Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model
'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood...
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| Published in | Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 66; no. 1; pp. 131 - 143 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing
01.02.2004
Blackwell Publishers Blackwell Royal Statistical Society Oxford University Press |
| Series | Journal of the Royal Statistical Society Series B |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1369-7412 1467-9868 |
| DOI | 10.1046/j.1369-7412.2003.05211.x |
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| Abstract | 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual. |
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| AbstractList | ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by‐product of the fitting process. We illustrate the effect of the deletion of individual observations, of ‘subjects’ and of arbitrary subsets. Central to the identity and its application is the conditional residual. 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual. 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual. Reprinted by permission of Blackwell Publishers 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual. [PUBLICATION ABSTRACT] 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual. Copyright 2004 Royal Statistical Society. |
| Author | Haslett, John Dillane, Dominic |
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| Cites_doi | 10.1111/1467-9868.00195 10.1016/S0024-3795(97)10047-7 10.1111/1467-9884.00277 10.1111/1467-9868.00287 10.1080/03610929808832267 10.1080/00031305.1997.10473581 10.1111/j.0006-341X.2001.01166.x 10.1007/978-1-4757-2477-6 10.1214/aos/1176347130 10.1080/01621459.1997.10474055 10.2307/3109764 10.1080/00401706.1977.10489493 10.1002/sim.4780110210 10.1080/00031305.1999.10474493 10.1002/9780470316856 10.1111/1467-9868.00119 10.1111/j.2517-6161.1986.tb01398.x 10.1002/(SICI)1097-0258(19990415)18:7<835::AID-SIM75>3.0.CO;2-7 10.1016/0167-9473(94)00043-I 10.1111/1467-985X.00201 10.1007/978-1-4757-2719-7 10.1080/03610929208830840 10.1111/1467-9868.00137 10.2307/1269550 10.1039/an9871200679 |
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| Keywords | Statistical method Conditional distribution Fitting Variance estimation Mixed model Linear estimation Maximum likelihood Regression residual Variance analysis Variance component Linear model Variance |
| Language | English |
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| References | Lesaffre, E. and Verbeke, G. (1998) Local influence in linear mixed models. Biometrics, 54, 570-582. Banerjee, M. and Frees, E. W. (1997) Influence diagnostics for linear longitudinal models. J. Am. Statist. Ass., 92, 999-1005. Wagner, J. R. and Thaggard, N. A. (1979) Gas-liquid chromotographic determination of nicotine contained on cambridge filter pads. J. Ass. Off. Anal. Chem., 62, 229-236. Cook, R. D. (1977) Detection of influential observations in linear regression. Technometrics, 19, 15-18. Critchley, F., Atkinson, R. A., Lu, G. and Biazi, E. (2001) Influence analysis based on the case sensitivity function. J. R. Statist. Soc. B, 63, 307-323. Ouwens, M. J. N. M., Tan, F. E. S. and Berger, M. P. F. (2001) Local influence to detect influential data structures for generalized linear mixed models. Biometrics, 57, 1166-1172. Oman, S. D. (1995) Checking the assumptions in mixed-model analysis of variance: a residual analysis approach. Comput. Statist. Data Anal., 20, 309-330. Doganskoy, N. and Balakrishnan, N. (1997) A useful property of best linear unbiased predictors with application to life testing. Am. Statistn, 51, 22-28. Venables, W. N. and Ripley B. D. (1997) Modern Applied Statistics with S-PLUS, 2nd edn. New York: Springer. Jammalamadaka, S. R. and Sengupta, D. (1999) Changes in the general linear models: a unified approach. Lin. Alg. Appl., 289, 225-242. Haslett, J. (1999) A simple derivation of deletion diagnostic results for the general linear model with correlated errors. J. R. Statist. Soc. B, 61, 603-609. Longford, N. T. (2001) Simulation-based diagnostics in random-coefficient models. J. R. Statist. Soc. A, 164, 259-273. Christensen, R. (1996) Plane Answers to Complex Questions. Berlin: Springer. Molenberghs, G. and Verbeke, G. (eds) (1997) Linear Mixed Models in Practice: a SAS-oriented Approach. Berlin: Springer. Tan, F. E. S., Ouwens, M. J. N. and Berger, M. P. F. (2001) Detection of influential observations in longitudinal mixed effects regression models. Statistician, 50, 271-284. Lesaffre, E., Asefa, M. and Verbeke, G. (1999) Assessing the goodness-of-fit of the Laird and Ware model-an example: the Jimma infant survival differential longitudinal study. Statist. Med., 18, 835-854. Martin, R. J. (1992) Leverage, influence and residuals in regression models when observations are correlated. Communs Statist. Theory Meth., 21, 1183-1212. Haslett, J. and Hayes, K. (1998) Residuals for the linear model with general covariance structure. J. R. Statist. Soc. B, 60, 201-215. Carter, R. L., Resnick, M. B., Ariet, M., Shieh, G. and Vonesh, E. F. (1992) A random coefficient growth curve analysis of mental development in low-birth-weight infants. Statist. Med., 11, 243-256. Goldstein, H. (1995) Multilevel Statistical Models. London: Arnold. Lange, N. and Ryan, L. (1989) Assessing normality in random effects models. Ann. Statist., 17, 624-642. Atkinson, A. C. (1998) Discussion on 'Some algebra and geometry for hierarchical models, applied to diagnostics' (by J. S. Hodges). J. R. Statist. Soc. B, 60, 521-523. Christensen, R., Pearson, L. M. and Johnson, W. (1992) Case-deletion diagnostics for mixed models. Technometrics, 34, 38-45. Cook, R. D. (1986) Assessment of local influence (with discussion). J. R. Statist. Soc. B, 48, 133-169. Bryk, A. S. and Raudenbush, S. W. (1992) Advanced Qualitative Techniques in the Social Sciences, vol. 1, Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park: Sage. Hayes, K. and Haslett, J. (1999) Simplifying general least squares. Am. Statistn, 53, 376-381. McCulloch, C. E. and Searle, S. R. (2001) Generalized, Linear and Mixed Models. New York: Wiley. Banerjee, M. (1998) Cook's distance in linear longitudinal models. Communs Statist. Theory Meth., 27, 2973-2983. Hodges, J. S. (1998) Some algebra and geometry for hierarchical models, applied to diagnostics (with discussion). J. R. Statist. Soc. B, 60, 497-536. Analytical Methods Committee (1987) Recommendations for the conduct and interpretation of co-operative trials. Analyst, 112, 679-686. Diggle, P., Liang, K.-Y. and Zeger, S. L. (1994) Analysis of Longitudinal Data. Oxford: Oxford University Press. Longford, N. T. (1993) Random Coefficient Models. Oxford: Oxford University Press. Atkinson, A. C. (1985) Plots, Transformations, and Regression. Oxford: Clarendon. Searle, S. R., Casella, G. and McCulloch, C. E. (1992) Variance Components. New York: Wiley. 1998; 27 2001; 50 2001; 164 1998 1997 1996 1995 1994 1999; 289 1993 1992 1998; 60 1999; 61 1992; 11 1992; 34 2001; 63 1995; 20 1987; 112 1997; 51 1997; 92 2001 1999; 18 1977; 19 1986; 48 1985 1999; 53 1992; 21 1998; 54 2001; 57 1989; 17 1979; 62 Hayes (2023040304305416900_) 1999; 53 Lange (2023040304305416900_) 1989; 17 Hodges (2023040304305416900_) 1998; 60 McCulloch (2023040304305416900_) 2001 Tan (2023040304305416900_) 2001; 50 Carter (2023040304305416900_) 1992; 11 Critchley (2023040304305416900_) 2001; 63 Ouwens (2023040304305416900_) 2001; 57 Lesaffre (2023040304305416900_) 1998; 54 Searle (2023040304305416900_) 1992 Atkinson (2023040304305416900_) 1998; 60 Bryk (2023040304305416900_) 1992 Diggle (2023040304305416900_) 1994 Haslett (2023040304305416900_) 1998; 60 Analytical Methods Committee (2023040304305416900_) 1987; 112 Nurhonen (2023040304305416900_) 1998 Wagner (2023040304305416900_) 1979; 62 Doganskoy (2023040304305416900_) 1997; 51 Cook (2023040304305416900_) 1986; 48 Christensen (2023040304305416900_) 1992; 34 Jammalamadaka (2023040304305416900_) 1999; 289 Atkinson (2023040304305416900_) 1985 Goldstein (2023040304305416900_) 1995 Banerjee (2023040304305416900_) 1998; 27 Haslett (2023040304305416900_) 1999; 61 Christensen (2023040304305416900_) 1996 Venables (2023040304305416900_) 1997 Oman (2023040304305416900_) 1995; 20 Longford (2023040304305416900_) 2001; 164 Longford (2023040304305416900_) 1993 Martin (2023040304305416900_) 1992; 21 Molenberghs (2023040304305416900_) 1997 Banerjee (2023040304305416900_) 1997; 92 Lesaffre (2023040304305416900_) 1999; 18 Cook (2023040304305416900_) 1977; 19 |
| References_xml | – reference: Carter, R. L., Resnick, M. B., Ariet, M., Shieh, G. and Vonesh, E. F. (1992) A random coefficient growth curve analysis of mental development in low-birth-weight infants. Statist. Med., 11, 243-256. – reference: Lange, N. and Ryan, L. (1989) Assessing normality in random effects models. Ann. Statist., 17, 624-642. – reference: Lesaffre, E., Asefa, M. and Verbeke, G. (1999) Assessing the goodness-of-fit of the Laird and Ware model-an example: the Jimma infant survival differential longitudinal study. Statist. Med., 18, 835-854. – reference: Christensen, R. (1996) Plane Answers to Complex Questions. Berlin: Springer. – reference: McCulloch, C. E. and Searle, S. R. (2001) Generalized, Linear and Mixed Models. New York: Wiley. – reference: Cook, R. D. (1986) Assessment of local influence (with discussion). J. R. Statist. Soc. B, 48, 133-169. – reference: Longford, N. T. (2001) Simulation-based diagnostics in random-coefficient models. J. R. Statist. Soc. A, 164, 259-273. – reference: Doganskoy, N. and Balakrishnan, N. (1997) A useful property of best linear unbiased predictors with application to life testing. Am. Statistn, 51, 22-28. – reference: Atkinson, A. C. (1985) Plots, Transformations, and Regression. Oxford: Clarendon. – reference: Bryk, A. S. and Raudenbush, S. W. (1992) Advanced Qualitative Techniques in the Social Sciences, vol. 1, Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park: Sage. – reference: Tan, F. E. S., Ouwens, M. J. N. and Berger, M. P. F. (2001) Detection of influential observations in longitudinal mixed effects regression models. Statistician, 50, 271-284. – reference: Christensen, R., Pearson, L. M. and Johnson, W. (1992) Case-deletion diagnostics for mixed models. Technometrics, 34, 38-45. – reference: Cook, R. D. (1977) Detection of influential observations in linear regression. Technometrics, 19, 15-18. – reference: Lesaffre, E. and Verbeke, G. (1998) Local influence in linear mixed models. Biometrics, 54, 570-582. – reference: Haslett, J. and Hayes, K. (1998) Residuals for the linear model with general covariance structure. J. R. Statist. Soc. B, 60, 201-215. – reference: Oman, S. D. (1995) Checking the assumptions in mixed-model analysis of variance: a residual analysis approach. Comput. Statist. Data Anal., 20, 309-330. – reference: Ouwens, M. J. N. M., Tan, F. E. S. and Berger, M. P. F. (2001) Local influence to detect influential data structures for generalized linear mixed models. Biometrics, 57, 1166-1172. – reference: Banerjee, M. and Frees, E. W. (1997) Influence diagnostics for linear longitudinal models. J. Am. Statist. Ass., 92, 999-1005. – reference: Molenberghs, G. and Verbeke, G. (eds) (1997) Linear Mixed Models in Practice: a SAS-oriented Approach. Berlin: Springer. – reference: Venables, W. N. and Ripley B. D. (1997) Modern Applied Statistics with S-PLUS, 2nd edn. New York: Springer. – reference: Martin, R. 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| Snippet | 'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms... ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms... ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms... |
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| SubjectTerms | Approximation Conditional residuals Estimation Exact sciences and technology General topics Generalized least squares Least squares Leverage Linear inference, regression Linear models Mathematical expressions Mathematics Matrix identities Maximum likelihood estimation Modeling Modelling Observational research Probability and statistics Restricted maximum likelihood Sciences and techniques of general use Statistical methods Statistical variance Statistics Studies Waste byproducts |
| Title | Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model |
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