The content in this “book”, as the title suggests, is related to statistical modeling and computation. More specifically, the content focuses on using the General Linear Model (GLM) to provide statistical evidence that can help answer substantive questions in the educational and social sciences. It is a book intended for applied practitioners in the educational or social sciences. The statistical content is hopefully presented in a manner that these domian scientists will find useful, including practical suggestions for analysis and the presentation of results intended to help researchers clearly communicate the results of a data analysis.
While the content is not overly mathematical in nature, the reader will need a solid understanding of the principles in algebra for maximum benefit. The burden of caclulation that typically accompanied statisical work in previous generations is now primarily carried out in a scientific computing environment. As Thisted & Velleman (1992) point out, “computational advances have changed the face of statistical practice by transforming what we do and by challenging how we think about scientific problems.”
And to that end, to support and help facilitate the use of scientific computing, examples using the R computer language will be used throughout this work.
The organization of content is consistent with the sequence this content is taught in EPsy 8251 and EPsy 8252, two applied statistics courses that form the foundational sequence for many graduate students in the educational and social sciences at the University of Minnesota. These courses require that students have taken a previous statistics course at either the undergraduate or graduate level. Because of that, many introducotry ideas are assumed.
The content for EPsy 8251 focuses on introducing ideas of statistical computation, and foundations of building, interpreting, and evaluating GLMs. In particular, this content includes OLS estimation, coefficient- and model-based inference, dummy-coded variables, and statistical interactions.
The content for EPsy 8252 focuses on extending ideas of scientific computation and statistical modeling. In particular, this content focuses on dealing with some of the issues that crop up in practical work including modeling non-linearity using statistical transformations, and modeling non-independent data using mixed-effects models. Additional tools for model evaluation (e.g., information criteria) are also presented.
This book refers to and uses several data sets throughout the text. Each of these data sets and their codebooks are available online at the book’s github repository, https://github.com/zief0002/modeling/.