Prediction intervals for non-linear projection to latent structures regression models

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

Download Full-text

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

Mathematics ◽

10.3390/math9040299 ◽

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.

Download Full-text

Quality-Relevant Monitoring and Diagnosis with Dynamic Concurrent Projection to Latent Structures

IFAC Proceedings Volumes ◽

10.3182/20140824-6-za-1003.02329 ◽

2014 ◽

Vol 47 (3) ◽

pp. 2740-2745 ◽

Cited By ~ 5

Author(s):

Qiang Liu ◽

S. Joe Qin ◽

Tianyou Chai

Keyword(s):

Projection To Latent Structures ◽

Monitoring And Diagnosis ◽

Latent Structures

Download Full-text

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

Sensors ◽

10.3390/s22010130 ◽

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.

Download Full-text

Forecasting stock returns on the Amman Stock Exchange: Do neural networks outperform linear regressions?

Investment Management and Financial Innovations ◽

10.21511/imfi.18(4).2021.24 ◽

2021 ◽

Vol 18 (4) ◽

pp. 280-296

Author(s):

Abdel Razzaq Al Rababa’a ◽

Zaid Saidat ◽

Raed Hendawi

Keyword(s):

Stock Market ◽

Regression Models ◽

Linear Models ◽

Stock Exchange ◽

Market Returns ◽

Stock Market Returns ◽

Statistical Measures ◽

Amman Stock Exchange ◽

Non Linear ◽

Ann Models

Different models have been used in the finance literature to predict the stock market returns. However, it remains an open question whether non-linear models can outperform linear models while providing accurate predictions for future returns. This study examines the prediction of the non-linear artificial neural network (ANN) models against the baseline linear regression models. This study aims specifically to compare the prediction performance of regression models with different specifications and static and dynamic ANN models. Thus, the analysis was conducted on a growing market, namely the Amman Stock Exchange. The results show that the trading volume and interest rates on loans tend to explain the monthly returns the most, compared to other predictors in the regressions. Moreover, incorporating more variables is not found to help in explaining the fluctuations in the stock market returns. More importantly, using the root mean square error (RMSE), as well as the mean absolute error statistical measures, the static ANN becomes the most preferred model for forecasting. The associated forecasting errors from these metrics become equal to 0.0021 and 0.0005, respectively. Lastly, the analysis conducted with the dynamic ANN model produced the highest RMSE value of 0.0067 since November 2018 following the amendment to the Jordanian income tax law. The same observation is also seen since the emerging of the COVID-19 outbreak (RMSE = 0.0042).

Download Full-text