Analysis of childhood diseases and malnutrition in developing countries of Africa [Elektronische Ressource] / vorgelegt von Khaled Khatab

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Publié par	ludwig-maximilians-universitat_munchen
Publié le	01 janvier 2007
Nombre de lectures	26
Langue	English
Poids de l'ouvrage	5 Mo

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Analysis of Childhood Diseases and
Malnutrition in Developing Countries
of Africa
Khaled Khatab
Munchen,˜ 6. March 2007Analysis of Childhood Diseases and
Malnutrition in Developing Countries
of Africa
Khaled Khatab
Dissertation
zur Erlangung des Grades Doctor oeconomiae publicae
(Dr. oec. publ.)
an der Ludwig{Maximilians{Universit˜at, Munc˜ hen
vorgelegt von
Khaled Khatab
2007
Institut fur˜ Statistik, Fakult˜at fur˜ Mathematik, Informatik und StatistikReferent: Prof.Dr Ludwig Fahrmeir
Korreferent: Prof. Dr Joachim Winter
Promotionsabschlussberatung: 2007
Rigorosum 9. July 2007Contents
1 Descriptive and Explanatory Analysis of Variables 5
1.1 Data Set and Methods . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Childhood Disease . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Childhood Malnutrition . . . . . . . . . . . . . . . . . 9
1.3 Descriptive and Explanatory Analysis of Variables . . . . . . 13
1.3.1 Spatial Covariates . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Metrical Covariates. . . . . . . . . . . . . . . . . . . . 15
1.3.3 Categorical Covariates . . . . . . . . . . . . . . . . . . 17
2 Bayesian Geoadditive Models 23
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.1 Generalized linear models . . . . . . . . . . . . . . . . 24
2.1.2 Models for Continuous Responses . . . . . . . . . . . . 25
2.1.3 Models for Binary and Binomial Responses . . . . . . 25
2.2 Bayesian Geoadditive Models . . . . . . . . . . . . . . . . . . 27
2.3 Prior Distributions . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 The General Form of the Priors . . . . . . . . . . . . . 29
2.3.2 Priors for Fixed Eﬁects . . . . . . . . . . . . . . . . . 30
2.3.3 Priors for Metrical (Continuous) Eﬁects . . . . . . . . 30
2.4 MCMC Inference . . . . . . . . . . . . . . . . . . . . . . . . . 35
3 Modelling of Child Diseases in Egypt and Nigeria 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Bayesian Models . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Semiparametric Bayesian Regression Models . . . . . 41
iii CONTENTS
3.3 Statistical Inference . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . 60
3.6 A Reanalysis Excluding Some Factors . . . . . . . . . . . . . 65
3.7 Summary and Concluding Remarks . . . . . . . . . . . . . . . 68
4 Latent Variable Models 83
4.1 Basic Ideas of Latent Variable Models . . . . . . . . . . . . . 83
4.1.1 Notation and General Formulation . . . . . . . . . . . 87
4.1.2 LatentVariableModels(onefactor)withoutCovariate
Eﬁects . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1.3 Linear latent Variable Models (one factor) with Co-
variate Eﬁects . . . . . . . . . . . . . . . . . . . . . . 88
4.1.4 Underlying Variable and Item Response Theory . . . . 89
4.1.5 Bayesian Approach to LVM . . . . . . . . . . . . . . . 92
4.2 A Bayesian Geoadditive LVM . . . . . . . . . . . . . . . . . . 93
4.2.1 Measurement model . . . . . . . . . . . . . . . . . . . 93
4.2.2 Structural Model . . . . . . . . . . . . . . . . . . . . . 95
4.2.3 Identiﬂcation Problems . . . . . . . . . . . . . . . . . 96
4.2.4 Prior Distributions . . . . . . . . . . . . . . . . . . . . 97
4.2.5 Fully Posterior Inference . . . . . . . . . . . . . . . . . 98
5 Analysis of Childhood Disease with Geoadditive Probit and
Latent Variable Models 99
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2 Bayesian Geoadditive Regression and Latent Variable Models 101
5.2.1e Probit Regression . . . . . . . . . . . . . 102
5.2.2 Latent Variable Models for Binary Responses . . . . . 103
5.2.3 Priors and Bayesian Inference . . . . . . . . . . . . . . 106
5.3 Statistical Analyses and Results . . . . . . . . . . . . . . . . . 106
5.3.1 Analyses with Separate Geoadditive Models . . . . . . 107
5.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.3 Comparison with Previous Results . . . . . . . . . . . 127
5.4 Analyses with Latent Variable Models . . . . . . . . . . . . . 128
5.4.1 Comments. . . . . . . . . . . . . . . . . . . . . . . . . 131CONTENTS iii
6 Semiparametric Modelling of Malnutrition Status of Chil-
drenusingGeoadditiveGaussianRegressionandLatentVari-
able Models 153
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.2 BayesianGeoadditiveRegressionandLatentVariableModels
of Childhood Malnutrition . . . . . . . . . . . . . . . . . . . . 155
6.2.1 Geoadditive Gaussian Regression . . . . . . . . . . . . 155
6.2.2 Latent Variable Model for Continuous Responses . . . 156
6.3 Statistical Inference and Results . . . . . . . . . . . . . . . . 157
6.3.1 Application to Childhood Malnutrition, using Sepa-
rate Geoadditive Gaussian Models . . . . . . . . . . . 158
6.3.2 AnalysesusingLatentVariableModelsforContinuous
Responses . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7 Geoadditive Latent Variable Models for Disease and Nutri-
tion Indicators 203
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.2 Latent Variable Models for Mixed Response Variables . . . . 204
7.3 Model Estimation with One Factor Analysis . . . . . . . . . . 207
7.4 Model with Two Latent Variables . . . . . . . . . 209iv CONTENTS

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