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Asar Ö, Bolin D, Diggle PJ, Wallin J. Linear mixed effects models for non‐Gaussian continuous repeated measurement data. J R Stat Soc Ser C Appl Stat 2020. [DOI: 10.1111/rssc.12405] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Özgür Asar
- Acibadem Mehmet Ali Aydinlar University İstanbul Turkey
| | - David Bolin
- King Abdullah University of Science and Technology Thuwal Saudi Arabia
- University of Gothenburg Sweden
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Forkman J. Generalized Confidence Intervals for Intra- and Inter-subject Coefficients of Variation in Linear Mixed-effects Models. Int J Biostat 2017; 13:/j/ijb.ahead-of-print/ijb-2016-0093/ijb-2016-0093.xml. [PMID: 28672773 DOI: 10.1515/ijb-2016-0093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Linear mixed-effects models are linear models with several variance components. Models with a single random-effects factor have two variance components: the random-effects variance, i. e., the inter-subject variance, and the residual error variance, i. e., the intra-subject variance. In many applications, it is practice to report variance components as coefficients of variation. The intra- and inter-subject coefficients of variation are the square roots of the corresponding variances divided by the mean. This article proposes methods for computing confidence intervals for intra- and inter-subject coefficients of variation using generalized pivotal quantities. The methods are illustrated through two examples. In the first example, precision is assessed within and between runs in a bioanalytical method validation. In the second example, variation is estimated within and between main plots in an agricultural split-plot experiment. Coverage of generalized confidence intervals is investigated through simulation and shown to be close to the nominal value.
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Affiliation(s)
- Rahim Alhamzawi
- Department of Statistics, College of Administration and Economics, University of Al-Qadisiyah, Al Diwaniyah, Iraq
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Affiliation(s)
- Kalyan Das
- Department of Statistics University of Calcutta 35; Ballygunge Circular Road Kolkata 700019 India
| | - Mohamad Elmasri
- Department of Mathematics and Statistics McGill University Burnside Hall; Room 1134 805 Sherbrooke W. Montreal QC H3A 0B9 Canada
| | - Arusharka Sen
- S-LB 921-23 J.W. McConnell Building, 1400 De Maisonneuve W. Montreal; QC H3G 1M8 Canada
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Lesperance M, Saab R, Neuhaus J. Nonparametric estimation of the mixing distribution in logistic regression mixed models with random intercepts and slopes. Comput Stat Data Anal 2014. [DOI: 10.1016/j.csda.2013.05.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Vock DM, Davidian M, Tsiatis AA. SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models. J Stat Softw 2014; 56:2. [PMID: 24688453 DOI: 10.18637/jss.v056.c02] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022] Open
Abstract
Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time.
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Gebregziabher M, Egede L, Gilbert GE, Hunt K, Nietert PJ, Mauldin P. Fitting parametric random effects models in very large data sets with application to VHA national data. BMC Med Res Methodol 2012; 12:163. [PMID: 23095325 PMCID: PMC3542162 DOI: 10.1186/1471-2288-12-163] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2012] [Accepted: 10/18/2012] [Indexed: 11/11/2022] Open
Abstract
Background With the current focus on personalized medicine, patient/subject level inference is often of key interest in translational research. As a result, random effects models (REM) are becoming popular for patient level inference. However, for very large data sets that are characterized by large sample size, it can be difficult to fit REM using commonly available statistical software such as SAS since they require inordinate amounts of computer time and memory allocations beyond what are available preventing model convergence. For example, in a retrospective cohort study of over 800,000 Veterans with type 2 diabetes with longitudinal data over 5 years, fitting REM via generalized linear mixed modeling using currently available standard procedures in SAS (e.g. PROC GLIMMIX) was very difficult and same problems exist in Stata’s gllamm or R’s lme packages. Thus, this study proposes and assesses the performance of a meta regression approach and makes comparison with methods based on sampling of the full data. Data We use both simulated and real data from a national cohort of Veterans with type 2 diabetes (n=890,394) which was created by linking multiple patient and administrative files resulting in a cohort with longitudinal data collected over 5 years. Methods and results The outcome of interest was mean annual HbA1c measured over a 5 years period. Using this outcome, we compared parameter estimates from the proposed random effects meta regression (REMR) with estimates based on simple random sampling and VISN (Veterans Integrated Service Networks) based stratified sampling of the full data. Our results indicate that REMR provides parameter estimates that are less likely to be biased with tighter confidence intervals when the VISN level estimates are homogenous. Conclusion When the interest is to fit REM in repeated measures data with very large sample size, REMR can be used as a good alternative. It leads to reasonable inference for both Gaussian and non-Gaussian responses if parameter estimates are homogeneous across VISNs.
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Affiliation(s)
- Mulugeta Gebregziabher
- Center for Disease Prevention and Health Interventions for Diverse Populations, Ralph H Johnson Veterans Affairs Medical Center, Charleston, SC, USA.
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Improved inference for a linear mixed-effects model when the subpopulation effects are clustered. J Stat Plan Inference 2011. [DOI: 10.1016/j.jspi.2011.05.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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10
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Martin R, Tokdar ST. Semiparametric inference in mixture models with predictive recursion marginal likelihood. Biometrika 2011. [DOI: 10.1093/biomet/asr030] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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McCulloch CE, Neuhaus JM. Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter. Stat Sci 2011. [DOI: 10.1214/11-sts361] [Citation(s) in RCA: 134] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Todem D, Kim K, Fine J, Peng L. Semiparametric regression models and sensitivity analysis of longitudinal data with nonrandom dropouts. STAT NEERL 2010; 64:133-156. [PMID: 21258610 DOI: 10.1111/j.1467-9574.2009.00435.x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
We propose a family of regression models to adjust for nonrandom dropouts in the analysis of longitudinal outcomes with fully observed covariates. The approach conceptually focuses on generalized linear models with random effects. A novel formulation of a shared random effects model is presented and shown to provide a dropout selection parameter with a meaningful interpretation. The proposed semiparametric and parametric models are made part of a sensitivity analysis to delineate the range of inferences consistent with observed data. Concerns about model identifiability are addressed by fixing some model parameters to construct functional estimators that are used as the basis of a global sensitivity test for parameter contrasts. Our simulation studies demonstrate a large reduction of bias for the semiparametric model relatively to the parametric model at times where the dropout rate is high or the dropout model is misspecified. The methodology's practical utility is illustrated in a data analysis.
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Affiliation(s)
- David Todem
- Division of Biostatistics, Department of Epidemiology, Michigan State University, B601 West Fee Hall, East Lansing, MI 48824, U.S.A
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Chen H, Manatunga AK, Lyles RH, Peng L, Marcus M. Flexible modeling of longitudinal highly skewed outcomes. Stat Med 2009; 28:3811-28. [DOI: 10.1002/sim.3754] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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14
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A hierarchical model for binary data with dependence between the design and outcome success probabilities. Stat Med 2009; 28:2967-88. [DOI: 10.1002/sim.3675] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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15
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Staudenmayer J, Lake EE, Wand MP. Robustness for general design mixed models using the t-distribution. STAT MODEL 2009. [DOI: 10.1177/1471082x0800900304] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The t-distribution allows the incorporation of outlier robustness into statistical models while retaining the elegance of likelihood-based inference. In this paper, we develop and implement a linear mixed model for the general design of the linear mixed model using the univariate t-distribution. This general design allows a considerably richer class of models to be fit than is possible with existing methods. Included in this class are semi-parametric regression and smoothing and spatial models.
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Affiliation(s)
- J Staudenmayer
- Department of Mathematics and Statistics, University of Massachusetts, USA
| | - E E Lake
- Eigenstat Inc., Newton, Massachusetts, USA
| | - M P Wand
- School of Mathematics and Applied Statistics, University of Wollongong, Australia
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Hall P, Maiti T. Deconvolution methods for non-parametric inference in two-level mixed models. J R Stat Soc Series B Stat Methodol 2009. [DOI: 10.1111/j.1467-9868.2009.00705.x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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17
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Montenegro LC, Lachos VH, Bolfarine H. Local Influence Analysis for Skew-Normal Linear Mixed Models. COMMUN STAT-THEOR M 2009. [DOI: 10.1080/03610920802238647] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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18
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Hall P, Maiti T. Non-parametric inference for clustered binary and count data when only summary information is available. J R Stat Soc Series B Stat Methodol 2008. [DOI: 10.1111/j.1467-9868.2008.00658.x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Abstract
Compared to modelling observable data, it is more difficult to choose a suitable distribution to describe latent variables since no prior knowledge or observable information can be used and only normal or nonparametric distributions are mainly applied to random effects for generalized linear mixed models (GLMMs) in the literature. To enhance the modelling toolkit, this article investigates a class of parametric skew elliptical random effects in multilevel binomial regression models using a Bayesian approach; the class includes skew normal, skew Students’ t-distributions and others. Skewness mechanism is considered through multiplying skewness parameter Δ by standardized folded elliptical random variables, and the posterior sampling is realized by working on a binary skewness indicator (BSI) instead of continuous Δ for parameter identifiability. Simulation study shows that the original continuous skewness parameter Δ and the posterior mean of BSI may have dichotomous signs to describe the directional (right/left) skewness; thus we address the importance of assuming specific random effects distribution and interpreting the skewness carefully. The methodology is exemplified through reanalyzing a teratogenic activity study of two niacin analogs published in the biological literature, and sampling-based model comparison shows that the parametric skew normal random effects model works largely better than nonparametric Dirichlet process mixture models for this data set.
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Affiliation(s)
- Junfeng Liu
- Biometrics Division, The Cancer Institute of New Jersey, USA and Department of Biostatistics, School of Public Health, University of Medicine and Dentistry of New Jersey, USA
| | - Dipak K Dey
- Department of Statistics, University of Connecticut, Storrs, USA
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20
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Zhou T, He X. Three-step estimation in linear mixed models with skew-t distributions. J Stat Plan Inference 2008. [DOI: 10.1016/j.jspi.2007.04.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Ho RK, Hu I. Flexible modelling of random effects in linear mixed models—A Bayesian approach. Comput Stat Data Anal 2008. [DOI: 10.1016/j.csda.2007.09.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Lachos VH, Bolfarine H, Arellano-Valle RB, Montenegro LC. Likelihood-Based Inference for Multivariate Skew-Normal Regression Models. COMMUN STAT-THEOR M 2007. [DOI: 10.1080/03610920601126241] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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23
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A sensitivity approach to modeling longitudinal bivariate ordered data subject to informative dropouts. HEALTH SERVICES AND OUTCOMES RESEARCH METHODOLOGY 2006. [DOI: 10.1007/s10742-006-0008-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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24
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Abstract
Covariate measurement error in regression is typically assumed to act in an additive or multiplicative manner on the true covariate value. However, such an assumption does not hold for the measurement error of sleep-disordered breathing (SDB) in the Wisconsin Sleep Cohort Study (WSCS). The true covariate is the severity of SDB, and the observed surrogate is the number of breathing pauses per unit time of sleep, which has a nonnegative semicontinuous distribution with a point mass at zero. We propose a latent variable measurement error model for the error structure in this situation and implement it in a linear mixed model. The estimation procedure is similar to regression calibration but involves a distributional assumption for the latent variable. Modeling and model-fitting strategies are explored and illustrated through an example from the WSCS.
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Affiliation(s)
- Liang Li
- Department of Biostatistics and Epidemiology/Wb4, Cleveland Clinic Foundation, Cleveland, Ohio 44195, USA.
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Abstract
A linear mixed model with a smooth random effects density is proposed. A similar approach to P-spline smoothing of Eilers and Marx (1996, Statistical Science 11, 89-121) is applied to yield a more flexible estimate of the random effects density. Our approach differs from theirs in that the B-spline basis functions are replaced by approximating Gaussian densities. Fitting the model involves maximizing a penalized marginal likelihood. The best penalty parameters minimize Akaike's Information Criterion employing Gray's (1992, Journal of the American Statistical Association 87, 942-951) results. Although our method is applicable to any dimensions of the random effects structure, in this article the two-dimensional case is explored. Our methodology is conceptually simple, and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by Zhang and Davidian (2001, Biometrics 57, 795-802). A simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings. Consistency of the estimates is shown in a particular case.
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Affiliation(s)
- Wendimagegn Ghidey
- Biostatistical Centre, Catholic University of Leuven, Kapucynenvoer 35, B-3000 Leuven, Belgium
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26
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Zhang D, Davidian M. Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data. J MULTIVARIATE ANAL 2004. [DOI: 10.1016/j.jmva.2004.04.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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27
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Basu S, Chib S. Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models. J Am Stat Assoc 2003. [DOI: 10.1198/01621450338861947] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Song X, Davidian M, Tsiatis AA. A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 2002; 58:742-53. [PMID: 12495128 DOI: 10.1111/j.0006-341x.2002.00742.x] [Citation(s) in RCA: 162] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Joint models for a time-to-event (e.g., survival) and a longitudinal response have generated considerable recent interest. The longitudinal data are assumed to follow a mixed effects model, and a proportional hazards model depending on the longitudinal random effects and other covariates is assumed for the survival endpoint. Interest may focus on inference on the longitudinal data process, which is informatively censored, or on the hazard relationship. Several methods for fitting such models have been proposed, most requiring a parametric distributional assumption (normality) on the random effects. A natural concern is sensitivity to violation of this assumption; moreover, a restrictive distributional assumption may obscure key features in the data. We investigate these issues through our proposal of a likelihood-based approach that requires only the assumption that the random effects have a smooth density. Implementation via the EM algorithm is described, and performance and the benefits for uncovering noteworthy features are illustrated by application to data from an HIV clinical trial and by simulation.
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Affiliation(s)
- Xiao Song
- Department of Statistics, Box 8203, North Carolina State University, Raleigh, North Carolina 27695-8203, USA.
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Ishwaran H, Takahara G. Independent and Identically Distributed Monte Carlo Algorithms for Semiparametric Linear Mixed Models. J Am Stat Assoc 2002. [DOI: 10.1198/016214502388618951] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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30
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Abstract
Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics 55, 363-390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.
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Affiliation(s)
- D Zhang
- Department of Statistics, North Carolina State University, Raleigh 27695-8203, USA.
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31
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Hartford A, Davidian M. Consequences of misspecifying assumptions in nonlinear mixed effects models. Comput Stat Data Anal 2000. [DOI: 10.1016/s0167-9473(99)00076-6] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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