GLMM approach to study the spatial and temporal evolution of spikes in the small intestine

Mixed models can be applied in a wide range of settings. Probably, they are most commonly used to handle grouping in the data. In addition, mixed models can be used for smoothing purposes as well. When dealing with non-normal data, the use of smoothing methods within the generalized linear mixed models (GLMM) framework is less familiar. We explore the use of GLMM for smoothing purposes in both spatial and longitudinal dimensions. The methodology is illustrated by analysis of spike potentials in the small intestine of different cats. Spatio-temporal models that use two-dimensional smoothing splines across the spatial dimension and random effects to account for the correlations during successive slow-waves are developed. A major advantage of the mixed-model approach is that it can handle smoothing together with grouping (or other types of correlations) in a unified model. In this way, areas with high spike incidence compared with other areas can be detected. Also, the temporal and spatial characteristics of spikes during successive slow-waves can be identified.

[1]  Jean Duchon,et al.  Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces , 1976 .

[2]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[3]  G. Wahba Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression , 1978 .

[4]  J. Meinguet Multivariate interpolation at arbitrary points made simple , 1979 .

[5]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[6]  N. Breslow Extra‐Poisson Variation in Log‐Linear Models , 1984 .

[7]  Murray Aitkin,et al.  Variance Component Models with Binary Response: Interviewer Variability , 1985 .

[8]  P. Green Penalized Likelihood for General Semi-Parametric Regression Models. , 1987 .

[9]  J. Friedman,et al.  FLEXIBLE PARSIMONIOUS SMOOTHING AND ADDITIVE MODELING , 1989 .

[10]  Scott L. Zeger,et al.  Generalized linear models with random e ects: a Gibbs sampling approach , 1991 .

[11]  Terry Speed,et al.  [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment , 1991 .

[12]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[13]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[14]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[15]  B. Silverman,et al.  Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[16]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[17]  B. Silverman,et al.  Nonparametric regression and generalized linear models , 1994 .

[18]  B. Silverman,et al.  Nonparametric Regression and Generalized Linear Models: A roughness penalty approach , 1993 .

[19]  Noreen Goldman,et al.  An assessment of estimation procedures for multilevel models with binary responses , 1995 .

[20]  W. Lammers,et al.  High resolution electrical mapping in the gastrointestinal system: initial results , 1996, Neurogastroenterology and motility : the official journal of the European Gastrointestinal Motility Society.

[21]  Harvey Goldstein,et al.  Improved Approximations for Multilevel Models with Binary Responses , 1996 .

[22]  Michael L. Stein,et al.  Interpolation of spatial data , 1999 .

[23]  K. Schulze-Delrieu Visual parameters define the phase and the load of contractions in isolated guinea pig ileum. , 1999, American journal of physiology. Gastrointestinal and liver physiology.

[24]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[25]  J. R. Slack,et al.  Two‐dimensional high‐resolution motility mapping in the isolated feline duodenum: methodology and initial results , 2001, Neurogastroenterology and motility : the official journal of the European Gastrointestinal Motility Society.

[26]  D. Ruppert Selecting the Number of Knots for Penalized Splines , 2002 .

[27]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[28]  Matt P. Wand,et al.  Smoothing and mixed models , 2003, Comput. Stat..

[29]  M. Wand,et al.  Geoadditive models , 2003 .

[30]  L. Bijnens,et al.  Spatial determination of successive spikes in the isolated cat duodenum , 2004, Neurogastroenterology and motility : the official journal of the European Gastrointestinal Motility Society.

[31]  M. Wand,et al.  Smoothing with Mixed Model Software , 2004 .

[32]  B. Ripley,et al.  Semiparametric Regression: Preface , 2003 .

[33]  W. Lammers Spatial and temporal coupling between slow waves and pendular contractions. , 2005, American journal of physiology. Gastrointestinal and liver physiology.

[34]  M. Wand,et al.  Simple fitting of subject‐specific curves for longitudinal data , 2005, Statistics in medicine.

[35]  Ciprian M. Crainiceanu,et al.  Bayesian Analysis for Penalized Spline Regression Using WinBUGS , 2005 .

[36]  B. Webb,et al.  PAK1 induces podosome formation in A7r5 vascular smooth muscle cells in a PAK-interacting exchange factor-dependent manner. , 2005, American journal of physiology. Cell physiology.

[37]  G. Kauermann A note on smoothing parameter selection for penalized spline smoothing , 2005 .

[38]  M. Wand,et al.  Exact likelihood ratio tests for penalised splines , 2005 .

[39]  Application of Semiparametric Mixed Models and Simultaneous Confidence Bands in a Cardiovascular Safety Experiment with Longitudinal Data , 2008, Journal of biopharmaceutical statistics.