Preserving correlation while modelling diameter distributions

2004 ◽  
Vol 34 (1) ◽  
pp. 221-232 ◽  
Author(s):  
A Robinson
Keyword(s):  
Mixed Effects ◽  
Seemingly Unrelated Regression ◽  
Mixed Effects Models ◽  
Diameter Distribution ◽  
Distribution Models ◽  
Unrelated Regression ◽  
Simultaneous Prediction ◽  
Components Analysis ◽  
Diameter Distributions

The construction of diameter-distribution models sometimes calls for the simultaneous prediction of population parameters from hierarchical data. Appropriate data for such models have characteristics that should be preserved or accommodated: clustering and contemporaneous correlations. Fitting techniques for such data must allow for these characteristics. Using a case study, I compare two techniques — seemingly-unrelated regression (SUR) and principal components analysis (PCA) — whilst using mixed-effects models. I adapt and apply a metric that focuses on volume prediction, which is a key application for diameter distributions. The results suggest that using mixed-effects models provides useful insights into environmental variation, and that SUR is more convenient and produces a slightly better fit than PCA. Both techniques are acceptable with regard to regression assumptions.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

2020 ◽  
Author(s):  
Adrian Norman Goodwin
Keyword(s):  
Lower Bound ◽  
Blind Spot ◽  
Forest Growth ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Absolute Difference ◽  
Weibull Function ◽  
Distribution Models ◽  
Difference Statistic ◽  
Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

scholarly journals Forecasting and Mapping Coffee Borer Beetle Attacks Using GSTAR-SUR Kriging and GSTARX-SUR Kriging Models

2020 ◽  
Vol 11 (2) ◽  
pp. 65-73
Author(s):  
Henny Pramoedyo ◽  
Arif Ashari ◽  
Alfi Fadliana
Keyword(s):  
Spatial Clustering ◽  
Kriging Model ◽  
Seemingly Unrelated Regression ◽  
Kriging Interpolation ◽  
Percentage Error ◽  
Eastern Region ◽  
Unrelated Regression ◽  
Interpolation Technique ◽  
The Mean

The research aimed to use Generalized Space Time Autoregressive (GSTAR) and GSTARX modeling with the Seemingly Unrelated Regression (SUR) approach and combine them with the Kriging interpolation technique in an unobserved location. The case study was coffee borer beetle forecasting in Probolinggo Regency, East Java, Indonesia, with Watupanjang Village as the unobserved location. The results show that GSTAR-SUR Kriging and GSTARX-SUR Kriging models can predict coffee borer beetle attacks in unobserved areas with high accuracy. It is indicated by the Mean Absolute Percentage Error (MAPE) values of less than 10%. The addition of exogenous variables (rainfall) into the model is proven to improve the accuracy of the model. The Root-Mean-Square Error (RMSE) value of the GSTARX-SUR Kriging model is smaller than the GSTAR-SUR Kriging model. The structure of the model produced from the research, GSTARX-SUR (1,[1,12])(10,0,0), can be used as a reference in modeling coffee borer beetle attacks in other regencies. Map of forecasting coffee borer beetle attack shows that the spread of coffee borer beetle attack is spatial clustering with the attack center located in the eastern region of Probolinggo Regency.

Detecting the violation of variance homogeneity in mixed models

2016 ◽  
Vol 25 (6) ◽  
pp. 2506-2520 ◽  
Author(s):  
Xicheng Fang ◽  
Jialiang Li ◽  
Weng Kee Wong ◽  
Bo Fu
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Systematic Approach ◽  
Covariance Structure ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Simulation Studies ◽  
Homogeneity Assumption ◽  
Variance Homogeneity

Mixed-effects models are increasingly used in many areas of applied science. Despite their popularity, there is virtually no systematic approach for examining the homogeneity of the random-effects covariance structure commonly assumed for such models. We propose two tests for evaluating the homogeneity of the covariance structure assumption across subjects: one is based on the covariance matrices computed from the fitted model and the other is based on the empirical variation computed from the estimated random effects. We used simulation studies to compare performances of the two tests for detecting violations of the homogeneity assumption in the mixed-effects models and showed that they were able to identify abnormal clusters of subjects with dissimilar random-effects covariance structures; in particular, their removal from the fitted model might change the signs and the magnitudes of important predictors in the analysis. In a case study, we applied our proposed tests to a longitudinal cohort study of rheumatoid arthritis patients and compared their abilities to ascertain whether the assumption of covariance homogeneity for subject-specific random effects holds.

scholarly journals Bayes factors for mixed-effects models

2021 ◽  
Author(s):  
Catriona Silvey ◽  
Zoltan Dienes ◽  
Elizabeth Wonnacott
Keyword(s):  
Significance Test ◽  
Mixed Effects ◽  
Bayes Factors ◽  
Mixed Effects Models ◽  
Effect Sizes ◽  
States Of Affairs ◽  
Simple Method ◽  
Frequentist Statistics ◽  
To Come

In psychology, we often want to know whether or not an effect exists. The traditional way of answering this question is to use frequentist statistics. However, a significance test against a null hypothesis of no effect cannot distinguish between two states of affairs: evidence of absence of an effect, and absence of evidence for or against an effect. Bayes factors can make this distinction; however, uptake of Bayes factors in psychology has so far been low for two reasons. Firstly, they require researchers to specify the range of effect sizes their theory predicts. Researchers are often unsure about how to do this, leading to the use of inappropriate default values which may give misleading results. Secondly, many implementations of Bayes factors have a substantial technical learning curve. We present a case study and simulations demonstrating a simple method for generating a range of plausible effect sizes based on the output from frequentist mixed-effects models. Bayes factors calculated using these estimates provide intuitively reasonable results across a range of real effect sizes. The approach provides a solution to the problem of how to come up with principled estimates of effect size, and produces comparable results to a state-of-the-art method without requiring researchers to learn novel statistical software.

scholarly journals Effect of tofogliflozin on arterial stiffness in patients with type 2 diabetes: prespecified sub-analysis of the prospective, randomized, open-label, parallel-group comparative UTOPIA trial

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Naoto Katakami ◽  
◽  
Tomoya Mita ◽  
Hidenori Yoshii ◽  
Toshihiko Shiraiwa ◽  
...  
Keyword(s):  
Risk Factors ◽  
Blood Pressure ◽  
Type 2 Diabetes ◽  
Conventional Treatment ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Open Label ◽  
Parallel Group ◽  
History Of

Abstract Background Tofogliflozin, an SGLT2 inhibitor, is associated with favorable metabolic effects, including improved glycemic control and serum lipid profile and decreased body weight, visceral adipose tissue, and blood pressure (BP). This study evaluated the effects of tofogliflozin on the brachial-ankle pulse wave velocity (baPWV) in patients with type 2 diabetes (T2DM) without a history of apparent cardiovascular disease. Methods The using tofogliflozin for possible better intervention against atherosclerosis for type 2 diabetes patients (UTOPIA) trial is a prospective, randomized, open-label, multicenter, parallel-group, comparative study. As one of the prespecified secondary outcomes, changes in baPWV over 104 weeks were evaluated in 154 individuals (80 in the tofogliflozin group and 74 in the conventional treatment group) who completed baPWV measurement at baseline. Results In a mixed-effects model, the progression in the right, left, and mean baPWV over 104 weeks was significantly attenuated with tofogliflozin compared to that with conventional treatment (– 109.3 [– 184.3, – 34.3] (mean change [95% CI] cm/s, p = 0.005; – 98.3 [– 172.6, – 24.1] cm/s, p = 0.010; – 104.7 [– 177.0, – 32.4] cm/s, p = 0.005, respectively). Similar findings were obtained even after adjusting the mixed-effects models for traditional cardiovascular risk factors, including body mass index (BMI), glycated hemoglobin (HbA1c), total cholesterol, high-density lipoprotein (HDL)-cholesterol, triglyceride, systolic blood pressure (SBP), hypertension, smoking, and/or administration of drugs, including hypoglycemic agents, antihypertensive agents, statins, and anti-platelets, at baseline. The findings of the analysis of covariance (ANCOVA) models, which included the treatment group, baseline baPWV, and traditional cardiovascular risk factors, resembled those generated by the mixed-effects models. Conclusions Tofogliflozin significantly inhibited the increased baPWV in patients with T2DM without a history of apparent cardiovascular disease, suggesting that tofogliflozin suppressed the progression of arterial stiffness. Trial Registration UMIN000017607. Registered 18 May 2015. (https://www.umin.ac.jp/icdr/index.html)

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