Statistics Assignment代写:近代历史

This chapter tying up the various similar studies related to modeling responses multivariately in a multilevel frame work. As a start, this chapter begins by laying out the recent history of univariate techniques for analyzing categorical data in a multilevel context. Then it gradually presents the literature available on fitting multivariate multilevel models for categorical and continuous data. More over this chapter reviews the evidence for imputing missing values for partially observed multivariate multilevel data sets.

A multivariate multilevel model can be considered as a collection of multiple dependent variables in a hierarchical nature. Though the multivariate analysis increases the complexity in a multilevel context, it is an essential tool which facilitates to carry out a single test of the joint effects of some explanatory variables on several dependent variables (Snijders & Bosker (2000). These models have the power of increasing the construct validity of the analysis for complex concepts in the real world. Consider a study on school effectiveness which can be measured on three different output variables math achievement, reading proficiency and well-being at school. These data are collected on students those who are clustered within schools by implying a hierarchical nature. Although it is certainly possible to handle three outcomes separately, it is unable to show the overall picture about school effectiveness. Therefore multivariate analysis would be more preferable in these types of scenarios since it has the capability of decreasing the type 1 error and increasing the statistical power (Maeyer, Rymenans, Petegem and Bergh) (Draft).

Hierarchical natures of multivariate models are not like as the univariate response models. Let us focus on above example; it implies a two level multivariate model. But in reality it has three levels. In this case, the measurements are the level 1 units, the students the level 2 units and the schools the level three units.