Introduction to Multi-Level Modeling (original) (raw)

2021, Statistical Regression Modeling with R

With the overview of classical linear regression and its model diagnostics in Chap. 1, we now have a good understanding of linear regression modeling and the associated assumptions that make a classical regression model valid. If data are clustered (i.e., in multi-level data), the independent assumption in classical linear regression is violated. In this situation, we need to have new regression modeling techniques. Therefore, this chapter is to introduce multi-level modeling with implementation in R to analyze multi-level data structures. 2.1 Multi-Level Data Structure 2.1.1 Sampling All studies face time and budgetary restrictions. As such, sampling an entire population is generally unfeasible. Instead, most studies sample a subset of a larger population because carefully selected samples can provide highly accurate measures of a larger population. Therefore, sampling is an efficient means of examining one or more variables of interest within a target population. In social interventions and public health research, sampling refers to selecting a subset of individuals from a target population (i.e., population of interest). Characteristics of the target population are then estimated based on the subsample. For example, we would like to estimate the properties of a target population, such as education level, income, and other outcomes. From these outcomes, statistical analyses of the sample allow us to make inferences about the target population's outcomes. These inferences are grounded in both statistical and probability theory. We review three commonly used sampling techniques: simple random sampling, stratified sampling, and cluster sampling. More comprehensive presentation of