# Chapter 8: Multivariate Survey Analysis

In Chapter 8 of the textbook **Practical Methods for Design and Analysis of Complex Surveys**, multivariate analysis for complex surveys is discussed in the case of one response variable and a set of predictor or explanatory variables. For this kind of analysis situation, logistic models and linear models are widely used. Proper methods are introduced for fitting these models for intra-cluster correlated response variables from complex sampling designs. Design-based analysis of categorical data using a logit ANOVA model, and methods for design-based logistic and linear regression analysis, are discussed and applied for data from a complex sample survey.

In **Training Key 277**, design-based logit ANOVA modelling is examined reproducing the results of Example 8.1. A step-wise ANOVA model building procedure is demonstrated. A program for generalized weighted least squares (GWLS) estimation is examined in detail. The Occupational Health Care Survey data set is used.

In **Training Key 288**, logistic analysis of covariance (ANCOVA) is demonstrated for a binary response variable and the results of Example 8.2 are reproduced. Pseudolikelihood (PML) estimation is used for the OHC Survey data set, accounting for the sampling complexities. An option is provided for a detailed examination of the role of interaction effects in a logistic ANCOVA model.

In **Training Key 293**, a linear ANCOVA model is fitted for a continuous response variable from the OHC Survey data set by using weighted least squares estimation.

The results of Example 8.4 will be reproduced.

In **Training Key 298**, alternative multivariate analyses for a binary response variable and a continuous response variable from the OHC Survey data set are demonstrated. The methods include the PML and generalized estimating equations (GEE) estimation for fixed-effects logistic and linear models and residual maximum likelihood (REML) estimation for logistic and linear mixed models. The methods extend the methodology presented in the textbook. It will be noted that closely agreeing numerical results can be obtained by the different methods available.

NOTE: Instructions for the use of Training Keys are given in the Instructions section.