Have you been told you need to do multilevel modeling, but you can't get past the forest of equations? Do you need the techniques explained with words and practical examples so they make sense? Help is here! This book unpacks these statistical techniques in easy-to-understand language with fully annotated examples using the statistical software Stata. The techniques are explained without reliance on equations and algebra so that new users will understand when to use these approaches and how they are really just special applications of ordinary regression. Using real life data, the authors show you how to model random intercept models and random coefficient models for cross-sectional data in a way that makes sense and can be retained and repeated. This book is the perfect answer for anyone who needs a clear, accessible introduction to multilevel modeling.
Arising from the growing interest in dynamical systems theory, this book explores the derivation of relatively simple dynamical equations that model complex physical interactions. It unifies into one coherent approach many varied extant methods for model reduction and approximation. Using mathematical models at various levels of resolution and ......
Emerging Ideas for Dimension Reduction in Parameter Studies
Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the ......
This monograph provides a framework for students and practitioners who are working on the solution of electromagnetic imaging in geophysics. Bridging the gap between theory and practical applied material (for example, inverse and forward problems), it provides: A simple explanation of finite volume discretization. Basic concepts in solving ......
Climate modeling and simulation teach us about past, present, and future conditions of life on earth and help us understand observations about the changing atmosphere and ocean and terrestrial ecology. Focusing on high-end modeling and simulation of earth's climate, Climate Modeling for Scientists and Engineers: Presents observations about the ......
B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this book provides a unified introduction to the basic components of B-spline theory: approximation methods, ......
Until recently, measurable dynamics has been regarded as a highly theoretical mathematical topic with few obvious links to areas of applied mathematics. The advent of high-speed computers, rapidly-developing algorithms, and new numerical methods has, however, allowed for a tremendous amount of progress and sophistication in efforts to represent ......
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter ......
Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that ......
