scholarly journals A Bayesian Nonlinear Mixed-Effects Location Scale Model for Learning

2018 ◽  
Author(s):  
Donald Ray Williams ◽  
Philippe Rast
Keyword(s):  
Random Effects ◽  
Verbal Memory ◽  
Predictive Accuracy ◽  
Age Groups ◽  
Nonlinear Function ◽  
Mixed Effects ◽  
Individual Variability ◽  
Scale Model ◽  
Nonlinear Mixed Effects ◽  
Context Of Learning

We present a Bayesian nonlinear mixed-effects location scale model (NL-MELSM). The NL-MELSM allows for fitting nonlinear functions to the location, or individual means, and the scale, or within-person variance. Specifically, in the context of learning, this model allows the within-person variance to follow a nonlinear trajectory, where it can be determined whether variability reduces while in the process learning. It incorporates a sub-model that can predictnonlinear parameters for the location and/or scale. This specification estimates random effects for all nonlinear location and scale parameters that are drawn from a common multivariate distribution. This allows estimation of covariances among the random effects, within and across the location and the scale. These covariances offer new insights into the interplay between individual mean structures and intra-individual variability in nonlinear parameters. We take a fully Bayesian approach, not only for ease of estimation, but also because it provides the necessaryand consistent information for use in psychological applications, such as model selection and hypothesis testing. To illustrate the model, we use data from 333 individuals, consisting of three age groups, who participated in five learning trials that assessed verbal memory. In an exploratory context we demonstrate that fitting a nonlinear function to the within-person variance, and allowing for individual variation therein, improves predictive accuracy compared to customary modeling techniques (e.g., assuming constant variance). We conclude by discussingthe usefulness, limitations, and future directions of the NL-MELSM.

scholarly journals A Mixed-Effects Location Scale Model for Dyadic Interactions

2018 ◽  
Author(s):  
Philippe Rast ◽  
Emilio Ferrer
Keyword(s):  
Monte Carlo ◽  
Random Effects ◽  
Monte Carlo Methods ◽  
Negative Emotions ◽  
Mixed Effects ◽  
Individual Variability ◽  
Scale Model ◽  
Dyadic Interactions ◽  
Scale Parameters ◽  
Mean Structures

We present a mixed-effects location scale model (MELSM) for examining thedaily dynamics of affect in dyads. The MELSM includes person and timevarying variables to predict the location, or individual means, and the scale,or within-person variances. It also incorporates a sub-model to account forbetween-person variances. The dyadic specification can accommodate individual and partner effects in both the location and the scale components,and allows random effects for all location and scale parameters. All covariances among the random effects, within and across the location and the scaleare also estimated. These covariances offer new insights into the interplayof individual mean structures, intra-individual variability, and the influenceof partner effects on such factors. To illustrate the model, we use data from274 couples who provided daily ratings on their positive and negative emotions toward their relationship – up to 90 consecutive days. The model is fitusing Hamiltonian Monte Carlo methods, and includes subsets of predictorsin order to demonstrate the flexibility of this approach. We conclude witha discussion on the usefulness and the limitations of the MELSM for dyadicresearch.

scholarly journals A Bayesian nonlinear mixed-effects location scale model for learning

2019 ◽  
Vol 51 (5) ◽  
pp. 1968-1986 ◽  
Author(s):  
Donald R. Williams ◽  
Daniel R. Zimprich ◽  
Philippe Rast
Keyword(s):  
Mixed Effects ◽  
Scale Model ◽  
Nonlinear Mixed Effects

scholarly journals Prediction of Individual Tree Diameter Using a Nonlinear Mixed-Effects Modeling Approach and Airborne LiDAR Data

2020 ◽  
Vol 12 (7) ◽  
pp. 1066 ◽  
Author(s):  
Liyong Fu ◽  
Guangshuang Duan ◽  
Qiaolin Ye ◽  
Xiang Meng ◽  
Peng Luo ◽  
...  
Keyword(s):  
Random Effects ◽  
Prediction Accuracy ◽  
Remotely Sensed ◽  
Mixed Effects ◽  
Airborne Lidar ◽  
Sample Plot ◽  
Nonlinear Mixed Effects ◽  
Estimation Model ◽  
Individual Tree ◽  
Airborne Lidar Data

Rapidly advancing airborne laser scanning technology has become greatly useful to estimate tree- and stand-level variables at a large scale using high spatial resolution data. Compared with that of ground measurements, the accuracy of the inferred information of diameter at breast height (DBH) from a remotely sensed database and the models developed with traditional regression approaches (e.g., ordinary least square regression) may not be sufficient. Thus, this regression approach is no longer appropriate to develop accurate models and predict DBH from remotely sensed-related variables because DBH is subject to the random effects of forest stands. This study developed a generalized nonlinear mixed-effects DBH estimation model from remotely sensed imagery data. The light detection and ranging (LiDAR)-derived stand canopy density, crown projection area, and tree height were used as predictors in the DBH estimation model. These variables can be more readily measured over an extensive forest area with higher accuracy compared to the conventional field-based methods. The airborne LiDAR data for a total of 402 Picea crassifolia Kom trees on a sample plot that were divided into 16 sub-sample plots and located in the most important distribution region of western China were used. The leave-one sub-sample plot-out cross-validation method was applied to evaluate the model’s prediction accuracy. The results indicated that the random effects of the sub-sample plot on the prediction of DBH were large and their inclusion into the DBH model significantly improved the prediction accuracy. The prediction accuracy of the proposed model at the mean (M) response was also substantially improved relative to the accuracy obtained from the base model. Among several tree selection alternatives evaluated, a sample size of the two largest trees per sub-sample plot used in estimating the random effects showed a significantly higher accuracy compared to other sampling alternatives. This sample size would balance both the measurement cost and potential prediction errors. The nonlinear mixed-effects DBH estimation model at the M response can also be applied if obtaining the estimates of individual tree DBH with a relatively lower cost, and a lower prediction accuracy was the purpose of the study.

Fitting Growth Model Using Nonlinear Regression with Random Parameters

2011 ◽  
Vol 480-481 ◽  
pp. 1308-1312
Author(s):  
Yao Xiang Li ◽  
Li Chun Jiang
Keyword(s):  
Random Effects ◽  
Repeated Measures ◽  
Fixed Effects ◽  
Model Building ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Ratio Test ◽  
Nonlinear Mixed Effects ◽  
Nonlinear Mixed Effects Models ◽  
Mixed Effect

Mixed Effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. The Chapman-Richards model was fitted using nonlinear mixed-effects modeling approach. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Information criterion statistics (AIC, BIC and Likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.

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