Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities,where variables of interest may include not only scalar(point-like)indicators,but also functional(curve-like)and compositional(pie-like)ones.In many research topics,the variables are also chronologically collected across individuals,which falls into the paradigm of longitudinal analysis.The complicated nature of data,however,increases the difficulty of modeling these variables under the classic longitudinal frame-work.In this study,we investigate the linear mixed-effects model(LMM)for such complex data.Different types of variables arefirst consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them,which gener-alizes the theoretical framework of LMM to complex data analysis.A number of simulation studies indicate the feasibility and effectiveness of the proposed model.We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.

BLUP Estimation of Linear Mixed-effects Models with Measurement Errors and Its Applications to the Estimation of Small Areas

The linear mixed-effects model （LMM） is a very useful tool for analyzing cluster data. In practice, however, the exact values of the variables are often difficult to observe. In this paper, we consider the LMM with measurement errors in the covariates. The empirical BLUP estimator of the linear combination of the fixed and random effects and its approximate conditional MSE are derived. The application to the estimation of small area is provided. Simulation study shows good performance of the proposed estimators.

纵向数据与生存数据联合模型中多变点识别问题

提出了共享协变量和随机效应的纵向响应中含有多个变点识别的线性混合效应(LME)模型和加速失效时间(AFT)模型的联合模型,并通过Gauss-Hermite近似解决极大似然函数中的复杂积分以得到参数的估计.通过模拟研究验证了该方法的有效性,并将其应用于原发性胆汁性肝硬化(PBC)病变过程,研究发现:PBC患者的血清胆红素只在初期治疗阶段有所降低,两个月之后迅速开始反弹,直到3.5a后增速才有所放缓,说明治疗方法仍需改进.

Posterior propriety of an objective prior for generalized hierarchical normal linear models

Bayesian Hierarchical models has been widely used in modern statistical application.To deal with the data having complex structures,we propose a generalized hierarchical normal linear(GHNL)model which accommodates arbitrarily many levels,usual design matrices and'vanilla'covari-ance matrices.Objective hyperpriors can be employed for the GHNL model to express ignorance or match frequentist properties,yet the common objective Bayesian approaches are infeasible or fraught with danger in hierarchical modelling.To tackle this issue,[Berger,J,Sun,D.&Song,C.(2020b).An objective prior for hyperparameters in normal hierarchical models.Journal of Multi-variate Analysis,178,104606.https://doi.org/10.1016/jmva.2020.104606]proposed a particular objective prior and investigated its properties comprehensively.Posterior propriety is important for the choice of priors to guarantee the convergence of MCMC samplers.James Berger conjec-tured that the resulting posterior is proper for a hierarchical normal model with arbitrarily many levels,a rigorous proof of which was not given,however.In this paper,we complete this story and provide an user friendly guidance.One main contribution of this paper is to propose a new technique for deriving an elaborate upper bound on the integrated likelihood but also one uni-fied approach to checking the posterior propriety for linear models.An eficient Gibbs sampling method is also introduced and outperforms other sampling approaches considerably.

Associations of short-term ambient temperature exposure with lung function in middle-aged and elderly people:A longitudinal study in China

The short-term associations of ambient temperature exposure with lung function in middle-aged and elderly Chinese remain obscure.The study included 19,128 participants from the Dongfeng-Tongji cohort's first(2013)and second(2018)follow-ups.The lung function for each subject was determined between April and December 2013 and re-assessed in 2018,with three parameters(forced vital capacity[FVC],forced expiratory volume in 1 s[FEV1],and peak expiratory flow[PEF])selected.The China Meteorological Data Sharing Service Center provided temperature data during the study period.In the two follow-ups,a total of 25,511 records(average age:first,64.57;second,65.80)were evaluated,including 10,604 males(41.57%).The inversely J-shaped associations between moving average temperatures(lag01–lag07)and FVC,FEV1,and PEF were observed,and the optimum temperatures at lag04 were 16.5C,18.7C,and 16.2C,respectively.At lag04,every 1C increase in temperature was associated with 14.07 mL,9.78 mL,and 62.72 mL/s increase in FVC,FEV1,and PEF in the lowtemperature zone(<the optimum temperatures),whereas 5.72 mL,2.01 mL,and 11.64 mL/s decrease in the high-temperature zone(the optimum temperatures),respectively(all P<0.05).We observed significant effect modifications of gender,age,body mass index,body surface area,smoking status,drinking status,and physical activity on the associations(all Pmodification<0.05).Non-optimal temperatures may cause lung function decline.Several individual characters and lifestyles have effect modification on the temperature effects.

On the effects of landscape configuration on summer diurnal temperatures in urban residential areas: application in Phoenix, AZ

The impacts of land-cover composition on urban temperatures, including temperature extremes, are well documented. Much less attention has been devoted to the consequences of land-cover configuration, most of which addresses land surface temperatures. This study explores the role of both composition and configuration—or land system architecture—of residential neighborhoods in the Phoenix metropolitan area, on near-surface air temperature. It addresses two-dimensional, spatial attributes of buildings, impervious surfaces, bare soil/ rock, vegetation and the “urbanscape” at large, from 50 m to 550 m at 100 m increments, for a representative 30-day high sun period. Linear mixed-effects models evaluate the significance of land system architecture metrics at different spatial aggregation levels. The results indicate that, controlling for land-cover composition and geographical variables, land-cover configuration, specifically the fractal dimension of buildings, is significantly associated with near-surface temperatures. In addition, statistically significant predictors related to composition and configuration appear to depend on the adopted level of spatial aggregation.