RESEARCH ARTICLE

Mixture network autoregressive model with application on students' successes

  • Weizhong TIAN , 1 ,
  • Fengrong WEI 2 ,
  • Thomas BROWN 1
Expand
  • 1. Department of Mathematical Sciences, Eastern New Mexico University, Portales, NM 88130, USA
  • 2. Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA

Received date: 08 Nov 2018

Accepted date: 21 Dec 2019

Published date: 15 Feb 2020

Copyright

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

We propose a mixture network regression model which considers both response variables and the node-specific random vector depend on the time. In order to estimate and compare the impacts of various connections on a response variable simultaneously, we extend it into p different types of connections. An ordinary least square estimators of the effects of different types of connections on a response variable is derived with its asymptotic property. Simulation studies demonstrate the effectiveness of our proposed method in the estimation of the mixture autoregressive model. In the end, a real data illustration on the students' GPA is discussed.

Cite this article

Weizhong TIAN , Fengrong WEI , Thomas BROWN . Mixture network autoregressive model with application on students' successes[J]. Frontiers of Mathematics in China, 2020 , 15(1) : 141 -154 . DOI: 10.1007/s11464-020-0813-5

1
Alhamide A A, Ibrahim K, Alodat M T. Multiple linear regression estimators with skew normal errors. AIP Conference Proceedings, 2015, 1678(1): 060013

DOI

2
Azzalini A. A class of distributions which includes the normal ones. Scand J Stat, 1985, 12(2): 171–178

3
Azzalini A, Dalla A. The multivariate skew-normal distribution. Biometrika, 1996, 83(4): 715–726

DOI

4
Dogru F Z, Arslan O. Robust mixture regression based on the skew t distribution. Rev Colombiana Estadíst, 2017, 40(1): 45–64

DOI

5
Durante D, Dunson D B. Nonparametric Bayes dynamic modelling of relational data. Biometrika, 2014, 101(4): 883–898

DOI

6
Nowicki K, Snijders T A B. Estimation and prediction for stochastic blockstructures. J Amer Statist Assoc, 2001, 96(455): 1077–1087

DOI

7
Rubio F J, Genton M G. Bayesian linear regression with skew-symmetric error distributions with applications to survival analysis. Stat Med, 2016, 35(14): 2441–2454

DOI

8
Wang Y J, Wong G Y.Stochastic blockmodels for directed graphs. J Amer Statist Assoc, 1987, 82(397): 8–19

DOI

9
Wei F, Tian W. Heterogeneous connection effects. Statist Probab Lett, 2018, 133: 9–14

DOI

10
Zhu X, Pan R, Li G, Liu Y, Wang H. Network vector autoregression. Ann Statist, 2017, 45(3): 1096–1123

DOI

Outlines

/