Multilevel Statistical Models

Through the social, medical and other sciences the importance of understanding complex hierarchical data structures is well understood. Multilevel modelling is now the accepted statistical technique for handling such data and is widely available in computer software packages. A thorough understanding of these techniques is therefore important for all those working in these areas. Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available. Multilevel models are particularly appropriate for research designs where data for participants are organized at more than one level (i.e., nested data). Multilevel models can be used on data with many levels, although 2-level models are the most common and the rest of this article deals only with these. The dependent variable must be examined at the lowest level of analysis. The book Multilevel Statistical Models brings these techniques together, starting from basic ideas and illustrating how more complex models are derived. This book is a comprehensive tool for postgraduate courses. This book will be beneficial for applied statisticians in the social sciences, economics, biological and medical disciplines.