scholarly journals Development of New Robust Optimal Score Function for the Weibull Distributed Error Term in Multilevel Models

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Sehar Saleem ◽  
Rehan Ahmad Khan Sherwani ◽  
Muhammad Amin ◽  
Maryam Khalid ◽  
Nouman Ali
Keyword(s):  
Multilevel Model ◽  
Error Term ◽  
Shape Parameter ◽  
Multilevel Models ◽  
Linear Models ◽  
Optimization Problems ◽  
Score Function ◽  
Least Square ◽  
Efficient Estimation ◽  
Wilcoxon Score

A popular robust estimation technique for linear models is the rank-based method as an alternative to the ordinary least square (OLS) and restricted maximum likelihood (REML) in the presence of extreme observations. This method is applied in machine reliability analysis and quantum engineering, especially in artificial intelligence and optimization problems where outliers are commonly observed. This technique is also extended for the multilevel model, where the shape of error distribution contributes a significant role in more efficient estimation. In this study, we proposed the Weibull score function for the Weibull distributed error terms in the multilevel model. The efficiency of the proposed score function is compared with the existing Wilcoxon score function and the traditional method REML via Monte Carlo simulations after adding simulated extreme observations. For small values of shape parameter in Weibull distribution of error term showing the presence of outliers, the Weibull score function was found to be efficient as compared to the Wilcoxon and REML methods. However, for a large value of shape parameter, Wilcoxon score appeared either equally efficient than the Weibull score function. REML is observed least precise in all situations. These findings are verified through a real application on test scores data, with a small value of shape parameter, and the Weibull score function turned out the most efficient.

Modeling Intraindividual Variability in Three-Level Multilevel Models

Methodology ◽  
2018 ◽  
Vol 14 (3) ◽  
pp. 95-108 ◽  
Author(s):  
Steffen Nestler ◽  
Katharina Geukes ◽  
Mitja D. Back
Keyword(s):  
Multilevel Model ◽  
Multilevel Models ◽  
Mixed Effects ◽  
Repeated Measurements ◽  
Scale Model ◽  
Suggested Approach ◽  
Psychological Study ◽  
Level Data ◽  
Ecological Momentary ◽  
Momentary Assessment

Abstract. The mixed-effects location scale model is an extension of a multilevel model for longitudinal data. It allows covariates to affect both the within-subject variance and the between-subject variance (i.e., the intercept variance) beyond their influence on the means. Typically, the model is applied to two-level data (e.g., the repeated measurements of persons), although researchers are often faced with three-level data (e.g., the repeated measurements of persons within specific situations). Here, we describe an extension of the two-level mixed-effects location scale model to such three-level data. Furthermore, we show how the suggested model can be estimated with Bayesian software, and we present the results of a small simulation study that was conducted to investigate the statistical properties of the suggested approach. Finally, we illustrate the approach by presenting an example from a psychological study that employed ecological momentary assessment.

scholarly journals Association of Serum Levels of Zinc, Copper, and Iron with Risk of Metabolic Syndrome

Nutrients ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 548
Author(s):  
Chia-Wen Lu ◽  
Yi-Chen Lee ◽  
Chia-Sheng Kuo ◽  
Chien-Hsieh Chiang ◽  
Hao-Hsiang Chang ◽  
...  
Keyword(s):  
Insulin Resistance ◽  
Metabolic Syndrome ◽  
Linear Models ◽  
Serum Zinc ◽  
Serum Levels ◽  
Least Square ◽  
Model Assessment ◽  
Serum Concentrations ◽  
Metabolic Factors ◽  
Homeostatic Model Assessment

The association between serum concentrations of zinc, copper, or iron and the risk of metabolic syndrome are inconclusive. Therefore, we conduct a case-control study to explore the relationship between serum levels of zinc, copper, or iron and metabolic syndrome as well as each metabolic factor and insulin resistance. We enrolled 1165 adults, aged ≥ 40 (65.8 ± 10) years in a hospital-based population to compare the serum levels of zinc, copper, and iron between subjects with and without metabolic syndrome by using multivariate logistic regression analyses. The least square means were computed by general linear models to compare serum concentrations of zinc, copper, and iron in relation to the number of metabolic factors. The mean serum concentrations of zinc, copper, and iron were 941.91 ± 333.63 μg/L, 1043.45 ± 306.36 μg/L, and 1246.83 ± 538.13 μg/L, respectively. The odds ratios (ORs) of metabolic syndrome for the highest versus the lowest quartile were 5.83 (95% CI: 3.35–10.12; p for trend < 0.001) for zinc, 2.02 (95% CI: 1.25–3.25; p for trend: 0.013) for copper, and 2.11 (95% CI: 1.24–3.62; p for trend: 0.021) for iron after adjusting for age, sex, personal habits, body mass index, and homeostatic model assessment insulin resistance. Additionally, the serum zinc, copper, and iron concentrations increased as the number of metabolic factors rose (p for trend < 0.001). This was the first study to clearly demonstrate that higher serum levels of zinc, copper, and iron were associated with the risk of metabolic syndrome and the number of metabolic factors independent of BMI and insulin resistance.

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

scholarly journals Integer linear models with a polynomial number of variables and constraints for some classical combinatorial optimization problems

2003 ◽  
Vol 23 (1) ◽  
pp. 161-168 ◽  
Author(s):  
Nelson Maculan ◽  
Gérard Plateau ◽  
Abdel Lisser
Keyword(s):  
Combinatorial Optimization ◽  
Linear Models ◽  
Optimization Problems ◽  
Combinatorial Optimization Problems

We present integer linear models with a polynomial number of variables and constraints for combinatorial optimization problems in graphs: optimum elementary cycles, optimum elementary paths and optimum tree problems.

scholarly journals Efficient estimation of bounded gradient-drift diffusion models for affect on CPU and GPU

2021 ◽  
Author(s):  
Tim Loossens ◽  
Kristof Meers ◽  
Niels Vanhasbroeck ◽  
Nil Anarat ◽  
Stijn Verdonck ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Continuous Time ◽  
Graphics Processing Units ◽  
Linear Models ◽  
Likelihood Function ◽  
Efficient Estimation ◽  
Closed Form Expression ◽  
Central Processing ◽  
Research Fields ◽  
Non Linear

AbstractComputational modeling plays an important role in a gamut of research fields. In affect research, continuous-time stochastic models are becoming increasingly popular. Recently, a non-linear, continuous-time, stochastic model has been introduced for affect dynamics, called the Affective Ising Model (AIM). The drawback of non-linear models like the AIM is that they generally come with serious computational challenges for parameter estimation and related statistical analyses. The likelihood function of the AIM does not have a closed form expression. Consequently, simulation based or numerical methods have to be considered in order to evaluate the likelihood function. Additionally, the likelihood function can have multiple local minima. Consequently, a global optimization heuristic is required and such heuristics generally require a large number of likelihood function evaluations. In this paper, a Julia software package is introduced that is dedicated to fitting the AIM. The package includes an implementation of a numeric algorithm for fast computations of the likelihood function, which can be run both on graphics processing units (GPU) and central processing units (CPU). The numerical method introduced in this paper is compared to the more traditional Euler-Maruyama method for solving stochastic differential equations. Furthermore, the estimation software is tested by means of a recovery study and estimation times are reported for benchmarks that were run on several computing devices (two different GPUs and three different CPUs). According to these results, a single parameter estimation can be obtained in less than thirty seconds using a mainstream NVIDIA GPU.

Combinatorial Fusion Analysis

2008 ◽  
pp. 1157-1181 ◽  
Author(s):  
D. Frank Hsu ◽  
Yun-Sheng Chung ◽  
Kristal Bruce S.
Keyword(s):  
Scoring System ◽  
Optimization Problems ◽  
Score Function ◽  
Scoring Systems ◽  
Accurate Information ◽  
Rank Score ◽  
Combinatorial Fusion ◽  
Classification Prediction ◽  
Fusion Analysis ◽  
System Selection

Combination methods have been investigated as a possible means to improve performance in multi-variable (multi-criterion or multi-objective) classification, prediction, learning, and optimization problems. In addition, information collected from multi-sensor or multi-source environment also often needs to be combined to produce more accurate information, to derive better estimation, or to make more knowledgeable decisions. In this chapter, we present a method, called Combinatorial Fusion Analysis (CFA), for analyzing combination and fusion of multiple scoring. CFA characterizes each Scoring system as having included a Score function, a Rank function, and a Rank/score function. Both rank combination and score combination are explored as to their combinatorial complexity and computational efficiency. Information derived from the scoring characteristics of each scoring system is used to perform system selection and to decide method combination. In particular, the rank/score graph defined by Hsu, Shapiro and Taksa (Hsu et al., 2002; Hsu & Taksa, 2005) is used to measure the diversity between scoring systems. We illustrate various applications of the framework using examples in information retrieval and biomedical informatics.

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