Multilevel diagnostics for mixed and hierarchical linear models

In this dissertation, I develop a multilevel approach to diagnosing and assessing t in mixed linear models and hierarchical linear models, which may be extended to other generalizations of mixed models. Since these models include multiple sources of error, I de ne several di erent types of residuals. Most residuals are confounded in the sense that they are subject to extraneous sources of error. The confounding of residuals reduces the analyst's power to detect violations of modeling assumptions. I present various approaches for reducing the confounding in residuals. I give a construction for uncorrelated standardized residuals which are also least confounded. I argue that a multilevel approach to diagnostics can overcome some confounding. Furthermore, the multilevel approach simpli es the diagnostician's task by justifying the use of well known procedures on within-unit models. I discuss the problem of identifying and discriminating between in uential cases and units. The case-deletion approach moti-vates the generalization of several common diagnostic measures. Unfortunately, the discrete approach to case-deletion, which I clarify, is imprecise relative to approaches bases on analytic approximations. Also I give some attention to the graphical presentation and interpretation of diagnostics while discussing various examples

J.A. Hilden-Minton, 'Multilevel diagnostics for mixed and hierarchical linear models', University of California, 2017