A note on estimating single-class piecewise mixed-effects models with unknown change points

2018 ◽  
Vol 42 (5) ◽  
pp. 518-524 ◽  
Author(s):  
Nidhi Kohli ◽  
Yadira Peralta ◽  
Cengiz Zopluoglu ◽  
Mark L. Davison
Keyword(s):  
Bayesian Estimation ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Mixed Effects Models ◽  
Change Points ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Residual Variance ◽  
Monte Carlo Simulation Study ◽  
Ml Estimation

Piecewise mixed-effects models are useful for analyzing longitudinal educational and psychological data sets to model segmented change over time. These models offer an attractive alternative to commonly used quadratic and higher-order polynomial models because the coefficients obtained from fitting the model have meaningful substantive interpretation. The current study thus focuses on the estimation of piecewise mixed-effects model with unknown random change points using maximum likelihood (ML) as described in Du Toit and Cudeck (2009). Previous simulation work (Wang & McArdle, 2008) showed that Bayesian estimation produced reliable parameter estimates for the piecewise model in comparison to frequentist procedures (i.e., first-order Taylor expansion and the adaptive Gaussian quadrature) across all simulation conditions. In the current article a small Monte Carlo simulation study was conducted to assess the performance of the ML approach, a frequentist procedure, and the Bayesian approach for fitting linear–linear piecewise mixed-effects model. The obtained findings show that ML estimation approach produces reliable and accurate estimates under the conditions of small residual variance of the observed variables, and that the size of the residual variance had the most impact on the quality of model parameter estimates. Second, neither ML nor Bayesian estimation procedures performed well under all manipulated conditions with respect to the accuracy and precision of the estimated model parameters.

Nitrogen mineralisation in sugarcane soils in Queensland, Australia: I. evaluation of soil tests for predicting nitrogen mineralisation

Soil Research ◽  
2019 ◽  
Vol 57 (7) ◽  
pp. 738 ◽  
Author(s):  
D. E. Allen ◽  
P. M. Bloesch ◽  
T. G. Orton ◽  
B. L. Schroeder ◽  
D. M. Skocaj ◽  
...  
Keyword(s):  
Soil Properties ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Co2 Production ◽  
Organic N ◽  
Model Parameters ◽  
Nitrogen Mineralisation ◽  
Short Term ◽  
Available N

We explored soil properties as indices of mineralisable nitrogen (N) in sugarcane soils and whether we could increase the accuracy of predicting N mineralisation during laboratory incubations. Utilising historical data in combination with samples collected during 2016, we: (i) measured mineralised N over the course of short-term (14 days) and long-term (301 days) laboratory incubations; (ii) compared models representing mineralisation; then (iii) related model parameters to measured soil properties. We found measures representing the labile organic N pool (Hydrolysable NaOH organic N; amino sugar Illinois soil N test) best related to short-term mineralised N (R2 of 0.50–0.57, P < 0.001), while measures of CO2 production (3, 7, 10 and 14 days) best related to longer-term mineralised N (R2 of 0.75–0.84, P < 0.001). Indices were brought together to model the active and slow pools of a two-pool mineralisation model in the statistical framework of a mixed-effects model. Of the models that relied on measurement of one soil property, cumulative CO2 production (7 days) performed the best when considering all soil types; in a cross-validation test, this model gave an external R2 of 0.77 for prediction of the 301-day mineralised N. Since the mixed-effects model accounts for the various sources of uncertainty, we suggest this approach as a framework for prediction of in-field available N, with further measurement of long-term mineralised N in other soils to strengthen predictive certainty of these soil indices.

An application of Dirichlet process in clustering subjects via variance shift models: A course-evaluation study

2017 ◽  
Vol 17 (6) ◽  
pp. 381-400 ◽  
Author(s):  
Reyhaneh Rikhtehgaran
Keyword(s):  
Change Point ◽  
Dirichlet Process ◽  
Sampling Technique ◽  
Evaluation Study ◽  
Course Evaluation ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Parameter Estimates ◽  
Proposed Model ◽  
Random Change

In this article, the Dirichlet process (DP) is applied to cluster subjects with longitudinal observations. The basis of clustering is the ability of subjects to adapt themselves to new circumstances. Indeed, the basis of clustering depends on the time of changing response variability. This is done by providing a random change-point time in the variance structure of mixed-effects models. The DP is assumed as a prior for the distribution of the random change point. The discrete nature of the DP is utilized to cluster subjects according to the time of adaption. The proposed model is useful to identify groups of subjects with distinctive time-based progressions or declines. Transition mixed-effects models are also used to account for the serial correlation among observations over time. A joint modelling approach is utilized to handle the bias created in these models. The Gibbs sampling technique is adopted to achieve parameter estimates. Performance of the proposed method is evaluated via conducting a simulation study. The usefulness of the proposed model is assessed on a course-evaluation dataset.

Bayesian inference for two-part mixed-effects model using skew distributions, with application to longitudinal semicontinuous alcohol data

2015 ◽  
Vol 26 (4) ◽  
pp. 1838-1853 ◽  
Author(s):  
Dongyuan Xing ◽  
Yangxin Huang ◽  
Henian Chen ◽  
Yiliang Zhu ◽  
Getachew A Dagne ◽  
...  
Keyword(s):  
Random Effects ◽  
Repeated Measures ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Mixed Effects Models ◽  
Model Specification ◽  
Model Errors ◽  
Skew Distributions ◽  
Semicontinuous Data ◽  
Logistic Mixed Effects Model

Semicontinuous data featured with an excessive proportion of zeros and right-skewed continuous positive values arise frequently in practice. One example would be the substance abuse/dependence symptoms data for which a substantial proportion of subjects investigated may report zero. Two-part mixed-effects models have been developed to analyze repeated measures of semicontinuous data from longitudinal studies. In this paper, we propose a flexible two-part mixed-effects model with skew distributions for correlated semicontinuous alcohol data under the framework of a Bayesian approach. The proposed model specification consists of two mixed-effects models linked by the correlated random effects: (i) a model on the occurrence of positive values using a generalized logistic mixed-effects model (Part I); and (ii) a model on the intensity of positive values using a linear mixed-effects model where the model errors follow skew distributions including skew- t and skew-normal distributions (Part II). The proposed method is illustrated with an alcohol abuse/dependence symptoms data from a longitudinal observational study, and the analytic results are reported by comparing potential models under different random-effects structures. Simulation studies are conducted to assess the performance of the proposed models and method.

scholarly journals Accounting for Item Response Process and Response Styles Using the Unfolding Item Response Tree (UIRTree) Model

2021 ◽  
Author(s):  
Zhaojun Li ◽  
Bo Zhang ◽  
Mengyang Cao ◽  
Louis Tay
Keyword(s):  
Item Response ◽  
Response Styles ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Response Process ◽  
Monte Carlo Simulation Study ◽  
Graded Response ◽  
Extreme Response ◽  
Generalized Graded Unfolding Model ◽  
Unfolding Models

Many researchers have found that unfolding models may better represent how respondents answer Liker-type items and response styles (RSs) often have moderate to strong presence in responses to such items. However, the two research lines have been growing largely in parallel. The present study proposed an unfolding item response tree (UIRTree) model that can account for unfolding response process and RSs simultaneously. An empirical illustration showed that the UIRTree model could fit a personality dataset well and produced more reasonable parameter estimates. Strong presence of the extreme response style (ERS) was also revealed by the UIRTree model. We further conducted a Monte Carlo simulation study to examine the performance of the UIRTree model compared to three other models for Likert-scale responses: the Samejima’s graded response model, the generalized graded unfolding model, and the dominance item response tree (DIRTree) model. Results showed that when data followed unfolding response process and contained the ERS, the AIC was able to select the UIRTree model, while BIC was biased towards the DIRTree model in many conditions. In addition, model parameters in the UIRTree model could be accurately recovered under realistic conditions, and wrongly assuming the item response process or ignoring RSs was detrimental to the estimation of key parameters. In general, the UIRTree model is expected to help in better understanding of responses to Liker-type items theoretically and contribute to better scale development practically. Future studies on multi-trait UIRTree models and UIRTree models accounting for different types of RSs are expected.

scholarly journals A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model using Markov Chain Monte Carlo

2021 ◽  
Author(s):  
Oliver Lüdtke ◽  
Alexander Robitzsch ◽  
Esther Ulitzsch
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reciprocal Effects ◽  
Ml Estimation ◽  
Model Parameterization ◽  
Lagged Effects ◽  
The Bayesian Approach ◽  
Over Time

The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.

scholarly journals Modelling the Tree Height, Crown Base Height, and Effective Crown Height of Pinus koraiensis Plantations Based on Knot Analysis

Forests ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1778
Author(s):  
Wancai Zhu ◽  
Zhaogang Liu ◽  
Weiwei Jia ◽  
Dandan Li
Keyword(s):  
Tree Height ◽  
Information Criterion ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Pinus Koraiensis ◽  
Tree Level ◽  
Model Parameters ◽  
Crown Height ◽  
Crown Base Height ◽  
Pruning Intensity

Taking 1735 Pinus koraiensis knots in Mengjiagang Forest Farm plantations in Jiamusi City, Heilongjiang Province as the research object, a dynamic tree height, effective crown height, and crown base height growth model was developed using 349 screened knots. The Richards equation was selected as the basic model to develop a crown base height and effective crown height nonlinear mixed-effects model considering random tree-level effects. Model parameters were estimated with the non-liner mixed effect model (NLMIXED) Statistical Analysis System (SAS) module. The akaike information criterion (AIC), bayesian information criterion (BIC), −2 Log likelihood (−2LL), adjusted coefficient (Ra2), root mean square error (RMSE), and residual squared sum (RSS) values were used for the optimal model selection and performance evaluation. When tested with independent sample data, the mixed-effects model tree effects-considering outperformed the traditional model regarding their goodness of fit and validation; the two-parameter mixed-effects model outperformed the one-parameter model. Pinus koraiensis pruning times and intensities were calculated using the developed model. The difference between the effective crown and crown base heights was 1.01 m at the 15th year; thus, artificial pruning could occur. Initial pruning was performed with a 1.01 m intensity in the 15th year. Five pruning were required throughout the young forest period; the average pruning intensity was 1.46 m. The pruning interval did not differ extensively in the half-mature forest period, while the intensity decreased significantly. The final pruning intensity was only 0.34 m.

scholarly journals Biological and statistical interpretation of size-at-age, mixed-effects models of growth

2020 ◽  
Vol 7 (4) ◽  
pp. 192146 ◽  
Author(s):  
Simone Vincenzi ◽  
Dusan Jesensek ◽  
Alain J. Crivelli
Keyword(s):  
Mixed Effects ◽  
Mixed Effects Models ◽  
Individual Growth ◽  
Model Parameters ◽  
Statistical Interpretation ◽  
Von Bertalanffy ◽  
Mixed Effect ◽  
Single Observation ◽  
Growth Functions ◽  
Size At Age

The differences in life-history traits and processes between organisms living in the same or different populations contribute to their ecological and evolutionary dynamics. We developed mixed-effect model formulations of the popular size-at-age von Bertalanffy and Gompertz growth functions to estimate individual and group variation in body growth, using as a model system four freshwater fish populations, where tagged individuals were sampled for more than 10 years. We used the software Template Model Builder to estimate the parameters of the mixed-effect growth models. Tests on data that were not used to estimate model parameters showed good predictions of individual growth trajectories using the mixed-effects models and starting from one single observation of body size early in life; the best models had R 2 > 0.80 over more than 500 predictions. Estimates of asymptotic size from the Gompertz and von Bertalanffy models were not significantly correlated, but their predictions of size-at-age of individuals were strongly correlated ( r > 0.99), which suggests that choosing between the best models of the two growth functions would have negligible effects on the predictions of size-at-age of individuals. Model results pointed to size ranks that are largely maintained throughout the lifetime of individuals in all populations.

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