Local influence in multilevel regression for growth curves

Abstract

Influence analysis is important in modelling and identification of special patterns in the data. It is well established in ordinary regression. However, analogous diagnostics are generally not available for the multilevel regression model, in which estimation involves a complex iterative algorithm. This paper studies the local influence of small perturbations on the parameter estimates in the multilevel regression model with application to growth curves. The estimation is based on the iterative generalized least-squares (IGLS) method suggested by Goldstein (Biometrika 73 (1986) 43). The generalized influence function and generalized Cook statistic (Biometrika 84(1) (1997) 175) of IGLS of unknown parameters under some specific simultaneous perturbations are derived to study the joint influence of subject units on parameter estimators. The perturbation scheme is introduced through a variance-covariance matrix of error variables. A one-step approximation formula is suggested for simplifying the computations. The method is examined on growth-curve data. r

Case deletion diagnostics in multilevel models

“…Patients 22 and 41 are highly influential, and patients 55, 61 and 28 are influential. These results are consistent with those of Shi and Ojeda [16]. Influential patterns forθ as shown in Fig.…”

“…The data from [17, p. 280-292] has been studied by Shi and Ojeda [16] using the following two-level model…”

“…patients) at level 2. Shio and Ojeda [16] concluded, using local influence, that patients 22, 61, 37, 55, 28 and 30 in order are influential onβ, and patients 41, 22, and 61 in order are influential onθ. Fig.…”

A mixed-effects model for growth curves analysis in a two-way crossed classification layout

“…Ojeda and Juárez-Cerrillo (1996) present guidelines and exploratory multivariate techniques for diagnostic checks of level-two residuals. Shi and Ojeda (2004) studied influence in regression models for growth curves. Predicted trend for each individual can be obtained in order to study the predicted variability patterns, by using multivariate techniques such as principal components analysis or cluster analysis (see, e.g., Ramsay and Silverman, 1997).…”

Local influence analysis in general spatial models

“…This method is applied or extended in influence diagnostics to many regression models and multivariate statistics; see, e.g. Backman et al (1987), Lawrance (1988), Thomas and Cook (1990), Wu and Luo (1993), Shi (1997), Poon and Poon (1999), Zhu and Lee (2001), Shi and Ojeda (2004), Shi and Huang (2011) and Paula et al (2012). However, no attention has been paid to the local influence analysis for the general spatial model in the current literature.…”