Meta-heuristic to estimate parameters in Non-Linear Regression Models

2011 ◽  
Vol 3 (5) ◽  
pp. 473
Author(s):  
K. Antony Arokia Durai Raj ◽  
B. Kanagasabapathi ◽  
Gopichand Agnihothram
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Non Linear

scholarly journals Non-Parametric Generalized Additive Models as a Tool for Evaluating Policy Interventions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 299
Author(s):  
Jaime Pinilla ◽  
Miguel Negrín
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Trend ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Linear Regression Models ◽  
Non Linear ◽  
Nonlinear Trends ◽  
The Impact ◽  
Non Parametric

The interrupted time series analysis is a quasi-experimental design used to evaluate the effectiveness of an intervention. Segmented linear regression models have been the most used models to carry out this analysis. However, they assume a linear trend that may not be appropriate in many situations. In this paper, we show how generalized additive models (GAMs), a non-parametric regression-based method, can be useful to accommodate nonlinear trends. An analysis with simulated data is carried out to assess the performance of both models. Data were simulated from linear and non-linear (quadratic and cubic) functions. The results of this analysis show how GAMs improve on segmented linear regression models when the trend is non-linear, but they also show a good performance when the trend is linear. A real-life application where the impact of the 2012 Spanish cost-sharing reforms on pharmaceutical prescription is also analyzed. Seasonality and an indicator variable for the stockpiling effect are included as explanatory variables. The segmented linear regression model shows good fit of the data. However, the GAM concludes that the hypothesis of linear trend is rejected. The estimated level shift is similar for both models but the cumulative absolute effect on the number of prescriptions is lower in GAM.

scholarly journals Non-Linear Regression Models with Vibration Amplitude Optimization Algorithms in a Microturbine

Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 130
Author(s):  
Omar Rodríguez-Abreo ◽  
Juvenal Rodríguez-Reséndiz ◽  
L. A. Montoya-Santiyanes ◽  
José Manuel Álvarez-Alvarado
Keyword(s):  
Linear Regression ◽  
Vibration Amplitude ◽  
Regression Models ◽  
Engineering Problem ◽  
Coefficient Of Determination ◽  
Model Parameters ◽  
Gray Wolf ◽  
Linear Regression Models ◽  
Machinery Condition Monitoring ◽  
Non Linear

Machinery condition monitoring and failure analysis is an engineering problem to pay attention to among all those being studied. Excessive vibration in a rotating system can damage the system and cannot be ignored. One option to prevent vibrations in a system is through preparation for them with a model. The accuracy of the model depends mainly on the type of model and the fitting that is attained. The non-linear model parameters can be complex to fit. Therefore, artificial intelligence is an option for performing this tuning. Within evolutionary computation, there are many optimization and tuning algorithms, the best known being genetic algorithms, but they contain many specific parameters. That is why algorithms such as the gray wolf optimizer (GWO) are alternatives for this tuning. There is a small number of mechanical applications in which the GWO algorithm has been implemented. Therefore, the GWO algorithm was used to fit non-linear regression models for vibration amplitude measurements in the radial direction in relation to the rotational frequency in a gas microturbine without considering temperature effects. RMSE and R2 were used as evaluation criteria. The results showed good agreement concerning the statistical analysis. The 2nd and 4th-order models, and the Gaussian and sinusoidal models, improved the fit. All models evaluated predicted the data with a high coefficient of determination (85–93%); the RMSE was between 0.19 and 0.22 for the worst proposed model. The proposed methodology can be used to optimize the estimated models with statistical tools.

Non-Linear Regression Models to Predict the Lamb and Sheep Weight Growth

2013 ◽  
Vol 12 (9) ◽  
pp. 865-869 ◽  
Author(s):  
Muhammad Aman Ullah ◽  
Muhammad Amin ◽  
Muhammad Ansar Abbas
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Regression Models ◽  
Weight Growth ◽  
Non Linear

scholarly journals Significant non-linearity in nitrous oxide chamber data and its effect on calculated annual emissions

2009 ◽  
Vol 6 (1) ◽  
pp. 115-141 ◽  
Author(s):  
P. C. Stolk ◽  
C. M. J. Jacobs ◽  
E. J. Moors ◽  
A. Hensen ◽  
G. L. Velthof ◽  
...  
Keyword(s):  
Nitrous Oxide ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Surface Fluxes ◽  
Linear Regression Models ◽  
Open Questions ◽  
Non Linear

Abstract. Chambers are widely used to measure surface fluxes of nitrous oxide (N2O). Usually linear regression is used to calculate the fluxes from the chamber data. Non-linearity in the chamber data can result in an underestimation of the flux. Non-linear regression models are available for these data, but are not commonly used. In this study we compared the fit of linear and non-linear regression models to determine significant non-linearity in the chamber data. We assessed the influence of this significant non-linearity on the annual fluxes. For a two year dataset from an automatic chamber we calculated the fluxes with linear and non-linear regression methods. Based on the fit of the methods 32% of the data was defined significant non-linear. Significant non-linearity was not recognized by the goodness of fit of the linear regression alone. Using non-linear regression for these data and linear regression for the rest, increases the annual flux with 21% to 53% compared to the flux determined from linear regression alone. We suggest that differences this large are due to leakage through the soil. Macropores or a coarse textured soil can add to fast leakage from the chamber. Yet, also for chambers without leakage non-linearity in the chamber data is unavoidable, due to feedback from the increasing concentration in the chamber. To prevent a possibly small, but systematic underestimation of the flux, we recommend comparing the fit of a linear regression model with a non-linear regression model. The non-linear regression model should be used if the fit is significantly better. Open questions are how macropores affect chamber measurements and how optimization of chamber design can prevent this.

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