Nonlinear Regression Function Research Articles

The influence of breed, dietary energy and lysine on laying persistency and body composition of laying hens

The effect of dietary energy and lysine levels on laying persistency and body composition in brown and white hens was studied. Dietary treatments with 2 Metabolizable Energy levels (ME lay; constant or reduction over time) and 2 apparent fecal digestible Lys levels (AFD Lys; constant or reduction over time), were fed to Lohmann white or brown hens, from 17 to 75 wk of age, in a 2 × 2 × 2 factorial design. Data were subjected to mixed model analyses. The egg production curve was modeled using a non-linear regression function. White hens showed an improved laying persistency and a higher number of total eggs per hen compared to brown hens, indicated by a shorter peak production phase but a significant lower slope of decline after peak (P < 0.05). Similarly, hensfed a reduced instead of a constant ME Lay diet had a better laying persistency, indicated by a shorter peak production phase and a significant smaller slope of decline after peak (P < 0.05). This improved laying persistency was probably related to a higher ADFI and nutrient intake of hens fed the reduced ME Lay diets (P < 0.05). A segmented regression analysis showed reasonable correlation between egg mass production and ME Lay intake, with an R2 adjusted of 0.78 for the overall model. The egg mass production was not increased for intakes above 330 kcal of ME Lay intake for white hens and 324 kcal for brown hens. Limited effects of dietary treatments on body crude fat and crude protein were found. Both energy and protein requirement seemed to increase over time, indicated by higher voluntary nutrient intake and a reducing body crude fat after wk 43 in all treatments. The egg mass production correlated poorly with the AFD Lys intake, with an R2 of 0.22. In conclusion, laying persistency was mostly influenced by breed and dietary ME Lay level, but not dietary AFD Lys level.

Constructing and Validating Estimation Models for Individual-Tree Aboveground Biomass of Salix suchowensis in China

Biomass serves as a crucial indicator of plant productivity, and the development of biomass models has become an efficient way for estimating tree biomass production rapidly and accurately. This study aimed to develop a rapid and accurate model to estimate the individual aboveground biomass of Salix suchowensis. Growth parameters, including plant height (PH), ground diameter (GD), number of first branches (NFB), number of second branches (NSB) and aboveground fresh biomass weight (FW), were measured from 892 destructive sample trees. Correlation analysis indicated that GD had higher positive correlations with FW than PH, NFB and NSB. According to the biological features and field observations of S. suchowensis, the samples were classified into three categories: single-stemmed type, first-branched type and second-branched type. Based on the field measurement data, regression models were constructed separately between FW and each growth trait (PH, GD, NFB and NSB) using linear and nonlinear regression functions (linear, exponential and power). Then, multiple power regression and multiple linear regression were conducted to estimate the fresh biomass of three types of S. suchowensis. For the single-stemmed plant type, model M1 with GD as the single parameter had the highest adj R2, outperforming the other models. Among the 16 constructed biomass-estimating equations for the first-branched plant type, model M32 FW = 0.010371 × PH1.15862 × GD1.250581 × NFB0.190707 was found to have the best fit, with the highest coefficient of determination (adj R2 = 0.6627) and lowest Akaike Information Criterion (AIC = 5997.3081). When it comes to the second-branched plant type, the best-fitting equation was proved to be the multiple power model M43 with PH, GD, NFB and NSB as parameters, which had the highest adj R2 value and best-fitting effect. The stability and reliability of the models were confirmed by the F-test, repeated k-fold cross-validation and paired-sample t-tests. The models developed in this study could provide efficient tools for accurately estimating the total aboveground biomass for S. suchowensis at individual tree levels. The results of this study could also be useful for optimizing the economic productivity of shrub willow plantations.

Experimental characterisation and statistical modelling of woven carbon fibre weld conductors for electrical resistance welding of thermoplastic composites

Resistance welding of high-performance thermoplastic composites is a promising joining technique for the structural assembly of aerospace components. Knowledge of the weld conductor resistance as a function of its dimensions, as well as external boundary conditions such as contact preparation and pressure, can be used to scale welding parameters. This paper presents a comprehensive review on the weld conductor contact preparation, length, width and contact pressure dependent resistance with respect to the Toray 5HS T300JB carbon woven prepreg 281 gsm fibre architecture. The study is based on a 4-wire resistance measurement of the carbon fibre fabric weld conductors and was conducted to provide a solid basis for defining the weld conductor’s resistance, considering the dependence on length, width and contact pressure. The experimentally determined resistance values were approximated using linear and non-linear regression functions and combined into a general formulation with respect to the investigated carbon fibre fabric architecture. The least squares fit of experimental versus model data confirmed a very high model confidence. Thus, the model allows a simplified transfer of electrical properties for process pre-design and scaling considering weld conductors with the same fibre architecture.

Determination of the radii of coated and uncoated silicon AFM sharp tips using a height calibration standard grating and a nonlinear regression function.

AFM sharp tips are used to characterize nanostructures and quantify the mechanical properties of the materials in several areas of research. The analytical results can show unpredicted errors if we do not know the exact values of the AFM tip radius. There are many techniques of in situ measurements for determining the actual AFM tip radius, but they are limited to uncoated tips. This paper presents an alternative and simple method to determine the radii of coated tips and an uncoated tip. Pt-coated, Cr/Au-coated, and uncoated Si tips were used to scan a calibration standard grating in AFM contact mode with sub-nanonewton load to obtain the curved scan profile of the edge corner of the grating structure. The data points of the curved profile of each tip were fitted with a nonlinear regression function to estimate the curvature radius of the tip. The results show that the estimated radius of the coated tips is in the range of nominal values provided by the tip manufacturer, while the estimated radius of the uncoated Si tip is bigger than the nominal radius because of tip blunting during the scan. However, this method yields an accurate estimate of the tip radius with a low root mean squared error of the curve fitting results.

A robust class of nonlinear autoregressive models with regression function and dependent innovations using semiparametric kernel estimation

In this study, researchers examine a nonlinear autoregressive (NLAR) time-series model with regression function and dependent innovations in which the errors of the model follow the two-piece scale mixtures of normal (TP-SMN) distributions. Robustness and atypical forms of the proposed class of two-piece distributions along with the flexibility of the nonlinear autoregressive model develop desirable properties which can be applied to several types of datasets. The nonlinear regression function part of the autoregressive time-series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation maximization (EM)-type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset.

Effects of Temperature on the Developmental and Reproductive Biology of North American Bean Thrips, Caliothrips fasciatus (Pergande) (Thysanoptera: Thripidae: Panchaetothripinae).

North American bean thrips, Caliothrips fasciatus, native to California U.S., has been detected inside the navels of navel oranges exported from California for more than 120 years. Despite this long history of accidental movement into new areas, this thrips has failed to establish populations outside of its native range. The cold accumulation hypothesis postulates that increasing levels of cold stress experienced by thrips overwintering inside navels is compounded when harvested fruit is shipped under cold storage conditions. Consequently, the fitness of surviving thrips is compromised, which greatly diminishes invasion potential. At the time this study was conducted, the effects of temperature on C. fasciatus fitness were unknown. To address this shortcoming, the effects of nine fluctuating temperatures that averaged 8, 10, 15, 20, 25, 30, 32, 35, and 37 °C over a 24 h period on the developmental and reproductive biology of C. fasciatus were evaluated. One linear and five nonlinear regression functions were fit to egg-to-adult development rate data for parent and offspring thrips to characterize thermal performance curves. Estimates of minimum, optimal, and maximum temperature thresholds for development were in the ranges of -4.37-6.52 °C (i.e., Tmin), 31.19-32.52 °C (i.e., Topt), and 35.07-37.98 °C (i.e., Tmax), respectively. Degree day accumulation to complete development, estimated from linear regression, ranged 370.37-384.61. Average development times for eggs, first and second instar larvae, propupae, pupae, and adult longevity, and mean lifetime fecundity of females were significantly affected by temperature. These biological responses to temperature may provide insight into how this abiotic variable affects the invasion potential of C. fasciatus.

A Theoretical Nonlinear Regression Model of Rainfall Surface Flow Accumulation and Basin Features in Park-Scale Urban Green Spaces Based on LiDAR Data

Green infrastructure is imperative for efficiently mitigating flood disasters in urban areas. However, inadequate green space planning under rapid urbanization is a critical issue faced by most Chinese cities. Aimed at theoretically understanding the rainwater storage capacity and improvement potential of urban green spaces, a synthetic simulation model was developed to quantify rainfall surface flow accumulation (FA) based on the morphological factors of a flow basin: the area, circumference, maximum basin length, and stream length sum. This model consisted of applying the Urban Forest Effects-Hydrology model (UFORE-Hydro) to simulate the actual precipitation-to-surface runoff ratio through a procedure involving canopy interception, soil infiltration, and evaporation; additionally, a relatively accurate multiple flow direction-maximum downslope (MFD-md) algorithm was applied to distribute the surface flow in a highly realistic manner, and a self-built “extraction algorithm” extracted the surface runoff corresponding to each studied basin alongside four fundamental morphological parameters. The various nonlinear regression functions were assessed from both univariable and multivariable perspectives. We determined that the Gompertz function was optimal for predicting the theoretical quantification of surface FA according to the morphological features of any given basin. This article provides parametric vertical design guidance for improving the rainwater storage capacities of urban green spaces.

Stereoscopic image discomfort prediction using dual-stream multi-level interactive network

Existing stereoscopic image discomfort prediction methods may fail to work well because they are difficult to extract discomfort features from stereoscopic image’s statistical information since the mechanism of human binocular vision is very complex. In this work, we propose a dual-stream multi-level interactive network that is completely end-to-end trainable for stereoscopic image discomfort prediction. This method first extracts multi-level fusion and difference features from stereoscopic images through a multi-level interaction network. Then, the low-, medium- and high-level feature maps are concatenated to simulate the complicated visual interaction mechanism of the human visual system (HVS). Finally, two fully connected layers are used as a non-linear regression function that maps the feature vectors to stereoscopic image discomfort scores. Extensive experiments demonstrate that our approach performs favorably against the existing prediction models on the IEEE-SA dataset and NBU-S3D dataset.

Modelling Moisture Sorption Isotherms of Superabsorbent Polymer Fabric for Desiccant Drying of Crops

Desiccants are important in the drying of temperature-sensitive grains such as seeds for planting. Superabsorbent polymers (SAPs) have previously been identified for possible application in the drying of crops. Applying the gravimetric technique to measure the sorption isotherms and the effectiveness of the desiccant in crop drying was determined at temperatures 20, 25, 30, 35, 40, 45, 50, and 55°C. Using R statistical software, eleven sorption isotherm models were fitted to the experimental data using the nonlinear regression functions. The coefficients of each model were obtained. The modified Freundlich, modified Henderson, and modified Oswin models best predicted the experimental data for the study temperature range. Using symbolic regression and nonlinear regression in R software, four mathematical models were obtained. R software codes were assembled for the analysis of sorption isotherm models. Compared to the existing models, the developed models were found to give a more statistically accurate association between the temperature, moisture content of SAP fabric, and relative humidity.

Spatial localization characteristics impact research at value determining of real estate objects situated in small settlements

The article behaves to the property economic measurements implementation using the Comparative Sales independent valuation approach. On example from the real commercial real estate evaluation practice the main methodological principles of valuation object spatial localization characteristics adjustment are considered. According to the described methodology, localization adjustment coefficient is determined by calculation method on the basis of market data cross-correlation regressive analysis. A basic hypothesis is a statement that the relation of valuation object single unit value index to the same of comparable object is determined by its model values relation in the mathematical model of statistical relationship between object single unit value index and its three settlements characteristics: population number; distance to the regional center; area (territory within the settlement boundaries). The research is grounded on mathematical simulation and mathematical statistic quantitative methods. The methodology of adjustment coefficients on investigated price-forming factors definition is based on nonlinear cross-correlation regressive analysis of market data research. This mathematical model is experimentally set by local market data research for the exactly similar real estate objects on the valuation date. It is set that there is observed different statistical relationship level between some of objects price-forming factors and its single square value indexes. The closest statistical relationship exists between settlements population number and single indicator of similar property situated in other compared settlements. It is shown that taking into account some recommended braking coefficients for regressive curve, are published in professional literature, is inadvisable, because it increases the result error is got. Certainly the regression curve characteristics of object spatial localization price-forming factors must be taken into account at adjustment coefficient determination procedure. It is well-proven that methodically correct result of object localization adjustment procedure implementation can be provided only in the case of local market situation research data applying, with determination of the nonlinear regression function characteristics for statistical dependence of single square value index from the object settlements population number. Research is described gives an opportunity to decrease evaluation result uncertainty through the use of new offered approach to mathematical model characteristics definition. The main result of researches described is a possibility to obtain appraising/valuation results with the higher reliability and better accuracy. Researches results are the objective confirmation of the fact, that nowadays methodical base of independent valuation is not able to provide the higher level of this class evaluation objects accuracy results. It does not depend only from an individual appraiser or concrete evaluation company, but, firstly, from unreliable arbitrarily chosen by appraisers adjustments - that usually are "expertly" determined, based on appraiser's own ideas about the dependence of real estate prices on the settlements characteristics. This elementary way of taking these characteristics into account may be a source of result additional errors and its uncertainty level increasing. Future investigations in this direction may deals with the consideration and analysis of other types nonlinear functions application possibilities, that is approximate the regression curve of statistical interdependence between the object single value index and its spatial localization characteristics. The quantitative indexes of absolute and relative methodological errors also may be determined and analyzed in detail in future researches. The importance of those researches for the further development of the independent valuation metrological-information paradigm are confirmed. Practical recommendations for the evaluation results accuracy and reliability increasing are formulated.

D-Optimal Designs for the Mitscherlich Non-Linear Regression Function

Mitscherlich's function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. Optimal designs for this function have been constructed only for normally distributed responses with homoscedastic variances. In this paper, we construct D-optimal designs for discrete and continuous responses having their distribution function in the exponential family. We also demonstrate the connection with D-optimality for weighted linear regression.

Prediction of the Height of Fracturing via Gene Expression Programming in Australian Longwall Panels: A Comparative Study

The caving and subsidence developments above a longwall panel usually result in fractures of the overburden, which decrease the strength of the rock mass and its function. The height of fracturing (HoF) includes the caved and continuous fractured zones affected by a high degree of bending. Among the various empirical models, Ditton’s geometry and geology models are widely used in Australian coalfields. The application of genetic programming (GP) and gene expression programming (GEP) in longwall mining is entirely new and original. This work uses a GEP method in order to predict HoF. The model variables, including the panel width (W), cover depth (H), mining height (T), unit thickness (t), and its distance from the extracted seam (y), are selected via the dimensional analysis and Buckingham’s P-theorem. A dataset involving 31 longwall panels is used to present a new nonlinear regression function. The statistical estimators, including the coefficient of determination (R2), the average error (AE), the mean absolute percentage error (MAPE), and the root mean square error (RMSE), are used to compare the performance of the discussed models. The R2 value for the GEP model (99%) is considerably higher than the corresponding values of Ditton’s geometry (61%) and geology (81%) models. Moreover, the maximum values of the statistical error estimators (AE, MAPE, and RMSE) for the GEP model are 12%, 14%, and 16%, respectively, of the corresponding values of Ditton’s models.

Three-factor mean reverting Ornstein-Uhlenbeck process with stochastic drift term innovations: Nonlinear autoregressive approach with dependent error

This paper introduces a novel approach, withen the context of energy market, by employing a three-factor mean reverting Ornstein-Uhlenbeck process with a stochastic nonlinear autoregressive drift term having a dependent error. Initially the unique solvability for the given nonlinear system is investigated. Then, to estimate the nonlinear regression function, a semiparametric method, based on the conditional least square estimator for the parametric approach, and the nonparametric kernel method for autoregressive modification estimation have been presented . A maximum likelihood estimator has been used for parameter estimation of the Ornstein-Uhlenbeck process. Finally, some numerical simulations and real data studies have been provided to support the main conclusions of the study.

Optimization of Grouting Material Mixture Ratio Based on Multi-Objective Optimization and Multi-Attribute Decision-Making

As a solid waste produced by coal combustion, fly ash will cause serious environmental pollution. However, it can be considered as a sustainable and renewable resource to replace partial cement in grouting materials. Fly ash grouting materials re-cement the broken rock mass and improve the mechanical properties of the original structure. It can reinforce the broken surrounding rock of mine roadway. The utilization of fly ash also reduces environmental pollution. Therefore, this paper establishes a new material mixture ratio optimization model to meet the requirement of material property through combining the methods of experimental design and numerical analysis. Based on the Box–Behnken design with 3 factors and 3 levels, a mathematical model is constructed to fit the nonlinear multiple regression functions between material properties and raw materials ratios. The influence of raw materials is analyzed on material properties (the material’s 7-day uniaxial compressive strength, initial setting time, and slurry viscosity). Then, 80 Pareto solutions are obtained through NASG-II algorithm which takes the regression functions as the objective functions for multi-objective optimization of the grouting material ratio. Finally, the best ratio solution of water-cement ratio—0.71, silica fume content—1.73%, and sodium silicate content—2.61% is obtained through the NNRP-TOPSIS method.

Mathematical modeling of egg production curve in a multivariety endangered hen breed

This study aimed to compare the egg laying performance of the four varieties (white, franciscan, black, and partridge) of a Spanish endangered Utrerana hen breed. A flock of 60 Utrerana hens (15 hen/variety) were individually housed to enable daily egg traceability. Compartmental, Gamma, linear hyperbolic, logistic curvilinear, McNally, Narushin-Takma, and quadratic logarithmic nonlinear regression functions were fitted. Goodness-of-fit (coefficient of determination (R2)) and flexibility criteria (mean squared error (MSE), Akaike information criteria (AIC), corrected Akaike information criteria (AICc), Bayesian information criteria (BIC)) were evaluated to identify the best-fitting function to model for egg production curve. Best-fitting values were reported by the six-parameter Narushin-Takma model for white (R2 = 0.828), franciscan (R2 = 0.888), and black (R2 = 0.899) varieties. By contrast, quadratic logarithmic was reported to be the best-fitting model for partridge Utrerana hen egg production curve (R2 = 0.917). The characterization of the laying cycle of endangered avian breeds varieties permits tailoring productive strategies which may ensure animal welfare at the same that they boost economic potentialities, enabling the productive model to better simultaneously fulfill animal needs and human demands. As a result, breed diversity may act as the motor element to improve economic profitability, but in turn may also ensure the conservation of the local genetic resources from which desirable products, such as the egg, are obtained.

A Nonparametric Lack-of-Fit Test of Constant Regression in the Presence of Heteroscedastic Variances

We consider a k-nearest neighbor-based nonparametric lack-of-fit test of constant regression in presence of heteroscedastic variances. The asymptotic distribution of the test statistic is derived under the null and local alternatives for a fixed number of nearest neighbors. Advantages of our test compared to classical methods include: (1) The response variable can be discrete or continuous regardless of whether the conditional distribution is symmetric or not and can have variations depending on the predictor. This allows our test to have broad applicability to data from many practical fields; (2) this approach does not need nonlinear regression function estimation that often affects the power for moderate sample sizes; (3) our test statistic achieves the parametric standardizing rate, which gives more power than smoothing-based nonparametric methods for moderate sample sizes. Our numerical simulation shows that the proposed test is powerful and has noticeably better performance than some well known tests when the data were generated from high frequency alternatives or binary data. The test is illustrated with an application to gene expression data and an assessment of Richards growth curve fit to COVID-19 data.

Colombian Women’s Life Patterns: A Multivariate Density Regression Approach

Women in Colombia face difficulties related to the patriarchal traits of their societies and well-known conflict afflicting the country since 1948. In this critical context, our aim is to study the relationship between baseline socio-demographic factors and variables associated to fertility, partnership patterns, and work activity. To best exploit the explanatory structure, we propose a Bayesian multivariate density regression model, which can accommodate mixed responses with censored, constrained, and binary traits. The flexible nature of the models allows for nonlinear regression functions and non-standard features in the errors, such as asymmetry or multi-modality. The model has interpretable covariate-dependent weights constructed through normalization, allowing for combinations of categorical and continuous covariates. Computational difficulties for inference are overcome through an adaptive truncation algorithm combining adaptive Metropolis-Hastings and sequential Monte Carlo to create a sequence of automatically truncated posterior mixtures. For our study on Colombian women’s life patterns, a variety of quantities are visualised and described, and in particular, our findings highlight the detrimental impact of family violence on women’s choices and behaviors.

Türkiye'de 17 Mart ile 12 Temmuz 2020 Arasında COVID-19 Vakaları Kullanılarak Büyüme Modellerinin Belirlenmesi Üzerine Bir Çalışma: Kesitsel Çalışma

Objective: We use the most frequently used growth functions in the literature for estimating Turkey's cumulative number of confirmed coronavirus disease-2019 (COVID-19) cases. We analyze Brody, Bertalanffy, Logistic, Generalized Logistic, Gompertz, Richards, Negative Exponential, Stevens, and Tanaka models for determining the appropriate model. Material and Methods: The number of cases of COVID-19 in Turkey between March 17, 2020 and July 12, 2020 were included in the study. The data used in the study were obtained from Johns Hopkins University. We used the most frequently used Non-linear growth models in the literature for estimating Turkey's cumulative number of confirmed COVID-19 cases. Matlab software was used to estimate the parameters in the models studied. non-linear least squares regression function is used in Matlab software. Results: According to the estimation results, the best fitting model is the Richards model in terms of both the mean squared error and R2 (coefficient of determination). Conclusion: We recommend to use the Richards model in modeling the cumulative COVID-19 cases. For estimating the future cases, it will be appropriate to use the Richards model. In addition, estimates of the number of daily cases obtained from the Richards model are not compatible with the actual number of daily cases. This may occur because estimations on these growth models can sometimes lead to erroneous results.

Nonlinear yield models for young Tectona grandis L. f. stands in Nnamdi Azikiwe University Awka, Southeastern Nigeria

Yield models are very important to forest management, especially for site quality assessment, subsequent inventories, timber valuation and assessment of stand growth. This study developed yield models for the young Tectona grandis stands in Nnamdi Azikiwe University Awka, Southeastern Nigeria. These models were necessary to the guide forest managers in timber valuation as well as monitoring growth of the stand. Data for this study was collected through complete enumeration method, tree height and stem diameters of the 295 Teak stands were measured. Non-destructive method (Newton’s formula) was used in computing individual tree volumes. The tree growth variables data were subjected to descriptive statistics and used for fitting five nonlinear regression functions. The mean stem height, diameter at breast height and volume were 10.6 m, 8.9 cm, 0.032 m3, respectively. Out of the five yield equations fitted; the generalized combined variable model had the best predictive ability; with the lowest root mean square error (0.0084 m3) and Akaike information criterion (-2809). Therefore, the generalized combined variable model was recommended for yield estimation of Tectona grandis.

Profitability and Resource Use Efficiency of Polycarp Production in Morang, Nepal

The study was designed to portray the resource use efficiency of polycarp production in Morang district of Nepal during December 2017 to April 2018. Total of 30 commercial and 30 subsistence farmers were selected for primary data collection. Cobb-Douglas non-linear regression function was used to determine inputs that affect productivity. Empirical results illustrated the enterprise to be profitable as indicated by Benefit Cost Ratio, 1.87 in commercial and 1.33 in subsistence farms. The income of commercial farms was significantly higher (NRs. 76.94/kg) than subsistent farms (p&lt;0.01). Estimates suggested feed and labor to be reduced; proper use of lime, fertilizer, other cost and pond rent to be increased. Therefore, the fishery enterprise is in the stage of higher potentiality to increase its production in the study area.