scholarly journals Non-linear Mixed Models in a Dose Response Modelling

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Madona Yunita Wijaya
Keyword(s):  
Linear Model ◽  
Dose Response ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Growth Curves ◽  
Limiting Factor ◽  
Dose Time ◽  
Non Linear ◽  
Diffusion Function

AbstractStudy designs in which an outcome is measured more than once from time to time result in longitudinal data. Most of the methodological works have been done in the setting of linear and generalized linear models, where some amount of linearity is retained. However, this still be considered a limiting factor and non-linear models is another option offering its flexibility. Non-linear model involves complexity of non-linear dependence on parameters than that in the generalized linear class. It has been utilized in many situations such as modeling of growth curves and dose-response modeling. The latter modeling will be the main interest in this study to construct a dose-response relationship, as a function of time to IBD (inflammatory bowel disease) dataset. The dataset comes from a clinical trial with 291 subjects measured during a 7 week period. Both linear and non-linear models are considered. A dose time response model with generalized diffusion function is utilized for the non-linear models. The fit of non-linear models are found to be more flexible than linear models hence able to capture more variability present in the data.Keywords: IBD; longitudinal; linear mixed model; non-linear mixed model. AbstrakDesain studi dimana hasil diukur berulang kali dari waktu ke waktu menghasilkan data longitudinal. Sebagian besar metodologi yang digunakan untuk menganalisis data longitudinal adalah model linear dan model linear umum (generalized linear model) dimana sejumlah linearitas tertentu dipertahankan. Asumsi linearitas ini masih dipandang memiliki keterbatasan dan model non-linear adalah pilihan metode lainnya yang menawarkan fleksibilitas. Model non-linear telah digunakan di berbagai macam situasi seperti model kurva pertumbuhan , model farmakokinetika, dan farmakodinamika, dan model respon-dosis. Model respon-dosis akan menjadi fokus dalam penelitian ini untuk membangun hubungan dosis-respon sebagai fungsi waktu dari data IBD dengan menggunakan model linear dan non-linear. Hasil penelitian menunjukan bahwa model non-linear lebih fleksibel daripada model linear sehingga mampu menangkap lebih banyak variabilitas yang ada di dalam data.Keywords: IBD; longitudinal; model linear; model non-linear.

scholarly journals Comparison of Generalized Linear Model and Generalized Linear Mixed Model – An Application to Low Birth Weight Data

2020 ◽  
pp. 31-37
Author(s):  
Michael Fosu Ofori ◽  
Stephen B. Twum ◽  
Jackson A. Y. Osborne
Keyword(s):  
Linear Model ◽  
Generalized Linear Models ◽  
Generalized Linear Model ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Generalized Linear Mixed Model ◽  
Correlated Data ◽  
Parameter Estimates ◽  
Over Dispersion

Background: Generalized Linear models are mostly fitted to data that are not correlated. However, very often data that are collected from health and epidemiological studies are correlated either as a result of the sampling methods or the randomness associated with the collection of such data. Therefore, fitting generalized linear models to such data that produce only fixed effects could lead to over dispersion in the model estimates. Objectives: The objective of this study is to fit both generalized linear and generalized linear mixed models to a correlated data and compare the results of the two models. Methods: Logistic regression is employed in fitting the generalized linear model since the dependent variable in the study is bivariate whilst the GLIMMIX model in SAS is used to fit the generalized linear mixed model. Results: The generalized linear model produces over dispersion with higher errors among the parameter estimates than the generalized linear mixed model. Conclusion: In dealing with a more correlated data, generalized linear mixed model, which can handle both fixed and random effects, is preferable to generalized linear model.

scholarly journals Experimental validation of wind energy estimation

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3795-3806
Author(s):  
Predrag Zivkovic ◽  
Mladen Tomic ◽  
Vukman Bakic
Keyword(s):  
Wind Speed ◽  
Linear Model ◽  
Linear Models ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Electricity Production ◽  
Navier Stokes ◽  
Energy Estimation ◽  
Navier Stokes Equations ◽  
Non Linear

Wind power assessment in complex terrain is a very demanding task. Modeling wind conditions with standard linear models does not sufficiently reproduce wind conditions in complex terrains, especially on leeward sides of terrain slopes, primarily due to the vorticity. A more complex non-linear model, based on Reynolds averaged Navier-Stokes equations has been used. Turbulence was modeled by modified two-equations k-? model for neutral atmospheric boundary-layer conditions, written in general curvelinear non-orthogonal co-ordinate system. The full set of mass and momentum conservation equations as well as turbulence model equations are numerically solved, using the as CFD technique. A comparison of the application of linear model and non-linear model is presented. Considerable discrepancies of estimated wind speed have been obtained using linear and non-linear models. Statistics of annual electricity production vary up to 30% of the model site. Even anemometer measurements directly at a wind turbine?s site do not necessarily deliver the results needed for prediction calculations, as extrapolations of wind speed to hub height is tricky. The results of the simulation are compared by means of the turbine type, quality and quantity of the wind data and capacity factor. Finally, the comparison of the estimated results with the measured data at 10, 30, and 50 m is shown.

Full Credibility with Generalized Linear and Mixed Models

2009 ◽  
Vol 39 (1) ◽  
pp. 61-80 ◽  
Author(s):  
José Garrido ◽  
Jun Zhou
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Link Function ◽  
Analysis Method ◽  
Risk Class ◽  
Statistical Analysis Method ◽  
Car Insurance ◽  
Insurance Data

AbstractGeneralized linear models (GLMs) are gaining popularity as a statistical analysis method for insurance data. For segmented portfolios, as in car insurance, the question of credibility arises naturally; how many observations are needed in a risk class before the GLM estimators can be considered credible? In this paper we study the limited fluctuations credibility of the GLM estimators as well as in the extended case of generalized linear mixed model (GLMMs). We show how credibility depends on the sample size, the distribution of covariates and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.

scholarly journals Hybrid MARMA-NARX model for flow forecasting based on the large-scale climate signals, sea-surface temperatures, and rainfall

2018 ◽  
Vol 49 (6) ◽  
pp. 1788-1803 ◽  
Author(s):  
Mohammad Ebrahim Banihabib ◽  
Arezoo Ahmadian ◽  
Mohammad Valipour
Keyword(s):  
Linear Model ◽  
Hybrid Model ◽  
Large Scale ◽  
Linear Models ◽  
Moving Average ◽  
Effective Parameters ◽  
Forecasting Accuracy ◽  
Local Factor ◽  
Non Linear ◽  
Climate Signals

Abstract In this study, to reflect the effect of large-scale climate signals on runoff, these indices are accompanied with rainfall (the most effective local factor in runoff) as the inputs of the hybrid model. Where one-year in advance forecasting of reservoir inflows can provide data to have an optimal reservoir operation, reports show we still need more accurate models which include all effective parameters to have more forecasting accuracy than traditional linear models (ARMA and ARIMA). Thus, hybridization of models was employed for improving the accuracy of flow forecasting. Moreover, various forecasters including large-scale climate signals were tested to promote forecasting. This paper focuses on testing MARMA-NARX hybrid model to enhance the accuracy of monthly inflow forecasts. Since the inflow in different periods of the year has in linear and non-linear trends, the hybrid model is proposed as a means of combining linear model, monthly autoregressive moving average (MARMA), and non-linear model, nonlinear autoregressive model with exogenous (NARX) inputs to upgrade the accuracy of flow forecasting. The results of the study showed enhanced forecasting accuracy through using the hybrid model.

scholarly journals Comparison of Linear and Nonlinear Behavior of Track Elements in Contact-Impact Models

2018 ◽  
Author(s):  
Jabbar Ali Zakeri ◽  
Mosab Reza Tajalli
Keyword(s):  
Linear Model ◽  
3D Model ◽  
Linear Models ◽  
Wave Length ◽  
Short Wave ◽  
Contact Forces ◽  
Reliable Estimate ◽  
Impact Forces ◽  
Linear Behavior ◽  
Non Linear

Existence of short wave length irregularities and discontinuities in the rail, such as corrugation, isolated rail joints, crossings and rail breakage, result in impact forces and an increase in wheel-rail contact force. Extreme forces in such could result in non-linear behavior of ballast and pads, and as a result, employing common linear models mihgt over/under estimate contact forces. A 3D model of wheel and rail is developed in this paper, and by considering rail breakage, validity of linear models and considering non-linear behavior of materials are studied. Wheel-rail interactions are studied for two common pads with high stiffness (HDPE) and low stiffness (Studded) for speeds of 20 to 160 km/h. Three behavioral patterns are considered for the developed 3D model: linear pad and ballast (LP-LB), nonlinear pad and linear ballast (NLP, LB), and nonlinear pad and ballast (NLP, NLB), and results are compared. According to the results, for HDPE pads and impact forces of up to 30 tons, linear model for material could estimate acceptable results. Yet for studded pads, linear model estimates forces that are comparably less than those estimated by non-linear model. Moreover employing NLP-LB model overestimates pad and wheel-rail contact forces by a rather small margin, compared to those estimated by NLP-NLB model, and hence, could be a suitable replacement for it. It is also observed that in order to have a reliable estimate of ballast forces, using non-linear ballast models are mandatory, and neither LP-LB nor NLP-LB could be acceptable replacements.

Machine Learning Techniques on Multidimensional Curve Fitting Data Based on R- Square and Chi-Square Methods

2016 ◽  
Vol 6 (3) ◽  
pp. 974 ◽  
Author(s):  
Vidyullatha P ◽  
D. Rajeswara Rao
Keyword(s):  
Machine Learning ◽  
Linear Model ◽  
Curve Fitting ◽  
Linear Models ◽  
Machine Learning Techniques ◽  
Chi Square ◽  
Curve Fit ◽  
Learning Techniques ◽  
Non Linear ◽  
Data Points

<p>Curve fitting is one of the procedures in data analysis and is helpful for prediction analysis showing graphically how the data points are related to one another whether it is in linear or non-linear model. Usually, the curve fit will find the concentrates along the curve or it will just use to smooth the data and upgrade the presence of the plot. Curve fitting checks the relationship between independent variables and dependent variables with the objective of characterizing a good fit model. Curve fitting finds mathematical equation that best fits given information. In this paper, 150 unorganized data points of environmental variables are used to develop Linear and non-linear data modelling which are evaluated by utilizing 3 dimensional ‘Sftool’ and ‘Labfit’ machine learning techniques. In Linear model, the best estimations of the coefficients are realized by the estimation of R- square turns in to one and in Non-Linear models with least Chi-square are the criteria. </p>

scholarly journals Describing fluctuating indoor aerosol dust measurements with application to house dust mite allergens

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
F. E. van Boven ◽  
N. W. de Jong ◽  
M. G. L. C. Loomans ◽  
G. J. Braunstahl ◽  
R. Gerth van Wijk ◽  
...  
Keyword(s):  
Particulate Matter ◽  
Linear Model ◽  
House Dust ◽  
House Dust Mite ◽  
Linear Models ◽  
Airborne Dust ◽  
Dust Mite ◽  
Non Linear ◽  
The Mean ◽  
Indoor Particulate Matter

Abstract Measuring house dust mite aeroallergen concentrations is essential in understanding mite allergen exposure. Physically, the aerolized house dust mite faeces are part of indoor particulate matter. We studied the statistical ways of summarizing measurements of fluctuating mite aeroallergen exposure inside homes through indoor particulate matter. To study emissions from beddings, we measured the time-related airborne dust concentration after shaking a duvet. Analysis was performed both by a method based on the estimated mean and by a non-linear model. Twenty-eight studies reported a sum of concentrations; only one also reported the peak. In our four experiments on shaking a duvet (245 to 275 measurements each), the peak value was two to four times higher than the mean. The mean-based and non-linear models both predicted the sum of concentrations exactly. A 1% upper prediction bound and the non-linear model predicted the peak emission rate moderately well (64 to 92%, and 63 to 93%, respectively). Mean levels of indoor particulate matter measurements differ substantially from peak concentrations. The use of the mean is only sufficient to predict the sum of concentrations. We suggest that, mite aeroallergen measurements should include information on the peak as well as the mean.

scholarly journals Linear and Non-Linear Models for Remotely-Sensed Hyperspectral Image Visualization

2020 ◽  
Vol 12 (15) ◽  
pp. 2479
Author(s):  
Radu-Mihai Coliban ◽  
Maria Marincaş ◽  
Cosmin Hatfaludi ◽  
Mihai Ivanovici
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Hyperspectral Image ◽  
Point Of View ◽  
Hyperspectral Images ◽  
Image Visualization ◽  
Color Formation ◽  
Amount Of Information ◽  
Non Linear ◽  
The Impact

The visualization of hyperspectral images still constitutes an open question and may have an important impact on the consequent analysis tasks. The existing techniques fall mainly in the following categories: band selection, PCA-based approaches, linear approaches, approaches based on digital image processing techniques and machine/deep learning methods. In this article, we propose the usage of a linear model for color formation, to emulate the image acquisition process by a digital color camera. We show how the choice of spectral sensitivity curves has an impact on the visualization of hyperspectral images as RGB color images. In addition, we propose a non-linear model based on an artificial neural network. We objectively assess the impact and the intrinsic quality of the hyperspectral image visualization from the point of view of the amount of information and complexity: (i) in order to objectively quantify the amount of information present in the image, we use the color entropy as a metric; (ii) for the evaluation of the complexity of the scene we employ the color fractal dimension, as an indication of detail and texture characteristics of the image. For comparison, we use several state-of-the-art visualization techniques. We present experimental results on visualization using both the linear and non-linear color formation models, in comparison with four other methods and report on the superiority of the proposed non-linear model.

Forecasting the macro determinants of bank credit quality: a non-linear perspective

2020 ◽  
Vol 21 (4) ◽  
pp. 423-443
Author(s):  
Maria Grazia Fallanca ◽  
Antonio Fabio Forgione ◽  
Edoardo Otranto
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Strong Dependence ◽  
Bank Loans ◽  
Bank Loan ◽  
Linear Perspective ◽  
Loan Default ◽  
Content Type ◽  
Non Linear ◽  
Bad Loans

Purpose This study aims to propose a non-linear model to describe the effect of macroeconomic shocks on delinquency rates of three kinds of bank loans. Indeed, a wealth of literature has recognized significant evidence of the linkage between macro conditions and credit vulnerability, perceiving the importance of the high amount of bad loans for economic stagnation and financial vulnerability. Design/methodology/approach Generally, this linkage was represented by linear relationships, but the strong dependence of bank loan default on the economic cycle, subject to changes in regime, could suggest non-linear models as more appropriate. Indeed, macroeconomic variables affect the performance of bank’s portfolio loan, but such a relationship is subject to changes disturbing the stability of parameters along the time. This study is an attempt to model three different kinds of bank loan defaults and to forecast them in the case of the USA, detecting non-linear and asymmetric behaviors by the adoption of a Markov-switching (MS) approach. Findings Comparing it with the classical linear model, the authors identify evidence for the presence of regimes and asymmetries, changing in correspondence of the recession periods during the span of 1987–2017. Research limitations/implications The data are at a quarterly frequency, and more observations and more extended research periods could ameliorate the MS technique. Practical implications The good forecasting performance of this model could be applied by authorities to fine-tune their policies and deal with different types of loans and to diversify strategies during the different economic trends. In addition, bank management can refer to the performance of macroeconomic conditions to predict the performance of their bad loans. Originality/value The authors show a clear outperformance of the MS model concerning the linear one.

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