## Complex Surveys: Analysis of Categorical DataThe primary objective of this book is to study some of the research topics in the area of analysis of complex surveys which have not been covered in any book yet. It discusses the analysis of categorical data using three models: a full model, a log-linear model and a logistic regression model. It is a valuable resource for survey statisticians and practitioners in the field of sociology, biology, economics, psychology and other areas who have to use these procedures in their day-to-day work. It is also useful for courses on sampling and complex surveys at the upper-undergraduate and graduate levels. The importance of sample surveys today cannot be overstated. From voters’ behaviour to fields such as industry, agriculture, economics, sociology, psychology, investigators generally resort to survey sampling to obtain an assessment of the behaviour of the population they are interested in. Many large-scale sample surveys collect data using complex survey designs like multistage stratified cluster designs. The observations using these complex designs are not independently and identically distributed – an assumption on which the classical procedures of inference are based. This means that if classical tests are used for the analysis of such data, the inferences obtained will be inconsistent and often invalid. For this reason, many modified test procedures have been developed for this purpose over the last few decades. |

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### Contents

1 | |

2 The Design Effects and Misspecification Effects | 27 |

3 Some Classical Models in Categorical Data Analysis | 67 |

4 Analysis of Categorical Data Under a Full Model | 97 |

5 Analysis of Categorical Data Under LogLinear Models | 135 |

6 Analysis of Categorical Data Under Logistic Regression Model | 157 |

7 Analysis in the Presence of Classification Errors | 179 |

8 Approximate MLE from Survey Data | 195 |

Appendix A
Asymptotic Properties of Multinomial
Distribution | 223 |

References | 241 |

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### Common terms and phrases

ˆθ analysis of categorical approximately assume asymptotic covariance matrix asymptotic distribution categorical data cell chi-square statistic cluster sampling considered consistent estimator contingency table covariance matrix deff defined denote design effect design-adjusted design-based Diag eigenvalues error estimation of variance factor finite population parameters first-order follows given goodness-of-fit Hence hth stratum IID assumption jackknifed likelihood function linear log-likelihood log-linear model logistic regression logistic regression model maximum likelihood mean method misclassification Mukhopadhyay multinomial distribution multinomial sampling null hypothesis observed obtained Pearson statistic population proportions probability procedure random variable Rao and Scott regularity conditions replacement respectively sample surveys sample units sampling design second-order simple random sampling ſº Springer Science+Business Media srswr statistic for testing strata stratified stratum superpopulation model Suppose test statistic Theorem unbiased estimator variance estimator vector Wald statistic weighted zero