Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance, 2nd Edition

Chapter 7Three case studies

7.1 Further development of mixed modelling concepts through the analysis of specific data sets

In this chapter, we shall apply the concepts introduced earlier to three data sets more elaborate than those considered so far. These were obtained from specialized investigations, the first into the causes of variation in bone mineral density (BMD) among human patients, the second into the possible value of lithium as a treatment for the degenerative neurological disease amyotrophic lateral sclerosis (ALS) and the third into the causes of variation in oil content in a grain crop. However, during the analysis of these data, new concepts and additional features of the mixed modelling process will be introduced which are widely applicable. In summary, these are as follows:

• In the investigation of the causes of variation in BMD
  • a fixed-effects model with several variates and factors
  • a polynomial model with quadratic and cross-product terms;
  • further interpretation of diagnostic plots of residuals, leading to the exclusion of outliers;
  • exploration and building of the fixed-effects model;
  • use of the marginality criterion to determine which terms to retain in a polynomial model;
  • predicted values from a model: their use as an aid to understanding the results of the modelling process;
  • graphical representation of predicted values;
  • the consequences of extrapolation of predictions outside the range of the data.
• In the investigation of lithium as a treatment for ...