Suchen und Finden
Service
Longitudinal Data Analysis - Autoregressive Linear Mixed Effects Models
Ikuko Funatogawa, Takashi Funatogawa
Verlag Springer-Verlag, 2019
ISBN 9789811000775 , 150 Seiten
Format PDF, OL
Kopierschutz Wasserzeichen
Geräte
Preface
6
Contents
8
1 Longitudinal Data and Linear Mixed Effects Models
12
1.1 Longitudinal Data
12
1.2 Linear Mixed Effects Models
14
1.3 Examples of Linear Mixed Effects Models
15
1.3.1 Means at Each Time Point with Random Intercept
16
1.3.2 Group Comparison Based on Means at Each Time Point with Random Intercept
18
1.3.3 Means at Each Time Point with Unstructured Variance Covariance
20
1.3.4 Linear Time Trend Models with Random Intercept and Random Slope
21
1.3.5 Group Comparison Based on Linear Time Trend Models with Random Intercept and Random Slope
23
1.4 Mean Structures and Variance Covariance Structures
24
1.4.1 Mean Structures
24
1.4.2 Variance Covariance Structures
25
1.5 Inference
29
1.5.1 Maximum Likelihood Method
29
1.5.2 Variances of Estimates of Fixed Effects
32
1.5.3 Prediction
32
1.5.4 Goodness of Fit for Models
34
1.5.5 Estimation and Test Using Contrast
34
1.6 Vector Representation
35
References
36
2 Autoregressive Linear Mixed Effects Models
38
2.1 Autoregressive Models of Response Itself
38
2.1.1 Introduction
38
2.1.2 Response Changes in Autoregressive Models
40
2.1.3 Interpretation of Parameters
43
2.2 Examples of Autoregressive Linear Mixed Effects Models
45
2.2.1 Example Without Covariates
46
2.2.2 Example with Time-Independent Covariates
47
2.2.3 Example with a Time-Dependent Covariate
48
2.3 Autoregressive Linear Mixed Effects Models
49
2.3.1 Autoregressive Form
49
2.3.2 Representation of Response Changes with Asymptotes
53
2.3.3 Marginal Form
55
2.4 Variance Covariance Structures
56
2.4.1 AR(1) Error and Measurement Error
56
2.4.2 Variance Covariance Matrix Induced by Random Effects
59
2.4.3 Variance Covariance Matrix Induced by Random Effects and Random Errors
61
2.4.4 Variance Covariance Matrix for Asymptotes
62
2.5 Estimation in Autoregressive Linear Mixed Effects Models
63
2.5.1 Likelihood of Marginal Form
63
2.5.2 Likelihood of Autoregressive Form
64
2.5.3 Indirect Methods Using Linear Mixed Effects Models
65
2.6 Models with Autoregressive Error Terms
67
References
69
3 Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates
70
3.1 Example with Time-Independent Covariate: PANSS Data
70
3.2 Missing Data
72
3.2.1 Missing Mechanism
72
3.2.2 Model Comparison: PANSS Data
74
3.3 Example with Time-Dependent Covariate: AFCR Data
79
3.4 Response-Dependent Modification of Time-Dependent Covariate
83
References
85
4 Multivariate Autoregressive Linear Mixed Effects Models
87
4.1 Multivariate Longitudinal Data and Vector Autoregressive Models
87
4.1.1 Multivariate Longitudinal Data
87
4.1.2 Vector Autoregressive Models
88
4.2 Multivariate Autoregressive Linear Mixed Effects Models
90
4.2.1 Example of Bivariate Autoregressive Linear Mixed Effects Models
90
4.2.2 Autoregressive Form and Marginal Form
92
4.2.3 Representation of Response Changes with Equilibria
95
4.2.4 Variance Covariance Structures
96
4.2.5 Estimation
98
4.3 Example with Time-Dependent Covariate: PTH and Ca Data
100
4.4 Multivariate Linear Mixed Effects Models
104
4.5 Appendix
106
4.5.1 Direct Product
106
4.5.2 Parameter Transformation
106
References
107
5 Nonlinear Mixed Effects Models, Growth Curves, and Autoregressive Linear Mixed Effects Models
109
5.1 Autoregressive Models and Monomolecular Curves
109
5.2 Autoregressive Linear Mixed Effects Models and Monomolecular Curves with Random Effects
114
5.3 Nonlinear Mixed Effects Models
115
5.3.1 Nonlinear Mixed Effects Models
115
5.3.2 Estimation
117
5.4 Nonlinear Curves
118
5.4.1 Exponential Functions
119
5.4.2 Gompertz Curves
119
5.4.3 Logistic Curves
120
5.4.4 Emax Models and Logistic Curves
122
5.4.5 Other Nonlinear Curves
123
5.5 Generalization of Growth Curves
124
References
127
6 State Space Representations of Autoregressive Linear Mixed Effects Models
128
6.1 Time Series Data
128
6.1.1 State Space Representations of Time Series Data
129
6.1.2 Steps for Kalman Filter for Time Series Data
130
6.2 Longitudinal Data
132
6.2.1 State Space Representations of Longitudinal Data
132
6.2.2 Calculations of Likelihoods
133
6.3 Autoregressive Linear Mixed Effects Models
134
6.3.1 State Space Representations of Autoregressive Linear Mixed Effects Models
134
6.3.2 Steps for Modified Kalman Filter for Autoregressive Linear Mixed Effects Models
137
6.3.3 Steps for Calculating Standard Errors and Predicted Values of Random Effects
140
6.3.4 Another Representation
141
6.4 Multivariate Autoregressive Linear Mixed Effects Models
141
6.5 Linear Mixed Effects Models
143
6.5.1 State Space Representations of Linear Mixed Effects Models
143
6.5.2 Steps for Modified Kalman Filter
145
References
147
Index
148
Shop
Kopierschutz
= Kopierschutzfrei
= Wasserzeichen
= DRM Kopierschutz
