clockwise relative to North America at rates of 0.4-1.0 ° Myr-1. No shear or extension along the Cascades volcanic arc has occurred at the mm/yr level during the past decade, suggesting that the shear deformation extending northward from the Walker Lane and eastern California shear zone south of Oregon is largely accommodated by block rotation in Oregon. The general agreement of vertical axis rotation rates derived from GPS velocities with those estimated from palaeomagnetic declination anomalies suggests that the rotations have been relatively steady for 10-15 Ma. Additional permanent dextral shear is indicated within the Oregon Coast Range near the coast. Block rotations in the Pacific Northwest do not result in net westward flux of crustal material¿the crust is simply spinning and not escaping. On Vancouver Island, where the convergence obliquity is less than in Oregon and Washington, the contractional strain at the coast is more aligned with Juan de Fuca¿North America motion. GPS velocities are fit significantly better when Vancouver Island and the southern Coast Mountains move relative to North America in a block-like fashion. The relative motions of the Oregon, western Washington and Vancouver Island crustal blocks indicate that the rate of permanent shortening, the type that causes upper plate earthquakes, across the Puget Sound region is 4.4 ± 0.3 mm yr-1. This shortening is likely distributed over several faults but GPS data alone cannot determine the partitioning of slip on them. The transition from predominantly shear deformation within the continent south of the Mendocino Triple Junction to predominantly block rotations north of it is similar to changes in tectonic style at other transitions from shear to subduction. This similarity suggests that crustal block rotations are enhanced in the vicinity of subduction zones possibly due to lower resisting stress