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Mixed-Effects Smoothing Spline ANOVA
- Journal of the Royal Statistical Association, Series B
, 1998
"... In this article we propose a general family of nonparametric mixed-effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modeled parametrically by assuming that the covariance fu ..."
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Cited by 20 (6 self)
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In this article we propose a general family of nonparametric mixed-effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modeled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a connection between a nonparametric mixed-effects model and a linear mixed-effects model. This connection suggests a way of fitting a nonparametric mixed-effects model by using existing programs. The classical two-way mixed models and the growth curve models are used as examples to demonstrate how to use smoothing spline ANOVA decompositions to build nonparametric mixed-effects models. Similar to the classical analysis of variance, components of these nonparametric mixed-effects models can be interpreted as main...
A non-linear mixed-effects model to predict cumulativebole volume of standing trees
- J. Appl. Stat
, 1996
"... SUMMARY For purposes of forest inventory and eventual management of the forest resource, it is essential to be able to predict the cumulative bole volume to any stipulated point on the standing tree bole, while requiring measurements of tree size that can be made easily, quickly and accurately. Equa ..."
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Cited by 8 (0 self)
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SUMMARY For purposes of forest inventory and eventual management of the forest resource, it is essential to be able to predict the cumulative bole volume to any stipulated point on the standing tree bole, while requiring measurements of tree size that can be made easily, quickly and accurately. Equations for this purpose are typically non-linear and are ® tted to data garnered from a sample of felled trees. Because the cumulative bole volume of each tree is measured to numerous upper-bole locations, correlations between measure-ments within a tree are likely. A mixed-effects model is ® tted to account for this within-subject (tree) correlation structure, while also portraying the sigmoidal shape of the cumulative bole volume pro ® le. 1
Height-diameter equations for boreal tree species in Ontario using a mixed-effects modelling approach.
- For. Ecol. Manage.,
, 2007
"... Abstract Height-diameter relationships based on stand characteristics (trees/ha, basal area, and dominant stand height) were investigated for balsam fir, balsam poplar, black spruce, jack pine, red pine, trembling aspen, white birch, and white spruce using data from permanent growth study plots in ..."
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Cited by 7 (1 self)
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Abstract Height-diameter relationships based on stand characteristics (trees/ha, basal area, and dominant stand height) were investigated for balsam fir, balsam poplar, black spruce, jack pine, red pine, trembling aspen, white birch, and white spruce using data from permanent growth study plots in northern Ontario, Canada. Approximately half the data were used to estimate model parameters with the rest used for model evaluation. Multiple Chapman-Richards functions with parameters expressed in terms of various stand characteristics were fit to determine the best models for predicting height. Models providing the most accurate prediction of height included basal area, trees/ha, dominant stand height, and diameter at breast height (DBH). A mixed-effects modeling approach was applied in fitting the models for all tree species. Heights predicted by models including randomeffects parameters (calibrated response) were compared with those developed without random-effects parameters (fixed-effects response). Including the random parameter consistently resulted in a better fit to the data (smaller AIC values) and an improved prediction accuracy. Crown
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Multilevel Non-Linear Random Effects Claims Reserving Models And Data Variability Structures
"... Characteristic of many reserving methods designed to analyse claims data aggregated by contract or sets of contracts, is the assumption that features typifying historical data are representative of the underwritten risk and of future losses likely to affect the contracts. Kremer (1982), Bomheutter a ..."
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Characteristic of many reserving methods designed to analyse claims data aggregated by contract or sets of contracts, is the assumption that features typifying historical data are representative of the underwritten risk and of future losses likely to affect the contracts. Kremer (1982), Bomheutter and Ferguson (1972), de Alba (2002), and many others, consider models with development patterns common to all underwriting years and known mean-variance relationships. Data amenable to such assumptions are indeed rare. More usual are large variations in settlement speeds, exposure and claim volumes. Also typifying many published models are Incurred But Not Reported (IBNR) predictions limited to periods with known claims, frequently adjusted with "tail factors " generated from market statistics. Of concern could be analytical approach inconsistencies behind reserves for delay periods before and after the last known claims, under reserving and unfair reserve allocation at underwriting year, array or contract levels. As applications of Markov Chain Monte Carlo (MCMC) methods, the models proposed in this paper depart from the neat assumptions of quasi-likelihood and extended quasi-likelihood, and introduce random effects models. The primary focus is the close dependency of the 1BNR on data variability structures and variance models, built with reference to the generic model derived in Vera (2003). The models have been implemented in BUGS
Covariance Models for Latent Structure in Longitudinal Data
"... We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influe ..."
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We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influence of covariates on the mean. Such analyses are particularly important in policy-related studies, in which the heterogeneity of the population is of interest. We describe several traditional approaches to this modeling and introduce a flexible, parsimonious class of covariance models appropriate to such analyses. This class, while rooted in the tradition of mixed effects and random coefficient models, merges several disparate modeling philosophies into what we view as a hybrid approach to longitudinal data modeling. We discuss the implications of this approach and its alternatives especially on model interpretation. We compare several implementations of this class to more commonly employed mixed effects models to describe the strengths and limitations of each. These alternatives are compared in an application to long-term trends in wage inequality for young workers. The findings provide additional guidance for the model formulation process in both statistical and substantive senses.
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"... Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain ..."
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Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain
Testing the Need for a Random Effects Modelin in a Two Compartment Model
"... The objective of this paper is to find a simple way to test whether random effects are needed in a nonlinear mixed effects model. We proposed a test statistic, approximately an F random variable, from the fixed parameter approach which compares the residual sum of squares from the full model and the ..."
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The objective of this paper is to find a simple way to test whether random effects are needed in a nonlinear mixed effects model. We proposed a test statistic, approximately an F random variable, from the fixed parameter approach which compares the residual sum of squares from the full model and the reduced model. From the difference of exponentials model simulations, the empirical size of the test is slightly higher than the nominal level a. The test offers very good power for detection. The achieved power depends on the error variance, the population coefficient of variation (CV) of the random effects, and the number of random effects in the model. For a fixed error variance, power increases as the population CV increases and/or the number of random effects increases. From our sensitivity analysis the performance of these test statistics is similar when the modei has fwo rate constants that are almost equal, or when the model is close to a one compartment model.
Detecting a Random Component in a Two Compartment Model: An Independent Random Effects Simulation Study
"... The coefficient of variations (CV) of each individual estimate and for all possible combinations of the estimates are used to see which parameters should be random in a nonlinear mixed effects model. From the difference of exponentials model simulations, when only one parameter is random, the sample ..."
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The coefficient of variations (CV) of each individual estimate and for all possible combinations of the estimates are used to see which parameters should be random in a nonlinear mixed effects model. From the difference of exponentials model simulations, when only one parameter is random, the sample CV of the coresponding estimate will be the highest rank and its mean is close to the population CV. When more than two independent random effects are considered, the corresponding sample CV of the individual estimate equally shares the highest and the mean of each individual CV estimate and their combinations are close to the population CV. An example on isolated perfused porcine skin flaps data is also presented and the multivariate coefficient of variation was applied to indicate which parameter appears to be random. The optimum solution agrees with other model selection criteria, e.g., AICC, AIC, or BIC.
