correlation structure
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2022 ◽  
Vol 9 ◽  
Author(s):  
Lu Lu ◽  
Zhiqiang Wang ◽  
Jiayi Yu ◽  
Chunhong Qiao ◽  
Rong Lin ◽  
...  

Coherence in a light beam has the potential to serve as a degree of freedom for manipulating the beam. In this work, the self-focusing property of a partially coherent beam with a non-uniform correlation structure propagating in a non-linear medium is investigated. The analysis of the evolution of beam width reveals that the coherence structure plays a vital role in the self-focusing formation. A threshold condition for the coherence radius is proposed for the first time, and the relation of self-focusing length and initial coherence radius is studied numerically and analytically. It is shown that a feasible approach for manipulating the self-focusing length by adjusting the initial coherence radius is achieved.


2021 ◽  
pp. 174077452110598
Author(s):  
Lee Kennedy-Shaffer ◽  
Michael D Hughes

Background/Aims Generalized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations. Methods We develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances. Results We show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically [Formula: see text]) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate. Conclusion The common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.


2021 ◽  
Vol 13 (4) ◽  
pp. 548-586
Author(s):  
Kei Kawai ◽  
Yuta Toyama ◽  
Yasutora Watanabe

We study how voter turnout affects the aggregation of preferences in elections. Under voluntary voting, election outcomes disproportionately aggregate the preferences of voters with low voting cost and high preference intensity. We show identification of the correlation structure among preferences, costs, and perceptions of voting efficacy, and explore how the correlation affects preference aggregation. Using 2004 US presidential election data, we find that young, low-income, less-educated, and minority voters are underrepresented. All of these groups tend to prefer Democrats, except for the less educated. Democrats would have won the majority of the electoral votes if all eligible voters had turned out. (JEL D12, D72)


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Gao-Feng Gu ◽  
Xiong Xiong ◽  
Hai-Chuan Xu ◽  
Wei Zhang ◽  
Yongjie Zhang ◽  
...  

AbstractWe propose an empirical behavioral order-driven (EBOD) model with price limit rules, which consists of an order placement process and an order cancellation process. All the ingredients of the model are determined based on the empirical microscopic regularities in the order flows of stocks traded on the Shenzhen Stock Exchange. The model can reproduce the main stylized facts in real markets. Computational experiments unveil that asymmetric setting of price limits will cause the stock price to diverge exponentially when the up price limit is higher than the down price limit and to vanish vice versa. We also find that asymmetric price limits have little influence on the correlation structure of the return series and the volatility series, but cause remarkable changes in the average returns and the tail exponents of returns. Our EBOD model provides a suitable computational experiment platform for academics, market participants, and policy makers.


2021 ◽  
Author(s):  
Anna Elisabeth Fürtjes ◽  
Ryan Arathimos ◽  
Jonathan RI Coleman ◽  
James H Cole ◽  
Simon R Cox ◽  
...  

The human brain is organised into networks of interconnected regions that have highly correlated volumes. In this study, we aim to triangulate insights into brain organisation and its relationship with cognitive ability and ageing, by analysing genetic data. We estimated general genetic dimensions of human brain morphometry within the whole brain, and nine predefined canonical brain networks of interest. We did so based on principal components analysis (PCA) of genetic correlations among grey-matter volumes for 83 cortical and subcortical regions (Nparticipants = 36,778). We found that the corresponding general dimension of brain morphometry accounts for 40% of the genetic variance in the individual brain regions across the whole brain, and 47-65% within each network of interest. This genetic correlation structure of regional brain morphometry closely resembled the phenotypic correlation structure of the same regions. Applying a novel multivariate methodology for calculating SNP effects for each of the general dimensions identified, we find that general genetic dimensions of morphometry within networks are negatively associated with brain age (rg = -0.34) and profiles characteristic of age-related neurodegeneration, as indexed by cross-sectional age-volume correlations (r = -0.27). The same genetic dimensions were positively associated with a genetic general factor of cognitive ability (rg = 0.17-0.21 for different networks). We have provided a statistical framework to index general dimensions of shared genetic morphometry that vary between brain networks, and report evidence for a shared biological basis underlying brain morphometry, cognitive ability, and brain ageing, that are underpinned by general genetic factors.


2021 ◽  
Vol 861 (6) ◽  
pp. 062020
Author(s):  
Ning Tian ◽  
Jian Chen ◽  
Song Yu ◽  
Juehao Huang ◽  
Kaiwei Tian ◽  
...  

2021 ◽  
Vol 50 (Supplement_1) ◽  
Author(s):  
Moleen Dzikiti ◽  
Barbara Laughton ◽  
Steve Innes ◽  
Mark Cotton

Abstract Background We explored the effects of predominant breastfeeding on infection-related hospitalization (uncommon outcome), over the first year of life, using the Mother Infant Health cohort study (MIHS), and the effect of early antiretroviral treatment (ART) on viral suppression (< 400 copies/mL) (common outcome), in children aged 7 to 12 weeks, using a subset of the Children with HIV Early AntiRetroviral Treatment (CHER) clinical trial data. We assessed the sensitivity of findings to different models to account for dependency of uncommon and common binary outcome. Methods We fitted generalized linear mixed model with (1) random intercept and (2) random slope, generalized estimating equations (GEE) with 3) an exchangeable correlation structure; 4) autoregressive correlation structure of order 1 (AR1) and 5) unstructured correlation structure and 6) logistic regression model. Results Eighty four and 119 children from MIHS were non-predominantly and predominantly breastfed, respectively. There were 34 infection-related hospitalizations overall. Most infants were hospitalized once, except for four with two hospitalizations. We analysed 88 HIV-infected children from the CHER trial. On average, a child achieved viral suppression twice, range of one to four. The effect of predominant breastfeeding on infection-related hospitalization was similar across all models, except for the GEE with AR1 that had a high estimate (wider confidence intervals). The effect of early ART exposure on viral suppression varied across models. Conclusions The sensitivity of estimates to the method of analysis was driven by frequency of the outcome.


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