Multivariate varying‐coefficient models for an ecological system

The monitoring of Loch Leven at Kinross in Scotland involves many physical, chemical and biological variables, which are interrelated and consequently are potentially both responses and covariates within the system. In order to explore relationships fully and make appropriate inferences about such a system, it is necessary to identify and incorporate all the important forms of dependence. Therefore, multivariate models are required to model multiple responses and covariates. Relationships between variables at Loch Leven also change throughout the year and hence a multivariate varying-coefficient model is presented here to explore changing relationships, whilst accounting for dependence between responses. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  A. Zellner.  Econometric Estimation with Temporally Dependent Disturbance Terms , 1961 .

[2]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[3]  Jianqing Fan,et al.  Statistical Estimation in Varying-Coefficient Models , 1999 .

[4]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[5]  Juan M. Rodríguez-Póo,et al.  Semiparametric Three Step Estimation Methods for Simultaneous Equation Systems , 2005 .

[6]  Stephen G. Donald,et al.  Local and Global Rank Tests for Multivariate Varying-Coefficient Models , 2011 .

[7]  D. Poirier,et al.  Semiparametric Bayesian inference in multiple equation models , 2005 .

[8]  Vasily Demyanov,et al.  Improving ecological impact assessment by statistical data synthesis using process‐based models , 2006 .

[9]  Xian Zhou,et al.  Statistical inference in a panel data semiparametric regression model with serially correlated errors , 2006 .

[10]  Timothy C. Haas,et al.  New systems for modeling, estimating, and predicting a multivariate spatio–temporal process , 2002 .

[11]  D. Huggins,et al.  Ecosystem Modeling with Lisrel: A New Approach for Measuring Direct and Indirect Effects. , 1991, Ecological applications : a publication of the Ecological Society of America.

[12]  Adrian Bowman,et al.  Assessing ecological responses to environmental change using statistical models , 2007 .

[13]  Alexander von Eye,et al.  Structural Equation Modeling: Theory , 2009 .

[14]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[15]  C. Wild,et al.  Vector Generalized Additive Models , 1996 .

[16]  Zongwu Cai,et al.  Trending time-varying coefficient time series models with serially correlated errors , 2007 .

[17]  Chunsheng Ma.  Spatio-temporal stationary covariance models , 2003 .

[18]  James O. Ramsay,et al.  Differential equation models for statistical functions , 2000 .

[19]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[20]  Phaedon C. Kyriakidis,et al.  Geostatistical Space–Time Models: A Review , 1999 .

[21]  Jianqing Fan,et al.  Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models , 2000 .

[22]  G. C. Tiao,et al.  A Course in Time Series Analysis , 2000 .

[23]  H. Grubb.  A Multivariate Time Series Analysis of Some Flour Price Data , 1992 .

[24]  Adrian Bowman,et al.  Model comparison for a complex ecological system , 2007 .

[25]  Thomas W. Yee,et al.  Vector generalized additive models in plant ecology , 2002 .

[26]  Li Ping Yang,et al.  Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data , 1998 .

[27]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[28]  I. Dryden,et al.  Non‐stationary spatiotemporal analysis of karst water levels , 2005 .

[29]  G. C. Tiao,et al.  Modeling Multiple Time Series with Applications , 1981 .