TY - JOUR
T1 - Influential observation in the growth curve model with unstructured covariance matrix
AU - Pan, Jian-Xin
AU - Fang, Kai Tai
N1 - Funding Information:
Supported partially by the WAI TAK Investment and Loan Company Ltd. Research Scholarship of Hong Kong for 1992 93. Supported partially by the Hong Kong UGC Grant.
PY - 1996/6/14
Y1 - 1996/6/14
N2 - Under a normal assumption, Liski (Biometrics 47 (1991) 659-668) gave some measurements for assessing influential observations in the growth curve model (GCM) with a known covariance. For the GCM with an unstructured covariance matrix (UCM), i.e., the covariance is an arbitrary positive definite matrix, the problems of detecting influential observations are discussed in this paper. Based on the empirical influence function of the regression coefficient, a generalized Cook's distance is proposed to measure the influence of a subset of observations on the MLE's fit. In order to make comparison with the generalized Cook's distance, some other diagnostic measurements for assessing the influence are investigated too, which are based on the change of the confidence ellipsoid's volume after deleting the observation's subset. In addition, the influences on some linear combinations of the regression coefficient are discussed. For illustration purpose, a numerical example is provided and the analysis results show that the approaches presented in this paper are useful in practice.
AB - Under a normal assumption, Liski (Biometrics 47 (1991) 659-668) gave some measurements for assessing influential observations in the growth curve model (GCM) with a known covariance. For the GCM with an unstructured covariance matrix (UCM), i.e., the covariance is an arbitrary positive definite matrix, the problems of detecting influential observations are discussed in this paper. Based on the empirical influence function of the regression coefficient, a generalized Cook's distance is proposed to measure the influence of a subset of observations on the MLE's fit. In order to make comparison with the generalized Cook's distance, some other diagnostic measurements for assessing the influence are investigated too, which are based on the change of the confidence ellipsoid's volume after deleting the observation's subset. In addition, the influences on some linear combinations of the regression coefficient are discussed. For illustration purpose, a numerical example is provided and the analysis results show that the approaches presented in this paper are useful in practice.
KW - Discordant outlier
KW - Growth curve model
KW - Influential observation
KW - Leverage point
KW - Statistical diagnostics
UR - http://www.scopus.com/inward/record.url?scp=0042688757&partnerID=8YFLogxK
U2 - 10.1016/0167-9473(95)00037-2
DO - 10.1016/0167-9473(95)00037-2
M3 - Journal article
AN - SCOPUS:0042688757
SN - 0167-9473
VL - 22
SP - 71
EP - 87
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 1
ER -