Influence Diagnostics for Linear Mixed Models

Abstract

Linear mixed models are extremely sensitive to outlying responses and extreme points in the fixed and random effect design spaces. Few diag- nostics are available in standard computing packages. We provide routine diagnostic tools, which are computationally inexpensive. The diagnostics are functions of basic building blocks: studentized residuals, error contrast matrix, and the inverse of the response variable covariance matrix. The ba- sic building blocks are computed only once from the complete data analysis and provide information on the influence of the data on different aspects of the model fit. Numerical examples provide analysts with the complete pictures of the diagnostics. The linear mixed model provides flexibility in fitting models with various combinations of fixed and random effects, and is often used to analyze data in a broad spectrum of areas. It is well known that not all observations in a data set play an equal role in determining estimates, tests and other statistics. Sometimes the character of estimates in the model may be determined by only a few cases while most of the data are essentially ignored. It is important that the data analyst be aware of particular observations that have an unusually large influence on the results of the analysis. Such cases may be assessed as being appropriate and retained in the analysis, may represent inappropriate data and be eliminated from the analysis, may suggest that additional data need to be collected, may suggest the current modeling scheme is inadequate, or may indicate a data reading or data entry error. Regardless of the ultimate assessment of such cases, their identification is necessary before intelligent subject-matter-based decisions can be drawn. In ordinary linear models such model diagnostics are generally available in statistical packages and standard textbooks on applied regression, see for ex- ample, Cook and Weisberg (1982), Chatterjee and Hadi (1986, 1988). Oman