scholarly journals On the Use of Empirical Bayes Estimates as Measures of Individual Traits

Assessment ◽  
2019 ◽  
pp. 107319111988501
Author(s):  
Siwei Liu ◽  
Peter Kuppens ◽  
Laura Bringmann
Keyword(s):  
Random Effects ◽  
Empirical Bayes ◽  
Multilevel Models ◽  
Simulated Data ◽  
Residual Variance ◽  
Data Set ◽  
Number Of Factors ◽  
Individual Traits ◽  
Level 1

Empirical Bayes (EB) estimates of the random effects in multilevel models represent how individuals deviate from the population averages and are often extracted to detect outliers or used as predictors in follow-up analysis. However, little research has examined whether EB estimates are indeed reliable and valid measures of individual traits. In this article, we use statistical theory and simulated data to show that EB estimates are biased toward zero, a phenomenon known as “shrinkage.” The degree of shrinkage and reliability of EB estimates depend on a number of factors, including Level-1 residual variance, Level-1 predictor variance, Level-2 random effects variance, and number of within-person observations. As a result, EB estimates may not be ideal for detecting outliers, and they produce biased regression coefficients when used as predictors. We illustrate these issues using an empirical data set on emotion regulation and neuroticism.

scholarly journals Bayesian Multilevel Models for Count Data

2021 ◽  
pp. 224-233
Author(s):  
Olumide Sunday Adesina
Keyword(s):  
Count Data ◽  
Multilevel Models ◽  
Geometric Model ◽  
Real Life ◽  
Simulated Data ◽  
Data Set ◽  
K Value ◽  
Real Life Data ◽  
Level Model ◽  
Multi Level

The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicate that all the observations are good. Also all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further analysis. Seven multi-level models were f itted and the Geometric model outperformed other model. 

scholarly journals On Ignoring the Random Effects Assumption in Multilevel Models: Review, Critique, and Recommendations

2019 ◽  
pp. 109442811987745 ◽  
Author(s):  
John Antonakis ◽  
Nicolas Bastardoz ◽  
Mikko Rönkkö
Keyword(s):  
Random Effects ◽  
Large Scale ◽  
Multilevel Models ◽  
Applied Psychology ◽  
Explanatory Variables ◽  
The Common ◽  
Level 1 ◽  
State Of The Science ◽  
Organizational Science ◽  
Practical Recommendations

Entities such as individuals, teams, or organizations can vary systematically from one another. Researchers typically model such data using multilevel models, assuming that the random effects are uncorrelated with the regressors. Violating this testable assumption, which is often ignored, creates an endogeneity problem thus preventing causal interpretations. Focusing on two-level models, we explain how researchers can avoid this problem by including cluster means of the Level 1 explanatory variables as controls; we explain this point conceptually and with a large-scale simulation. We further show why the common practice of centering the predictor variables is mostly unnecessary. Moreover, to examine the state of the science, we reviewed 204 randomly drawn articles from macro and micro organizational science and applied psychology journals, finding that only 106 articles—with a slightly higher proportion from macro-oriented fields—properly deal with the random effects assumption. Alarmingly, most models also failed on the usual exogeneity requirement of the regressors, leaving only 25 mostly macro-level articles that potentially reported trustworthy multilevel estimates. We offer a set of practical recommendations for researchers to model multilevel data appropriately.

scholarly journals Avoiding Bias When Estimating the Consistency and Stability of Value-Added School Effects

2018 ◽  
Vol 43 (4) ◽  
pp. 440-468 ◽  
Author(s):  
George Leckie
Keyword(s):  
Random Effects ◽  
Empirical Bayes ◽  
Multilevel Models ◽  
Traditional Approach ◽  
Value Added ◽  
School Effects ◽  
School Settings ◽  
Subject Areas ◽  
Unbiased Estimates ◽  
The Stability

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be avoided by simply correlating “unshruken” or “reflated” versions of these predicted random effects. In contrast, we show that fitting a joint value-added multilevel multivariate response model simultaneously to all subjects or cohorts directly gives unbiased estimates of the correlations of interest. There is no need to correlate the resulting empirical Bayes predictions and indeed we show that this should again be avoided as the resulting correlations are also biased. We illustrate our arguments with separate applications to measuring the consistency and stability of school effects in primary and secondary school settings. However, our arguments apply more generally to other areas of application where researchers routinely interpret correlations between predicted random effects rather than estimating and interpreting these correlation directly.

scholarly journals Prediction in Multilevel Models

2005 ◽  
Vol 30 (2) ◽  
pp. 109-139 ◽  
Author(s):  
David Afshartous ◽  
Jan de Leeuw
Keyword(s):  
Sample Size ◽  
Parameter Space ◽  
Multilevel Models ◽  
Intraclass Correlation ◽  
Prediction Rule ◽  
Hierarchical Data ◽  
Data Set ◽  
Prediction Rules ◽  
Level 1 ◽  
Level 2

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. This article addresses the problem of predicting a future observable y*j in thej th group of a hierarchical data set. Three prediction rules are considered and several analytical results on the relative performance of these prediction rules are demonstrated. In addition, the prediction rules are assessed by means of a Monte Carlo study that extensively covers both the sample size and parameter space. Specifically, the sample size space concerns the various combinations of Level 1 (individual) and Level 2 (group) sample sizes, while the parameter space concerns different intraclass correlation values. The three prediction rules employ OLS, prior, and multilevel estimators for the Level 1 coefficientsβj The multilevel prediction rule performs the best across all design conditions, and the prior prediction rule degrades as the number of groups, J, increases. Finally, this article investigates the robustness of the multilevel prediction rule to misspecifications of the Level 2 model.

scholarly journals Development and temporal external validation of a simple risk score tool for prediction of outcomes after severe head injury based on admission characteristics from level-1 trauma centre of India using retrospectively collected data

BMJ Open ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. e040778
Author(s):  
Vineet Kumar Kamal ◽  
Ravindra Mohan Pandey ◽  
Deepak Agrawal
Keyword(s):  
Hospital Mortality ◽  
External Validation ◽  
Trauma Centre ◽  
Unfavourable Outcome ◽  
Motor Score ◽  
Validation Data ◽  
Data Set ◽  
Development Data ◽  
Level 1 ◽  
Pupillary Reactivity

ObjectiveTo develop and validate a simple risk scores chart to estimate the probability of poor outcomes in patients with severe head injury (HI).DesignRetrospective.SettingLevel-1, government-funded trauma centre, India.ParticipantsPatients with severe HI admitted to the neurosurgery intensive care unit during 19 May 2010–31 December 2011 (n=946) for the model development and further, data from same centre with same inclusion criteria from 1 January 2012 to 31 July 2012 (n=284) for the external validation of the model.Outcome(s)In-hospital mortality and unfavourable outcome at 6 months.ResultsA total of 39.5% and 70.7% had in-hospital mortality and unfavourable outcome, respectively, in the development data set. The multivariable logistic regression analysis of routinely collected admission characteristics revealed that for in-hospital mortality, age (51–60, >60 years), motor score (1, 2, 4), pupillary reactivity (none), presence of hypotension, basal cistern effaced, traumatic subarachnoid haemorrhage/intraventricular haematoma and for unfavourable outcome, age (41–50, 51–60, >60 years), motor score (1–4), pupillary reactivity (none, one), unequal limb movement, presence of hypotension were the independent predictors as its 95% confidence interval (CI) of odds ratio (OR)_did not contain one. The discriminative ability (area under the receiver operating characteristic curve (95% CI)) of the score chart for in-hospital mortality and 6 months outcome was excellent in the development data set (0.890 (0.867 to 912) and 0.894 (0.869 to 0.918), respectively), internal validation data set using bootstrap resampling method (0.889 (0.867 to 909) and 0.893 (0.867 to 0.915), respectively) and external validation data set (0.871 (0.825 to 916) and 0.887 (0.842 to 0.932), respectively). Calibration showed good agreement between observed outcome rates and predicted risks in development and external validation data set (p>0.05).ConclusionFor clinical decision making, we can use of these score charts in predicting outcomes in new patients with severe HI in India and similar settings.

scholarly journals Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

2020 ◽  
pp. 1-20
Author(s):  
Chad Hazlett ◽  
Leonard Wainstein
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Multilevel Models ◽  
Standard Errors ◽  
Point Estimate ◽  
Fe Model ◽  
Grouped Data ◽  
Coefficient Estimates ◽  
Political Science Education ◽  
Robust Standard Errors

Abstract When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

scholarly journals SuperWASP variable stars: classifying light curves using citizen science

2021 ◽  
Vol 502 (1) ◽  
pp. 1299-1311
Author(s):  
Heidi B Thiemann ◽  
Andrew J Norton ◽  
Hugh J Dickinson ◽  
Adam McMaster ◽  
Ulrich C Kolb
Keyword(s):  
Variable Stars ◽  
Eclipsing Binaries ◽  
Light Curves ◽  
Data Set ◽  
Resultant Data ◽  
Sky Survey ◽  
Short Period ◽  
Contact Binaries ◽  
Analysis Of Results

ABSTRACT We present the first analysis of results from the SuperWASP variable stars Zooniverse project, which is aiming to classify 1.6 million phase-folded light curves of candidate stellar variables observed by the SuperWASP all sky survey with periods detected in the SuperWASP periodicity catalogue. The resultant data set currently contains >1 million classifications corresponding to >500 000 object–period combinations, provided by citizen–scientist volunteers. Volunteer-classified light curves have ∼89 per cent accuracy for detached and semidetached eclipsing binaries, but only ∼9 per cent accuracy for rotationally modulated variables, based on known objects. We demonstrate that this Zooniverse project will be valuable for both population studies of individual variable types and the identification of stellar variables for follow-up. We present preliminary findings on various unique and extreme variables in this analysis, including long-period contact binaries and binaries near the short-period cut-off, and we identify 301 previously unknown binaries and pulsators. We are now in the process of developing a web portal to enable other researchers to access the outputs of the SuperWASP variable stars project.

scholarly journals Effects of management decisions on genetic evaluation of simulated calving records using random regression

2021 ◽  
Author(s):  
M D MacNeil ◽  
J W Buchanan ◽  
M L Spangler ◽  
E Hay
Keyword(s):  
Reproductive Success ◽  
Simulated Data ◽  
Genetic Evaluation ◽  
Random Regression ◽  
Management Decisions ◽  
Third Order ◽  
Data Set ◽  
Binary Phenotype ◽  
Random Regression Model ◽  
Missing Observation

Abstract The objective of this study was to evaluate the effects of various data structures on the genetic evaluation for the binary phenotype of reproductive success. The data were simulated based on an existing pedigree and an underlying fertility phenotype with a heritability of 0.10. A data set of complete observations was generated for all cows. This data set was then modified mimicking the culling of cows when they first failed to reproduce, cows having a missing observation at either their second or fifth opportunity to reproduce as if they had been selected as donors for embryo transfer, and censoring records following the sixth opportunity to reproduce as in a cull-for-age strategy. The data were analyzed using a third order polynomial random regression model. The EBV of interest for each animal was the sum of the age-specific EBV over the first 10 observations (reproductive success at ages 2-11). Thus, the EBV might be interpreted as the genetic expectation of number of calves produced when a female is given ten opportunities to calve. Culling open cows resulted in the EBV for 3 year-old cows being reduced from 8.27 ± 0.03 when open cows were retained to 7.60 ± 0.02 when they were culled. The magnitude of this effect decreased as cows grew older when they first failed to reproduce and were subsequently culled. Cows that did not fail over the 11 years of simulated data had an EBV of 9.43 ± 0.01 and 9.35 ± 0.01 based on analyses of the complete data and the data in which cows that failed to reproduce were culled, respectively. Cows that had a missing observation for their second record had a significantly reduced EBV, but the corresponding effect at the fifth record was negligible. The current study illustrates that culling and management decisions, and particularly those that impact the beginning of the trajectory of sustained reproductive success, can influence both the magnitude and accuracy of resulting EBV.

Development and Validation of a Cognitive Reserve Index in HIV

2021 ◽  
pp. 1-9
Author(s):  
Navaldeep Kaur ◽  
Lesley K. Fellows ◽  
Marie-Josée Brouillette ◽  
Nancy Mayo
Keyword(s):  
Cognitive Reserve ◽  
Study Entry ◽  
Video Gaming ◽  
Everyday Functioning ◽  
Data Set ◽  
Multiple Indicators ◽  
And Performance ◽  
Competitive Games ◽  
Development And Validation

Abstract Objectives: In the neuroHIV literature, cognitive reserve has most often been operationalized using education, occupation, and IQ. The effects of other cognitively stimulating activities that might be more amenable to interventions have been little studied. The purpose of this study was to develop an index of cognitive reserve in people with HIV, combining multiple indicators of cognitively stimulating lifetime experiences into a single value. Methods: The data set was obtained from a Canadian longitudinal study (N = 856). Potential indicators of cognitive reserve captured at the study entry included education, occupation, engagement in six cognitively stimulating activities, number of languages spoken, and social resources. Cognitive performance was measured using a computerized test battery. A cognitive reserve index was formulated using logistic regression weights. For the evidence on concurrent and predictive validity of the index, the measures of cognition and self-reported everyday functioning were each regressed on the index scores at study entry and at the last follow-up [mean duration: 25.9 months (SD 7.2)], respectively. Corresponding regression coefficients and 95% confidence intervals (CIs) were computed. Results: Professional sports [odds ratio (OR): 2.9; 95% CI 0.59–14.7], visual and performance arts (any level of engagement), professional/amateur music, complex video gaming and competitive games, and travel outside North America were associated with higher cognitive functioning. The effects of cognitive reserve on the outcomes at the last follow-up visit were closely similar to those at study entry. Conclusion: This work contributes evidence toward the relative benefit of engaging in specific cognitively stimulating life experiences in HIV.

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