Home
This Title All WIREs
WIREs RSS Feed
How to cite this WIREs title:
WIREs Comp Stat

Diagnostic tools for hierarchical linear models

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

Abstract 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

Plot of serum bilirubin level by week for the placebo group (left) and the treatment group (right).

[ Normal View | Magnified View ]

Modified dotplot of Cook's distance for the fixed effects for the methylprednisolone study. The plot shows that subject 55 may have a large effect on the fixed effects estimates.

[ Normal View | Magnified View ]

Dotplot (left) and modified dotplot (right) of Cook's distance for the variance components for the methylprednisolone study. The modified dotplot collapses all subjects ‘within’ a specified cutoff for the statistic. Here, the boxplot criterion for outliers was used as a measure of internal standing to form the cutoff (vertical red line). The plots show that subject 41, indicating this subject has a large effect on the variance component estimates.

[ Normal View | Magnified View ]

A lineup of 20 plots of EB level‐2 residuals against baseline serum bilirubin from the log transformed model. One of the plots is constructed from the observed methylprednisolone study data while the others are simulated residuals. Can you spot the observed residuals?

[ Normal View | Magnified View ]

A lineup of 20 boxplots (ordered by IQR) of LS level‐1 residuals of the log transformed model. One of the plots is constructed from the observed methylprednisolone study data while the others are simulated residuals. Can you spot the observed residuals?

[ Normal View | Magnified View ]

A normal quantile plot of the standardized LS level‐1 residuals. The large deviations from the reference line indicate that we are dealing with a very heavy‐tailed distribution.

[ Normal View | Magnified View ]

A lineup of 20 boxplots (ordered by IQR) of LS level‐1 residuals. One of the plots is constructed from the observed methylprednisolone study data while the others are simulated residuals. Can you spot the observed residuals?

[ Normal View | Magnified View ]

Browse by Topic

Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Statistical Models > Bayesian Models
Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts