Examining the Multilevel Model’s Error Covariance Structure

2003 ◽  
pp. 243-265
Author(s):  
Judith D. Singer ◽  
John B. Willett
Keyword(s):  
Covariance Structure ◽  
Error Covariance ◽  
Error Covariance Structure

scholarly journals Effects of error covariance structure on estimation of model averaging weights and predictive performance

2013 ◽  
Vol 49 (9) ◽  
pp. 6029-6047 ◽  
Author(s):  
Dan Lu ◽  
Ming Ye ◽  
Philip D. Meyer ◽  
Gary P. Curtis ◽  
Xiaoqing Shi ◽  
...  
Keyword(s):  
Model Averaging ◽  
Covariance Structure ◽  
Predictive Performance ◽  
Error Covariance ◽  
Error Covariance Structure

A systematic approach for identifying level-1 error covariance structures in latent growth modeling

2016 ◽  
Vol 41 (3) ◽  
pp. 444-455 ◽  
Author(s):  
Cherng G. Ding ◽  
Ten-Der Jane ◽  
Chiu-Hui Wu ◽  
Hang-Rung Lin ◽  
Chih-Kang Shen
Keyword(s):  
Systematic Approach ◽  
Growth Modeling ◽  
Covariance Structure ◽  
Latent Growth Modeling ◽  
Covariance Structures ◽  
Latent Growth ◽  
Error Covariance ◽  
Nested Relations ◽  
Level 1 ◽  
Error Covariance Structure

It has been pointed out in the literature that misspecification of the level-1 error covariance structure in latent growth modeling (LGM) has detrimental impacts on the inferences about growth parameters. Since correct covariance structure is difficult to specify by theory, the identification needs to rely on a specification search, which, however, is not systematically addressed in the literature. In this study, we first discuss characteristics of various covariance structures and their nested relations, based on which we then propose a systematic approach to facilitate identifying a plausible covariance structure. A test for stationarity of an error process and the sequential chi-square difference test are conducted in the approach. Preliminary simulation results indicate that the approach performs well when sample size is large enough. The approach is illustrated with empirical data. We recommend that the approach be used in LGM empirical studies to improve the quality of the specification of the error covariance structure.

scholarly journals Robustness of Stein-type estimators under a non-scalar error covariance structure

2009 ◽  
Vol 100 (10) ◽  
pp. 2376-2388 ◽  
Author(s):  
Xinyu Zhang ◽  
Ti Chen ◽  
Alan T.K. Wan ◽  
Guohua Zou
Keyword(s):  
Covariance Structure ◽  
Error Covariance ◽  
Error Covariance Structure

scholarly journals Controlling Noise in Ensemble Data Assimilation Schemes

2010 ◽  
Vol 138 (5) ◽  
pp. 1502-1512 ◽  
Author(s):  
Malaquias Peña ◽  
Zoltan Toth ◽  
Mozheng Wei
Keyword(s):  
Data Assimilation ◽  
Ad Hoc ◽  
Forecast Accuracy ◽  
Covariance Structure ◽  
Sampling Errors ◽  
Background Error ◽  
Forecast Performance ◽  
Error Covariance ◽  
Additional Noise ◽  
Filter Divergence

Abstract A variety of ad hoc procedures have been developed to prevent filter divergence in ensemble-based data assimilation schemes. These procedures are necessary to reduce the impacts of sampling errors in the background error covariance matrix derived from a limited-size ensemble. The procedures amount to the introduction of additional noise into the assimilation process, possibly reducing the accuracy of the resulting analyses. The effects of this noise on analysis and forecast performance are investigated in a perfect model scenario. Alternative schemes aimed at controlling the unintended injection of noise are proposed and compared. Improved analysis and forecast accuracy is observed in schemes with minimal alteration to the evolving ensemble-based covariance structure.

scholarly journals Forecast error covariance structure in coupled atmosphere–chemistry data assimilation

2014 ◽  
Vol 7 (6) ◽  
pp. 8757-8767
Author(s):  
S. K. Park ◽  
S. Lim ◽  
M. Zupanski
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Wrf Model ◽  
Covariance Structure ◽  
Weather Research And Forecasting ◽  
Single Observation ◽  
Chemistry Data ◽  
Error Covariance ◽  
Atmospheric Observations

Abstract. In this study, we examined the structure of an ensemble-based coupled atmosphere–chemistry forecast error covariance. The Weather Research and Forecasting (WRF) model coupled with Chemistry (WRF-Chem), a coupled atmosphere–chemistry model, was used to create an ensemble error covariance. The control variable includes both the dynamical and chemistry model variables. A synthetic single observation experiment was designed in order to evaluate the cross-variable components of a coupled error covariance. The results indicate that the coupled error covariance has important cross-variable components that allow a physically meaningful adjustment of all control variables. The additional benefit of the coupled error covariance is that a cross-component impact is allowed, e.g., atmospheric observations can exert impact on chemistry analysis, and vice versa. Given the realistic structure of ensemble forecast error covariance produced by the WRF-Chem, we anticipate the ensemble-based coupled atmosphere–chemistry data assimilation will respond similarly to assimilation of real observations.

144 Temporal and Bidirectional Associations between Objectively Measured Physical Activity and Sleep in Preschoolers

SLEEP ◽  
2021 ◽  
Vol 44 (Supplement_2) ◽  
pp. A59-A59
Author(s):  
Christine St Laurent ◽  
Jennifer Holmes ◽  
Chloe Andre ◽  
Rebecca Spencer
Keyword(s):  
Physical Activity ◽  
Early Childhood ◽  
Sleep Duration ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Older Children ◽  
Percent Time ◽  
Error Covariance ◽  
Bidirectional Associations ◽  
Objectively Measured

Abstract Introduction Physical activity (PA) and sleep contribute to overall health in early childhood. To explore the interactive relationships of these behaviors in older children and adults, previous studies have examined temporal between- and within-person associations through micro-longitudinal designs. However, such analyses have not been conducted in early childhood, when behaviors are guided by adult caregivers. The purpose of this analysis was to examine temporal and bidirectional associations between SED, PA, and sleep in preschool children. Methods Wake (activity counts/min and percent time in SED, light PA [LPA], and moderate-to-vigorous PA [MVPA]) and overnight sleep (sleep duration, sleep efficiency [SE], mid-sleep point [MSP]) were assessed via wrist-based actigraphy (mean = 10.4 days and 9.8 nights) and recorded as repeated (daily) measures. Multilevel models with lagged effects and AR(1) error covariance structure were used to examine the temporal associations between wake and sleep measures and adjusted for age, sex, socioeconomic status, and nap frequency. Results With PA measures as predictors, between-person associations were positive between activity counts and SE (p=0.004), SED and SE (p=0.004), LPA and sleep duration (p=0.005), and negative between LPA and MSP (p=0.039) and MVPA and SE (p=0.003). Within-person associations were positive between activity counts and sleep duration (p=0.010), activity counts and SE (p=0.018), MVPA and sleep duration (p=0.003), MVPA and SE (p=0.004), and negative between SED and SE (p=0.034) and LPA and sleep duration (p=0.045). With sleep measures as predictors, associations were positive between sleep duration and LPA (p<0.001) and SE and SED (p=0.008), and negative between MSP and LPA (p=0.009), SE and activity counts (p=0.001), and SE and MVPA (p=0.003). Within-person associations were positive between SE and activity counts (p=0.001) and SE and MVPA (p=0.001), and negative between sleep duration and LPA (p=0.001) and SE and SED (p=0.012). Conclusion Generally, days with higher levels of activity or sleep were not associated with greater subsequent sleep or PA. Conversely, when participants obtained greater PA or sleep compared to their individual average, some beneficial associations were evident. These findings demonstrate some evidence of temporal associations between PA and sleep, although the bidirectional nature was not conclusive. Support (if any) NIH R01 HL111695

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