Diagnostic tools for hierarchical linear models

Hierarchical structures are omnipresent in today's society—this is reflected in the data that we collect on all aspects of this society. Hierarchical linear models allow a representation of structural levels in a statistical modeling framework. Diagnostic tools are used to assess the quality of model estimation and explore features of the data not well described by the model. Residual and influence diagnostics are familiar tools for the classical regression model with independent observations. For hierarchical linear models, these diagnostic tools must be adjusted to reflect the dependence introduced by the nested data structure. Residual analysis now includes the assessment of distributional assumptions at each level of the model. This requires the use of level‐dependent residual quantities. Similarly, the parameter estimates may be influenced at each level of the model, requiring influence diagnostics that can pinpoint specific levels of the model, as well as specific aspects of the model. We present an overview of the diagnostic tools available for hierarchical linear models that are familiar from linear models. Additionally, we discuss the utility of the lineup protocol for residual analysis with complex models. WIREs Comput Stat 2013, 5:48–61. doi: 10.1002/wics.1238 This article is categorized under: Statistical Models > Bayesian Models Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization