scholarly journals Modelling the growth of rearing cattle

2021 ◽  
Author(s):  
Hanna Unterauer ◽  
Norbert Brunner ◽  
Manfred Kühleitner
Keyword(s):  
Goodness Of Fit ◽  
Linear Growth ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Information Criterion ◽  
Squared Error ◽  
Akaike Criterion ◽  
Linear Growth Model ◽  
Bp Model ◽  
Scientific Growth

Scientific growth literature often uses the models of Brody, Gompertz, Verhulst, and von Bertalanffy. The versatile five-parameter Bertalanffy-Pütter (BP) model generalizes them. Using the least-squares method, we fitted the BP model to mass-at-age data of 161 calves, cows, bulls, and oxen of cattle breeds that are common in Austria and Southern Germany. We used three measures to assess the goodness of fit: R-squared, normalized root-mean squared error, and the Akaike information criterion together with a correction for sample size. Although the BP model improved the fit of the linear growth model considerably in terms of R-squared, the better fit did not, in general, justify the use of its additional parameters, because most of the data had a non-sigmoidal character. In terms of the Akaike criterion, we could identify only a small core of data (15%) where sigmoidal models were indispensable.    

scholarly journals Upgrading Model Selection Criteria with Goodness of Fit Tests for Practical Applications

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 447
Author(s):  
Riccardo Rossi ◽  
Andrea Murari ◽  
Pasquale Gaudio ◽  
Michela Gelfusa
Keyword(s):  
Model Selection ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Information Criterion ◽  
Original Form ◽  
Residual Distribution ◽  
Practical Applications ◽  
Goodness Of Fit Tests ◽  
Squared Error ◽  
The Mean

The Bayesian information criterion (BIC), the Akaike information criterion (AIC), and some other indicators derived from them are widely used for model selection. In their original form, they contain the likelihood of the data given the models. Unfortunately, in many applications, it is practically impossible to calculate the likelihood, and, therefore, the criteria have been reformulated in terms of descriptive statistics of the residual distribution: the variance and the mean-squared error of the residuals. These alternative versions are strictly valid only in the presence of additive noise of Gaussian distribution, not a completely satisfactory assumption in many applications in science and engineering. Moreover, the variance and the mean-squared error are quite crude statistics of the residual distributions. More sophisticated statistical indicators, capable of better quantifying how close the residual distribution is to the noise, can be profitably used. In particular, specific goodness of fit tests have been included in the expressions of the traditional criteria and have proved to be very effective in improving their discriminating capability. These improved performances have been demonstrated with a systematic series of simulations using synthetic data for various classes of functions and different noise statistics.

scholarly journals Comparison of different lactation curve models in Holstein cows raised on a farm in the south-eastern Anatolia region

2008 ◽  
Vol 51 (4) ◽  
pp. 329-337
Author(s):  
Ö. Koçak ◽  
B. Ekiz
Keyword(s):  
Milk Yield ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Exponential Model ◽  
Eastern Anatolia ◽  
Mean Squared Errors ◽  
Squared Error ◽  
Lactation Curve ◽  
Daily Milk Yield ◽  
Daily Milk

Abstract. The objective of this study was to compare the goodness of fit of seven mathematical models (including the gamma function, the exponential model, the mixed log model, the inverse quadratic polynomial model and their various modifications) on daily milk yield records. The criteria used to compare models were mean R2, root mean squared errors (RMSE) and difference between actual and predicted lactation milk yields. The effect of lactation number on curve parameters was significant for models with three parameters. Third lactation cows had the highest intercept post-calving, greatest incline between calving and peak milk yield and greatest decline between peak milk yield and end of lactation. Latest peak production occurred in first lactation for all models, while third lactation cows had the earliest day of peak production. The R2 values ranged between 0.590 and 0.650 for first lactation, between 0.703 and 0.773 for second lactation and between 0.686 and 0.824 for third lactation, depending on the model fitted. The root mean squared error values of different models varied between 1.748 kg and 2.556 kg for first parity cows, between 2.133 kg and 3.284 kg for second parity cows and between 2.342 kg and 7.898 kg for third parity cows. Lactation milk yield deviations of Ali and Schaeffer, Wilmink and Guo and Swalve Models were close to zero for all lactations. Ali and Schaeffer Model had the highest R2 for all lactations and also yielded smallest RMSE and actual and predicted lactation milk yield differences. Wilmink and Guo and Swalve Models gave better fit than other three parameter models.

scholarly journals Method to generate growth and degrowth models obtained from differential equations applied to agrarian sciences

2018 ◽  
Vol 39 (6) ◽  
pp. 2659 ◽  
Author(s):  
André Luiz Pinto dos Santos ◽  
Guilherme Rocha Moreira ◽  
Cicero Carlos Ramos de Brito ◽  
Frank Gomes-Silva ◽  
Maria Lindomárcia Leonardo da Costa ◽  
...  
Keyword(s):  
Differential Equations ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Growth Curves ◽  
Information Criterion ◽  
Coefficient Of Determination ◽  
Absolute Deviation ◽  
Marquardt Algorithm ◽  
Maturation Rate ◽  
Biological Interpretation

This study aims to propose a method to generate growth and degrowth models using differential equations as well as to present a model based on the method proposed, compare it with the classic linear mathematical models Logistic, Von Bertalanffy, Brody, Gompertz, and Richards, and identify the one that best represents the mean growth curve. To that end, data on Undefined Breed (UB) goats and Santa Inês sheep from the works of Cavalcante et al. (2013) and Sarmento et al. (2006a), respectively, were used. Goodness-of-fit was measured using residual mean squares (RMS), Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (MAD), and adjusted coefficient of determination . The models’ parameters (?, weight at adulthood; ?, an integration constant; ?, shape parameter with no biological interpretation; k, maturation rate; and m, inflection point) were estimated by the least squares method using Levenberg-Marquardt algorithm on the software IBM SPSS Statistics 1.0. It was observed that the proposed model was superior to the others to study the growth curves of goats and sheep according to the methodology and conditions under which the present study was carried out.

scholarly journals Correcting the Bias of the Root Mean Squared Error of Approximation under Missing Data

2018 ◽  
Author(s):  
Cailey Elizabeth Fitzgerald ◽  
Ryne Estabrook ◽  
Daniel Patrick Martin ◽  
Andreas Markus Brandmaier ◽  
Timo von Oertzen
Keyword(s):  
Missing Data ◽  
Structural Equation ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Equation Modeling ◽  
Fit Indices ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Acceptable Model ◽  
Downward Bias

Missing data are ubiquitous in both small and large datasets. Missing data may come about as a result of coding or computer error, participant absences, or it may be intentional, as in planned missing designs. We discuss missing data as it relates to goodness-of-fit indices in Structural Equation Modeling (SEM), specifically the effects of missing data on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. This results in an RMSEA which is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.

scholarly journals A hydrological model skill score and revised R-squared

2021 ◽  
Author(s):  
Charles Onyutha
Keyword(s):  
Mathematical Modeling ◽  
Goodness Of Fit ◽  
Hydrological Model ◽  
Mean Squared Error ◽  
Skill Score ◽  
Coefficient Of Determination ◽  
Model Skill ◽  
Squared Error ◽  
Quality Coefficient ◽  
Correlation Term

Abstract Despite the advances in methods of statistical and mathematical modeling, there is considerable lack of focus on improving how to judge models’ quality. Coefficient of determination (R2) is arguably the most widely applied ‘goodness-of-fit’ metric in modelling and prediction of environmental systems. However, known issues of R2 are that it: (i) can be low and high for an accurate and imperfect model, respectively; (ii) yields the same value when we regress observed on modelled series and vice versa; and (iii) does not quantify a model's bias (B). A new model skill score E and revised R-squared (RRS) are presented to combine correlation, term B and capacity to capture variability. Differences between E and RRS lie in the forms of correlation and the term B used for each metric. Acceptability of E and RRS was demonstrated through comparison of results from a large number of hydrological simulations. By applying E and RRS, the modeller can diagnostically identify and expose systematic issues behind model optimizations based on other ‘goodness-of-fits’ such as Nash–Sutcliffe efficiency (NSE) and mean squared error. Unlike NSE, which varies from −∞ to 1, E and RRS occur over the range 0–1. MATLAB codes for computing E and RRS are provided.

scholarly journals On the Use of Entropy to Improve Model Selection Criteria

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 394 ◽  
Author(s):  
Andrea Murari ◽  
Emmanuele Peluso ◽  
Francesco Cianfrani ◽  
Pasquale Gaudio ◽  
Michele Lungaroni
Keyword(s):  
Model Selection ◽  
Shannon Entropy ◽  
Selection Criteria ◽  
Mean Squared Error ◽  
Geodesic Distance ◽  
Information Criterion ◽  
Residual Distribution ◽  
Model Selection Criteria ◽  
Synthetic Indicators ◽  
Squared Error

The most widely used forms of model selection criteria, the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), are expressed in terms of synthetic indicators of the residual distribution: the variance and the mean-squared error of the residuals respectively. In many applications in science, the noise affecting the data can be expected to have a Gaussian distribution. Therefore, at the same level of variance and mean-squared error, models, whose residuals are more uniformly distributed, should be favoured. The degree of uniformity of the residuals can be quantified by the Shannon entropy. Including the Shannon entropy in the BIC and AIC expressions improves significantly these criteria. The better performances have been demonstrated empirically with a series of simulations for various classes of functions and for different levels and statistics of the noise. In presence of outliers, a better treatment of the errors, using the Geodesic Distance, has proved essential.

scholarly journals Point Process Models for the Spread of Coccidioidomycosis in California

2021 ◽  
Vol 13 (2) ◽  
pp. 558-570
Author(s):  
Jiajia Wang ◽  
Ryan J. Harrigan ◽  
Frederic P. Schoenberg
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
United States ◽  
Point Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Process Models ◽  
Squared Error ◽  
Point Process Models

Coccidioidomycosis is an infectious disease of humans and other mammals that has seen a recent increase in occurrence in the southwestern United States, particularly in California. A rise in cases and risk to public health can serve as the impetus to apply newly developed methods that can quickly and accurately predict future caseloads. The recursive and Hawkes point process models with various triggering functions were fit to the data and their goodness of fit evaluated and compared. Although the point process models were largely similar in their fit to the data, the recursive point process model offered a slightly superior fit. We explored forecasting the spread of coccidioidomycosis in California from December 2002 to December 2017 using this recursive model, and we separated the training and testing portions of the data and achieved a root mean squared error of just 3.62 cases/week.

scholarly journals Correcting the bias of the Root Mean Squared Error of Approximation under missing data

Methodology ◽  
2021 ◽  
Vol 17 (3) ◽  
pp. 189-204
Author(s):  
Cailey E. Fitzgerald ◽  
Ryne Estabrook ◽  
Daniel P. Martin ◽  
Andreas M. Brandmaier ◽  
Timo von Oertzen
Keyword(s):  
Missing Data ◽  
Structural Equation ◽  
Goodness Of Fit ◽  
Missing Values ◽  
Mean Squared Error ◽  
Psychological Research ◽  
Equation Modeling ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Downward Bias

Missing data are ubiquitous in psychological research. They may come about as an unwanted result of coding or computer error, participants' non-response or absence, or missing values may be intentional, as in planned missing designs. We discuss the effects of missing data on χ²-based goodness-of-fit indices in Structural Equation Modeling (SEM), specifically on the Root Mean Squared Error of Approximation (RMSEA). We use simulations to show that naive implementations of the RMSEA have a downward bias in the presence of missing data and, thus, overestimate model goodness-of-fit. Unfortunately, many state-of-the-art software packages report the biased form of RMSEA. As a consequence, the scientific community may have been accepting a much larger fraction of models with non-acceptable model fit. We propose a bias-correction for the RMSEA based on information-theoretic considerations that take into account the expected misfit of a person with fully observed data. The corrected RMSEA is asymptotically independent of the proportion of missing data for misspecified models. Importantly, results of the corrected RMSEA computation are identical to naive RMSEA if there are no missing data.

scholarly journals Optimal Binning of Peri-Event Time Histograms Using Akaike Information Criterion

2020 ◽  
Author(s):  
Ali Ghazizadeh ◽  
Frederic Ambroggi
Keyword(s):  
Firing Rate ◽  
Akaike Information Criterion ◽  
Mean Squared Error ◽  
Temporal Dynamics ◽  
Real Data ◽  
Information Criterion ◽  
Neuronal Firing ◽  
Computationally Efficient ◽  
Event Time ◽  
Squared Error

AbstractPeri-event time histograms (PETH) are widely used to study correlations between experimental events and neuronal firing. The accuracy of firing rate estimate using a PETH depends on the choice of binsize. We show that the optimal binsize for a PETH depends on factors such as the number of trials and the temporal dynamics of the firing rate. These factors argue against the use of a one-size-fits-all binsize when making PETHs for an inhomogeneous population of neurons. Here we propose a binsize selection method by adapting the Akaike Information Criterion (AIC). Simulations show that optimal binsizes estimated by AIC closely match the optimal binsizes using mean squared error (MSE). Furthermore, using real data, we find that optimal binning improves detection of responses and their dynamics. Together our analysis strongly supports optimal binning of PETHs and proposes a computationally efficient method for this optimization based on AIC approach to model selection.

scholarly journals Features of building a predictive neuro-fuzzy network

2020 ◽  
pp. 13-17
Author(s):  
А.И. Епихин ◽  
Е.В. Хекерт ◽  
А.Б. Каракаев ◽  
М.А. Модина
Keyword(s):  
Mean Squared Error ◽  
Least Squares Method ◽  
Finite Impulse Response ◽  
Mean Absolute Percentage Error ◽  
Percentage Error ◽  
Piston Engine ◽  
Absolute Percentage Error ◽  
Squared Error ◽  
Neuro Fuzzy ◽  
Fuzzy Network

В статье рассматриваются особенности построения прогностической нейро-фаззи сети. В процессе исследования представлена структура адаптивного нейро-фаззи-предиктора и многомерного нейро-фаззи-нейрона. Рассмотрен принцип обработки информации, поступающей в режиме реального времени, о работе поршневого двигателя СЭУ с использованием TSK-системы нулевого порядка с применением быстродействующих оптимизационных процедур второго порядка типа рекуррентного метода наименьших квадратов для настройки синаптических весов. Определена архитектура искусственной нейро-фаззи сети для прогноза ресурсной прочности поршневого двигателя СЭУ марки RND 105, состоящая из пяти последовательно соединенных слоев. Представлена структура динамических нейронов-фильтров с конечной импульсной характеристикой. Рассмотрена процедура обучения нейросети. При проведения численного эксперимента использовались следующие критерии оценки: MSE (mean squared error, среднеквадратичная погрешность); SMAPE (Symmetric mean absolute percentage error, симметрично абсолютная процентная погрешность) - характеризует погрешность прогноза в процентах. Экспериментальный анализ разработанной сети проводился на примере прогнозирования ресурсной прочности восьмицилиндрового двухтактного судового дизеля марки RND 105. The article discusses the features of building a predictive neuro-fuzzy network. During the research, the structure of an adaptive neuro-fuzzy predictor and a multidimensional neuro-fuzzy neuron is presented. The principle of processing information received in real time about the operation of a piston engine of a SEP using a TSK-system of zero order with the use of high-speed optimization procedures of the second order such as the recurrent least squares method for adjusting synaptic weights is considered. The architecture of an artificial neuro-fuzzy network for predicting the resource strength of a piston engine SEU brand RND 105, consisting of five layers connected in series, has been determined. The structure of dynamic filter neurons with finite impulse response is presented. The procedure for training a neural network is considered. During the numerical experiment, the following evaluation criteria were used: MSE (mean squared error); SMAPE (Symmetric mean absolute percentage error) - characterizes the forecast error in percentage. An experimental analysis of the developed network was carried out on the example of predicting the resource strength of an eight-cylinder two-stroke marine diesel engine of the RND 105 brand.

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