Longitudinal Data with Serial Correlation: A State-space Approach (Chapman & Hall/CRC Monographs on Statistics & Applied Probability 47)
By: Richard H. Jones (author)Hardback
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The emphasis in this book is on methods for analyzing unbalanced repeated measures of longitudinal data with possible serial correlation. This can be as simple as a repeated measures experiment with missing observations, or as complicated as time response curves for groups of subjects where each subject is observed at different times. These models can include co-variates that are time-varying or fixed for a subject. Within subject serial correlation can be modelled as a continuous time first-order autoregression or as a continuous time ARMA process. The basic model is a mixed fixed and random effects model often referred to as the Laird-Ware model. Maximum likelihood and restricted maximum likelihood methods of estimation are discussed in detail with examples. Nonlinear optimization is used to obtain these estimates. Methods of model selection are discussed as well as the testing of contrasts of the fixed coefficients. The Kalman filter is presented as a method of calculating likelihoods for this wide class of models. Models where the random parameters appear nonlinearly are discussed as well as models with multivariate responses.
Examples of nonlinear models are certain dose response curves used in bioassay. FORTRAN subroutines for carrying out many of the computational procedures are given in an appendix. This book should be of interest to research workers, data analysts and graduate students in biostatistics programmes.
A general linear mixed model. First order autoregressive errors. State Space representations. The Laird-Ware model in State Space form. Autoregressive moving average errors. Nonlinear models. Multivariate models. Appendix: FORTRAN subroutines.
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- ID: 9780412406508
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