Matvec Users’ Guide

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84 CHAPTER 11. GENERALIZED LINEAR MIXED MODEL ANALYSES -1.58156 1.89349 1.8521 3.93396 The file mouse3.info: some extra information in the model -------------------------------------------------------- AI REML converged maximum log restricted likelihood = -2200.06 variance for animal = 4.05386 -0.4364 0.412177 -0.0398331 -0.4364 5.60885 1.36832 -0.432407 0.412177 1.36832 1.58627 -1.58156 -0.0398331 -0.432407 -1.58156 1.8521 variance for dampe = 0.306701 0.163672 0.163672 1.93397 residual variance = 2.0784 2.74535 2.74535 12.8342 11.2.3 Cubic splines Data from a ELISA calibration study 4 and a constant variance with cubic splines model 5 will be used to illustrate the use of cubic splines and the M.var link() function. The model includes a fixed covariate for concentration, correlated random effects for trial and trial*concentration, and random effects for splines and splines by trial. The model equation is od ijk = µ + βconc ij + 5∑ γ l u ijl + T i + β i conc ij + l=1 5∑ γ il u ijl + e ijk where od ijk is the optical density for trial i with concentration conc j and sub-sample k, µ is the intercept, β is the overall slope, β i ∼ N(0, σ 2 C ) is the random trial specific slope, u ijl is the l spline covariate, γ l ∼ N(0, σ 2 s) is the overall l spline random effect, γ il ∼ N(0, σ 2 st) is the l spline random effect for trial i, T i ∼ N(0, σ 2 T ) is the trial random effect and is correlated with β i with covariance σ CT , and e ijk ∼ N(0, σ 2 ) is the residual. To fit a model with cubic splines the first step is to compute the spline covariates and this is accomplished with the following code D=Data(); D.input("../data/elisa.dat","trial conc od"); knots=[0 pow(2,-6:0)*12.5].t() nk=knots.nrow(); Dmat=D.mat(); conc=Dmat(*,3); X=conc.splines(knots,1); X.save("elisa-splines.dat"); Next the covariate data is merged with the original data system("paste -d\" \" ../data/elisa.dat elisa-splines.dat > elisa-fit.dat"); The model is then specified 4 Davidian, M. and D. M. Giltinan (1993). Some simple methods for estimating intraindividual variability in nonlinear mixed effects models. Biometrics 49: 59-73. 5 Verbyla, A. P., B. R. Cullis, M. G. Kenward and S. J. Welham (1999). The analysis of designed experiments and longitudinal data by using smoothing splines. Appl.Statist. 48: 269-311 l=1
11.2. PENALIZED QUASI-LIKELIHOOD 85 u=" "; tu=" "; for(i=1;i
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Matvec Users’ Guide Version 1.03
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iv CONTENTS 3.3.1 Accessing element
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vi CONTENTS 10.7 Variance Component
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Chapter 1 A Tour of Matvec 1.1 Runn
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1.5. GETTING ONLINE HELP 3 Example
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1.8. VARIABLES, EXPRESSIONS, AND ST
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1.9. INBREEDING COEFFICIENT COMPUTA
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Chapter 2 Working on Objects Matvec
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2.4. MATRIX OBJECT 11 Another metho
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2.7. DATA OBJECT 13 2.6.3 inbcoef P
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Chapter 3 Matrix Object Matrix comp
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3.3. MANIPULATION 17 3.2.2 Relation
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3.4. COMPUTATION 19 3.3.3 Selecting
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3.4. COMPUTATION 21 This member fun
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3.4. COMPUTATION 23 > A.fliplr() fl
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3.4. COMPUTATION 25 max A.max() ret
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3.4. COMPUTATION 27 reshape A.resha
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3.4. COMPUTATION 29 sort If A is a
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3.4. COMPUTATION 31 Col 1 Col 2 Col
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