Groupwise partial envelope model: efficient estimation in multivariate linear regression

2021 ◽  
pp. 1-19
Author(s):  
Jing Zhang ◽  
Zhensheng Huang ◽  
Zhiqiang Jiang
Keyword(s):  
Linear Regression ◽  
Multivariate Linear Regression ◽  
Efficient Estimation ◽  
Envelope Model

Efficient estimation of reduced-rank partial envelope model in multivariate linear regression

2020 ◽  
pp. 2150024
Author(s):  
Jing Zhang ◽  
Zhensheng Huang ◽  
Yan Xiong
Keyword(s):  
Data Analysis ◽  
Linear Regression ◽  
Real Data ◽  
Efficient Estimation ◽  
Simulation Studies ◽  
Reduced Rank Regression ◽  
Rank Regression ◽  
Reduced Rank ◽  
Real Data Analysis ◽  
Envelope Model

In order to further improve the efficiency of parameter estimation and reduce the number of estimated parameters, we adopt dimension reduction ideas of partial envelope model proposed by [Su and Cook, Partial envelopes for efficient estimation in multivariate linear regression, Biometrika 98 (2011) 133–146.] to center on some predictors of special interest. Based on the research results of [Cook et al., Envelopes and reduced-rank regression, Biometrika 102 (2015) 439–456.], we combine partial envelopes with reduced-rank regression to form reduced-rank partial envelope model which can reduce dimension efficiently. This method has the potential to perform better than both. Further, we demonstrate maximum likelihood estimators for the reduced-rank partial envelope model parameters, and exhibit asymptotic distribution and theoretical properties under normality. Meanwhile, we show selections of rank and partial envelope dimension. At last, under the normal and non-normal error distributions, simulation studies are carried out to compare our proposed reduced-rank partial envelope model with the other four methods, including ordinary least squares, reduced-rank regression, partial envelope model and reduced-rank envelope model. A real data analysis is also given to support the theoretic claims. The reduced-rank partial envelope estimators have shown promising performance in extensive simulation studies and real data analysis.

scholarly journals Association between triglyceride-glucose index and risk of arterial stiffness: a cohort study

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Shouling Wu ◽  
Luli Xu ◽  
Mingyang Wu ◽  
Shuohua Chen ◽  
Youjie Wang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Linear Regression ◽  
Arterial Stiffness ◽  
Multivariate Linear Regression ◽  
Annual Growth ◽  
Annual Growth Rate ◽  
Cross Sectional ◽  
Tyg Index ◽  
Longitudinal Association ◽  
The Cross

Abstract Background Triglyceride–glucose (TyG) index, a simple surrogate marker of insulin resistance, has been reported to be associated with arterial stiffness. However, previous studies were limited by the cross-sectional design. The purpose of this study was to explore the longitudinal association between TyG index and progression of arterial stiffness. Methods A total of 6028 participants were derived from the Kailuan study. TyG index was calculated as ln [fasting triglyceride (mg/dL) × fasting glucose (mg/dL)/2]. Arterial stiffness was measured using brachial-ankle pulse wave velocity (baPWV). Arterial stiffness progression was assessed by the annual growth rate of repeatedly measured baPWV. Multivariate linear regression models were used to estimate the cross-sectional association of TyG index with baPWV, and Cox proportional hazard models were used to investigate the longitudinal association between TyG index and the risk of arterial stiffness. Results Multivariate linear regression analyses showed that each one unit increase in the TyG index was associated with a 39 cm/s increment (95%CI, 29–48 cm/s, P < 0.001) in baseline baPWV and a 0.29 percent/year increment (95%CI, 0.17–0.42 percent/year, P < 0.001) in the annual growth rate of baPWV. During 26,839 person-years of follow-up, there were 883 incident cases with arterial stiffness. Participants in the highest quartile of TyG index had a 58% higher risk of arterial stiffness (HR, 1.58; 95%CI, 1.25–2.01, P < 0.001), as compared with those in the lowest quartile of TyG index. Additionally, restricted cubic spline analysis showed a significant dose–response relationship between TyG index and the risk of arterial stiffness (P non-linearity = 0.005). Conclusion Participants with a higher TyG index were more likely to have a higher risk of arterial stiffness. Subjects with a higher TyG index should be aware of the following risk of arterial stiffness progression, so as to establish lifestyle changes at an early stage.

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