By Ludwig Fahrmeir, Brian Francis, Robert Gilchrist, Gerhard Tutz
Read or Download Advances in GLIM and Statistical Modelling: Proceedings of the GLIM92 Conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July 1992 PDF
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Extra info for Advances in GLIM and Statistical Modelling: Proceedings of the GLIM92 Conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July 1992
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The proposed estimation of V(e o) generalizes the results ofPregibon (1981) forGLM's to multivariate mean structure models. The nG x I vector e of ordinary residuals in a sample is approximated by a first order Taylor expansion about iJo: 24 (25) Using equation (I 8) with iJ = n yields e '" £ - M(M' n- l M)-l M' n- l £ = (I _ M(M' n- l M)-l M' n- l )£ (26) If one considers the matrices in equation (26) as fixed and uses the notation where n = nl/2 nI/2" one finds estimates of the covariance matrix of the individual and joint residual vectors: With these results one finds the studentized residual for variable Yig and the quadratic form for Y i (29) where Higg is the gth diagonal element of iI ii.