Analysis Of Nonlinear Regression Models Research Articles

On computational analysis of nonlinear regression models addressing heteroscedasticity and autocorrelation issues: An application to COVID-19 data

This paper develops a method for nonlinear regression models estimation that is robust to heteroscedasticity and autocorrelation of errors. Using nonlinear least squares estimation, four popular growth models (Exponential, Gompertz, Verhulst, and Weibull) were computed. Some assumptions on the errors of these models (independence, normality, and homoscedasticity) being violated, the estimates are improved by modeling the residuals using the ETS method. For an application purpose, this approach has been used to predict the daily cumulative number of novel coronavirus (COVID-19) cases in Africa for the study period, from March 13, 2020, to June 26, 2021. The comparison of the proposed model to the competitors was done using statistical metrics such as MAPE, MAE, RMSE, AIC, BIC, and AICc. The findings revealed that the modified Gompertz model is the most accurate in forecasting the total number of COVID-19 cases in Africa. Moreover, the developed approach will be useful for researchers and policymakers for predicting purpose and for better decision making in different fields of its applications.

A statistical analysis of nonlinear regression models for different treatments for layers

As the cost of research increases, mathematical models become valuable tools to answer research questions. A major application of mathematical modeling is accurate estimation of production performance, growth, and feed consumption for poultry research and production. There are many ways that a given data set can be analyzed, and different models have been proposed to fit those curves. To explore the models available, data were investigated from a study on the effects of a series of balanced dietary protein levels on egg production and egg quality parameters in lying hens from 18 to 74 wk of age. Forty eight pullets were assigned to each of 3 different protein levels. The results clearly demonstrated that balanced dietary protein level was the limiting factor for body weight (BW), average daily feed intake (ADFI), egg weight, and egg production. To test differences of fitted curves, the sum of squared reduction test is used. Using a unique data set with data from individual hens, 6 commonly used models were fitted to hen performance technical data. The resulting statistical inferences from using individual and pooled data were compared. There are only differences in using individual or grouped data in fitting nonlinear models to laying hen response data. For the most important response variables, hen-day egg production, and feed intake, predicted responses are within 0.12 and 0.65%, respectively, throughout the production cycle.

FORECASTING PRICES IN THE RENTAL HOUSING MARKET WITH MACHINE LEARNING METHODS

The study of pricing factors in the market of the short-term rental has been done. Airbnb was chosen as the object of the study; it is a platform for accommodation, search, and rental around the world. At the beginning of 2021, the company offers 7 million homes from more than 220 countries. The Data Science methods play a significant role in the company's success. One of the key algorithms of the company is the pricing algorithm. Using the "Price Recommendations" feature, the homeowner can analyze which dates are most likely to be booked at the current price and which are not, it helps form a favorable offer. The system calculates the recommended cost of housing based on hundreds of parameters, some of which are easy to recognize, but there are less obvious factors that can also affect demand. The paper proposes an algorithm for identifying implicit pricing factors in the short-term rental market using machine learning methods, which includes: 1) data mining and data preparation; 2) building and analysis of linear regression models; 3) building and analysis of nonlinear regression models. The study was based on ads from the Airbnb site in Washington and New York using scripts developed in Python. The following models are built and analyzed: simple linear regression, multiple linear regression, polynomial regression, decision trees, random forest, and boosting. The results of the study showed that the most important factors are accommodates, cleaning_fee, room_type, bedrooms. But based on the model evaluation criteria, they cannot be used for implementation: linear models are of low quality, while the random forest, boosting, and trees are overfitted. Still the results can be used in conducting business analysis.

Random norming aids analysis of non-linear regression models with sequential informative dose selection

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies between data from the two stages. When the maximum likelihood estimator (MLE) is used under nonlinear regression models with independent normal errors in a pilot study where the first stage sample size is fixed, and the second stage sample size is large, the Fisher information fails to normalize the estimator adequately asymptotically, because of dependencies. In this situation, three alternative random information measures are presented and are shown to provide better normalization of the MLE asymptotically. The performance of random information measures is investigated in simulation studies, and the results suggest that the observed information performs best when the sample size is small.

Applying Monte Carlo methods to analysis of nonlinear regression models

This paper presents a criterion, called coefficient stability, for determining errors in the coefficients of nonlinear regression models describing inexact data. A method for the estimation of coefficient stability is also described. The criterion is illustrated by a computational experiment with data obtained by measuring the refractive index as a function of the wavelength in the 400–1000 nm band for a transparent polymer. The convergence of the criterion to a known analytical solution for the case of linear regression is also studied.

О возможности применения методов Монте-Карло в анализе нелинейных регрессионных моделей

О возможности применения методов Монте-Карло в анализе нелинейных регрессионных моделей

Large Sample Behavior in Bayesian Analysis of Nonlinear Regression Models

In this paper we examine the large sample behavior of Bayesian posterior distributions in a nonlinear regression model. In particular, we seek Bayesian forms of consistency for parameter estimation problems. We derive here convergence and rate of convergence results for independent, identically distributed error models. The rate of convergence results are based on large deviation ideas.

Nonlinear Regression Analysis and Its Applications

Wiley-Interscience Paperback Series Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. The authors have put together an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models ...highly recommend[ed] ...for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression -Technometrics [This book] provides a good balance of relevant theory and application with many examples ...[and it] provides the most balanced approach to theory and application appropriate for a first course in nonlinear regression modeling for graduate statistics students. -Mathematical Reviews [This book] joins a distinguished list of publications with a reputation for balancing technical rigor with readability, and theory with application. [It] upholds tradition ...[and is] a worthwhile reference for the marketing researcher with a serious interest in linear models. -Journal of Marketing Research This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares. authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. book also includes pseudocode for computing algorithms.

Correction: Marginal Curvatures and Their Usefulness in the Analysis of Nonlinear Regression Models

Correction: Marginal Curvatures and Their Usefulness in the Analysis of Nonlinear Regression Models

Marginal Curvatures and Their Usefulness in the Analysis of Nonlinear Regression Models

Abstract Interval estimation for individual parameters in nonlinear regression is examined in relation to curvature of the solution locus. Criteria are developed to define severe curvature and distinguish cases in which linear methods may be used from those in which parameter transformations are necessary. A formula for improving the linear approximation in cases of relatively mild curvature is proposed. For example, suppose that interest is focused on one specific parameter, θ j from among θ = {θ1 θ2, …, θ p } in a nonlinear regression model. A crude approach to setting 95% confidence limits to θ j might proceed as follows: First calculate the standard error of the estimate as the square root of its asymptotic variance. Then call the confidence limits. In this article, higher-order correction terms Γ and β are proposed that enable us to develop a power series expansion for the confidence limits, as and respectively. Here denotes some estimate of σ2, the variance of a single observation.

Marginal Curvatures and Their Usefulness in the Analysis of Nonlinear Regression Models

Abstract Interval estimation for individual parameters in nonlinear regression is examined in relation to curvature of the solution locus. Criteria are developed to define severe curvature and distinguish cases in which linear methods may be used from those in which parameter transformations are necessary. A formula for improving the linear approximation in cases of relatively mild curvature is proposed. For example, suppose that interest is focused on one specific parameter, θ j from among θ = {θ1 θ2, …, θ p } in a nonlinear regression model. A crude approach to setting 95% confidence limits to θ j might proceed as follows: First calculate the standard error of the estimate as the square root of its asymptotic variance. Then call the confidence limits. In this article, higher-order correction terms Γ and β are proposed that enable us to develop a power series expansion for the confidence limits, as and respectively. Here denotes some estimate of σ2, the variance of a single observation.

Analysis of nonlinear regression models with cubic spline functions: a systematic approach

Questa nota intende dare alcuni criteri generali per costruire stime di parametri da funzioni curve cubiche. Tali funzioni sono particolarmente utili nell'analisi di modelli non lineari per le loro proprieta di convergenza (Ahlberg e altri, 1967). Illustra quindi l'effetto dei coefficienti di correlazione multipla sulle proprieta delle stime quando il modello lineare sottinteso e una funzione esponenziale a tre parametri. Esempi numerici sono gia stati pubblicati dall'Autore (1982, 1984).

Merging Spline Approximations with Analysis of Nonlinear Regression Models

AbstractThe paper outlines a method of analysis of intricically non‐linear regression functions. The nonlinear model is first approximated by a cubic spline function. Thereafter, the standard methods of analysis in linear models are applied to obtain estimates and test statistics.

Reduction of dimensionality in Bayesian nonlinear regression with a pharmacokinetic application

Application of Bayes's theorem to the analysis of nonlinear regression models is limited by numerical problems associated with calculation of integrals of functions of several variables. For k-parameter models that are linear in l of the parameters, a dimension-reduction procedure is described for factoring the posterior distribution into the product of a multivariate normal density and a function of k- l nonlinear parameters. Integrals can then be calculated with ( k- l)-dimensional numerical integration. A four-parameter, two-compartment pharmacokinetic model of lidocaine disposition is analyzed using a change of variables in order to obtain a model that is linear in two parameters. It is shown that a Bayesian analysis, with reduction of dimensionality, applied to this model produces appropriate results with reasonable CPU-time requirements.