Modeling Egg Yield Values in Alectoris Chukar with Nonlinear models

In this study, the distributions of egg count (daily and cumulative), width, length and weight values of chukar partridges obtained in two different egg production seasons were statistically modeled. For this purpose, in modeling cumulative egg production curves; Logistic, Gompertz, Gamma, Schunute, Brody, Richard, Negative Exponential, Von Bertalanffy, Cubic Piecewise and Cubic models were used, and in evaluating daily egg production curves; Gompertz, Logistic, Richard, McNally, Gamma, Cubic Piecewise, Quadratic, Quadratic Piecewise and Modified Compartmental models were used. In modeling egg width values; Gompertz, Gamma, Cubic Piecewise and Cubic models were used, in modeling length values; Logistic, Gamma, Cubic Piecewise and Cubic models were used, and in modeling weight values; McNally, Gamma, Cubic Piecewise and Cubic models were used. In all modeling studies, as comparison and evaluation criteria; Error Mean Square, Corrected Coefficient of Determination, Accuracy Factor, Bias Factor, Durbin-Watson, Akaike Information Criterion, Corrected Akaike Information Criterion and Bayesian Information Criterion were taken into consideration. As a result of the study; Gamma was determined as the most suitable model for modeling cumulative egg yields and length values, McNally for modeling daily egg yields and weight values, and Gompertz and Gamma models for modeling egg width values.

Modeling the growth curve of Iranian Shall sheep using non-linear growth models

Background: Female breast cancer (BC) has surpassed lung cancer as the most prevalent reason for cancer-related diagnosis in the world. BC has geographical disparities in the intensity of effect of its associated risk factors on patients’ survival. Several models can be employed to determine the effect of risk factors on patients’ survival. The present study aims at evaluating these models.
 Methods: The secondary data of 558 BC patients diagnosed at Korle Bu teaching hospital during 2010-2015 and followed-up (right censored) to the end of 2015 were analysed. The survival status, demographic and tumour characteristics of these patients were determined by event history analysis. To compare various models of survival, Akaike Information Criterion (AIC) , Bayesian Information Criteria (BIC) and Receiver Operation Characteristic (ROC) curve were used. R software was used for data analyses. The data consisted of BC patients in the age range of 13 to 97 years. The dataset was partitioned into training (holding 70%) and validation set (30%).
 Results: Based on AIC, BIC and ROC curve values the Gompertz (AIC=2322, BIC=2391) was the best model fit for the survival data. Generalised Gamma (AIC=2378, BIC=2451) and Weibull (AIC=2382, BIC=2452) models were respectively the next alternatives among the nine (9) accelerated failure time (AFT) models considered in our study. Results from the three best fitted AFT models showed that covariates such as Age at diagnosis, Progesterone receptor, Molecular Subtype, Grade, Stage, Metastasis, number of Lymph nodes involved and genetic status were the significant factors that have an effect on the survival time of BC patients in Ghana (P<0.05). The Area under the ROC curve (AUC=0.945) shows an outstanding performance of the Gompertz AFT model to discriminate the true disease status of patients.
 Conclusion: Although the Cox proportional hazard model has seen wide usage and remains a robust approach in survival analyses for the past four decades; its proportional hazards assumption is most often violated by some covariates in medical research. Under such violations, AFT models are a strong alternative.

In molecular phylogenetics, partition models and mixture models provide different approaches to accommodating heterogeneity in genomic sequencing data. Both types of models generally give a superior fit to data than models that assume the process of sequence evolution is homogeneous across sites and lineages. The Akaike Information Criterion (AIC), an estimator of Kullback–Leibler divergence, and the Bayesian Information Criterion (BIC) are popular tools to select models in phylogenetics. Recent work suggests that AIC should not be used for comparing mixture and partition models. In this work, we clarify that this difficulty is not fully explained by AIC misestimating the Kullback–Leibler divergence. We also investigate the performance of the AIC and BIC at comparing amongst mixture models and amongst partition models. We find that under nonstandard conditions (i.e. when some edges have small expected number of changes), AIC underestimates the expected Kullback–Leibler divergence. Under such conditions, AIC preferred the complex mixture models and BIC preferred the simpler mixture models. The mixture models selected by AIC had a better performance in estimating the edge length, while the simpler models selected by BIC performed better in estimating the base frequencies and substitution rate parameters. In contrast, AIC and BIC both prefer simpler partition models over more complex partition models under nonstandard conditions, despite the fact that the more complex partition model was the generating model. We also investigated how mispartitioning (i.e., grouping sites that have not evolved under the same process) affects both the performance of partition models compared with mixture models and the model selection process. We found that as the level of mispartitioning increases, the bias of AIC in estimating the expected Kullback–Leibler divergence remains the same, and the branch lengths and evolutionary parameters estimated by partition models become less accurate. We recommend that researchers are cautious when using AIC and BIC to select among partition and mixture models; other alternatives, such as cross-validation and bootstrapping, should be explored, but may suffer similar limitations [AIC; BIC; mispartitioning; partitioning; partition model; mixture model].

In this study, nine non linear growth curve models were used to determine the goodness of fit by the body weight measurements of the total number of 178 partridges(Alectoris chukar), 93 females, and 85 males, respectively. The R 2(coefficients of determination) values for the total partridges, females and males in Brody, Gompertz, Logistic, von Bertalanffy, asymptote regression,exponential, Monomolecular, Richards and Weibull-type were 0.985, 0.980 and 0.984, 0.997, 0.998 and 0.998, 0.996, 0.999 and 0.999, 0.995, 0.995 and 0.996, 0.985, 0.980 and 0.984, 0.891, 0.871 and 0.892, 0.985, 0.980 and 0.984, 0.997, 0.999 and 0.999, 0.997, 0.999 and 0.999, respectively. The R 2 values for Gompertz, Logistic, von Bertalanffy, Richards and Weibull-type were >0.99, while the exponential (<0.90) had the lowest. What’s more, the Gompertz, Logistic, Richards and Weibull-type models best described the data because of lower MSE (mean square error), AIC(Akaike’s information criteria) and BIC(Schwarz Bayesian information criterion), higher adj. R 2(Adjusted coefficient of determination) and r(the correlation coefficient between measured body weight and estimated body weight) and there was not an autocorrelation between the residual values. As a result, based on goodness of fit criteria; R 2, adj.R 2, MSE, r, AIC, BIC values, the Weibull-type model best described live weight data of the Partridges(Alectoris chukar).

Alternative growth functions for predicting body, carcass, and breast weight in ducks: Lomolino equation and extreme value function

ABSTRACT: The objective of this study was to compare non-linear models fitted to the growth curves of quail to determine which model best describes their growth and check the similarity between models by analyzing parameter estimates.Weight and age data of meat-type European quail (Coturnix coturnix coturnix) of three lines were used, from an experiment in a 2 × 4 factorial arrangement in a completely randomized design, consisting of two metabolizable energy levels, four crude protein levels and six replicates. The non-linear Brody, Von Bertalanffy, Richards, Logistic and Gompertz models were used. To choose the best model, the Adjusted Coefficient of Determination, Convergence Rate, Residual Mean Square, Durbin-Watson Test, Akaike Information Criterion and Bayesian Information Criterion were applied as goodness-of-fit indicators. Cluster analysis was performed to check the similarity between models based on the mean parameter estimates. Among the studied models, Richards’ was the most suitable to describe the growth curves. The Logistic and Richards models were considered similar in the analysis with no distinction of lines as well as in the analyses of Lines 1, 2 and 3.

The aim of the work reported here was to investigate the appropriateness of a sinusoidal function by applying it to model the cumulative lactation curves for milk yield and composition in primiparous Holstein cows, and to compare it with three conventional growth models (linear, Richards and Morgan). Data used in this study were 911 144 test-day records for milk, fat and protein yields, which were recorded on 834 dairy herds from 2000 to 2011 by the Animal Breeding Centre and Promotion of Animal Products of Iran. Each function was fitted to the test-day production records using appropriate procedures in SAS (PROC REG for the linear model and PROC NLIN for the Richards, Morgan and sinusoidal equations) and the parameters were estimated. The models were tested for goodness of fit using adjusted coefficient of determination $\lpar {R_{{\rm adj}}^2 } \rpar $, root mean square error (RMSE), Akaike's information criterion (AIC) and the Bayesian information criterion (BIC). $R_{{\rm adj}}^2 $ values were generally high (>0.999), implying suitable fits to the data, and showed little differences among the models for cumulative yields. The sinusoidal equation provided the lowest values of RMSE, AIC and BIC, and therefore the best fit to the lactation curve for cumulative milk, fat and protein yields. The linear model gave the poorest fit to the cumulative lactation curve for all production traits. The current results show that classical growth functions can be fitted accurately to cumulative lactation curves for production traits, but the new sinusoidal equation introduced herein, by providing best goodness of fit, can be considered a useful alternative to conventional models in dairy research.

ObjectiveThe identification of nonlinear mixed models that describe the growth trajectory of New Zealand rabbits was performed based on weight records and carcass measures obtained using ultrasonography.MethodsPhenotypic records of body weight (BW) and loin eye area (LEA) were collected from 66 animals raised in a didactic-productive module of cuniculture located in the southern Piauí state, Brazil. The following nonlinear models were tested considering fixed parameters: Brody, Gompertz, Logistic, Richards, Meloun 1, modified Michaelis-Menten, Santana, and von Bertalanffy. The coefficient of determination (R2), mean squared error, percentage of convergence of each model (%C), mean absolute deviation of residuals, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were used to determine the best model. The model that best described the growth trajectory for each trait was also used under the context of mixed models, considering two parameters that admit biological interpretation (A and k) with random effects.ResultsThe von Bertalanffy model was the best fitting model for BW according to the highest value of R2 (0.98) and lowest values of AIC (6,675.30) and BIC (6,691.90). For LEA, the Logistic model was the most appropriate due to the results of R2 (0.52), AIC (783.90), and BIC (798.40) obtained using this model. The absolute growth rates estimated using the von Bertalanffy and Logistic models for BW and LEA were 21.51g/d and 3.16 cm2, respectively. The relative growth rates at the inflection point were 0.028 for BW (von Bertalanffy) and 0.014 for LEA (Logistic).ConclusionThe von Bertalanffy and Logistic models with random effect at the asymptotic weight are recommended for analysis of ponderal and carcass growth trajectories in New Zealand rabbits. The inclusion of random effects in the asymptotic weight and maturity rate improves the quality of fit in comparison to fixed models.

By fitting dynamic contrast-enhanced MRI data to an appropriate pharmacokinetic model, quantitative physiological parameters can be estimated. In this study, we compare four different models by applying four statistical measures to assess their ability to describe dynamic contrast-enhanced MRI data obtained in 28 human breast cancer patient sets: the chi-square test (χ(2)), Durbin-Watson statistic, Akaike information criterion, and Bayesian information criterion. The pharmacokinetic models include the fast exchange limit model with (FXL_v(p)) and without (FXL) a plasma component, and the fast and slow exchange regime models (FXR and SXR, respectively). The results show that the FXL_v(p) and FXR models yielded the smallest χ(2) in 45.64 and 47.53% of the voxels, respectively; they also had the smallest number of voxels showing serial correlation with 0.71 and 2.33%, respectively. The Akaike information criterion indicated that the FXL_v(p) and FXR models were preferred in 42.84 and 46.59% of the voxels, respectively. The Bayesian information criterion also indicated the FXL_v(p) and FXR models were preferred in 39.39 and 45.25% of the voxels, respectively. Thus, these four metrics indicate that the FXL_v(p) and the FXR models provide the most complete statistical description of dynamic contrast-enhanced MRI time courses for the patients selected in this study.

ABSTRACTIn order to describe the growth curves in Iranian Mehraban sheep, five non-linear mathematical equations (Brody, Negative exponential, Logistic, Gompertz and Von Bertalanffy) were used. The data set used in this study was obtained from the Agricultural Organization of Hamedan province and comprised 35,414 weight records of lambs which were collected from birth to 365 days of age during 1991–2011. Each model was fitted separately to body weight records of all lambs, male and female lambs and single and twin lambs using the NLIN and MODEL procedures in SAS. The models were tested for goodness of fit using adjusted coefficient of determination ( ), root mean square error (RMSE), Durbin–Watson statistic (DW), Akaike’s information criterion (AIC) and Bayesian information criterion (BIC). The Brody model provided the best fit of growth curve in all lambs, male and female lambs and single and twin lambs due to the lower values of AIC and BIC than other models. The Logistic model provided the worst fit of growth curve for all lambs, male and female lambs and single and twin lambs. Evaluation of different growth equations used in this study indicated the potential of the non-linear functions for fitting body weight records of Mehraban sheep.

In this study, 11 different growth curve models (Logistic, Gompertz, McNally, Schnute, Richards, Bertalanffy, Cubic, Cubic Piecewise, Wilmink, Wood, and Log-Logistic) were compared using live weight data of Japanese quails (Coturnix japonica). The predictive performance of the models was evaluated using statistical metrics such as mean square error, corrected coefficient of determination, accuracy and bias factors, Durbin-Watson statistics, Akaike information criterion, corrected Akaike information criterion, and Bayesian information criterion. The analyses determined that the Logistic model best represented the live weight data. The Logistic model provided advantages in terms of high fit, low error, and parametric simplicity. The results demonstrate that the Logistic model can be used in practical breeding applications in modeling the growth processes of Japanese quails (Coturnix japonica). Application of extended modeling approaches with different genotypes and individual data is recommended in future studies.

In Response: We thank Dr. Arunajadai for his comments about the statistical simulations in our editorial (text NLP, algorithm WMB) demonstrating the perils of stepwise logistic regression.1 This allows us to clarify an ambiguity in the nomenclature of the stepwise automatic variable selection algorithm. Correctly specified, the algorithm should be described as either stepwise forward selection, stepwise backward elimination, or stepwise with forward selection and/or backward elimination; however, the word stepwise itself is also commonly used to refer to any of the three variants or to just the third variant. Arunajadai2 has correctly stated that our particular simulations used the stepwise backward elimination variant. Our simulations used randomly created covariates to demonstrate how commonly there was the creation of spurious associations by stepwise modeling (backward elimination variant). Dr. Arunajadai has also provided R software code to perform the other two variants; he reports that there were no spurious associations with no covariate significant at P < 0.05 using either the forward selection or the forward selection/ backward elimination variants. In his code, Arunajadai estimates a mean intercept model object, i.e., “fit <- glm(y ∼ 1, data = w, family = binomial),” for submission to the stepwise function. The submission of a mean intercept model to the stepwise process cannot identify any association, true or spurious. When a full (all covariates) model, i.e., “fit <- glm(y ∼., data = w, family = binomial)” is used, all three variants have qualitatively the same results of numerous spurious associations (appendix available at www.anesthesia-analgesia.org). The inclusion of noise variables during stepwise modeling regardless of the variant has been demonstrated elsewhere.3–5 Dr. Arunajadai also raised the very interesting question of which information criterion should be used at each step for adding or removing a covariate; he advocates the Bayesian Information Criterion (BIC) in contrast to the Akaike Information Criterion (AIC) used in our simulation. Both the AIC and the BIC are indexes in which twice the negative maximized log likelihood of the model fit is penalized by subtracting either twice the number of model parameters (AIC) or the number of model parameters multiplied by the log of the sample size (BIC). Of the candidate models possible, the model with the higher AIC or higher BIC is favored. As Arunajadai noted, the BIC is more heavily penalized and will produce more parsimonious models (fewer significant covariates). However, there is a competition in choosing between AIC and BIC; the AIC will yield optimal regression estimation while the BIC represents consistent model identification rules. It is not possible to create models with the properties favored by both the AIC and the BIC.6 Using the BIC index in our simulation still produces spurious associations. Automatic variable selection via a stepwise process is a hazardous undertaking. As J. B. Copas3 humorously noted, “If you torture the data for long enough, in the end they will confess …. What more brutal torture can there be than subset selection? The data will always confess, and the confession will usually be wrong.” Nathan L. Pace, MD, MStat Department of Anesthesiology University of Utah Salt Lake City, Utah William M. Briggs, PhD Department of Emergency Medicine New York Methodist Hospital Brooklyn, New York [email protected]

The Laplace distribution and its extensions have been widely utilized in statistical modelling due to their ability to capture real-world data characteristics such as skewness and heavy tails. This study evaluated the performance of the classical Laplace (L) distribution against three of its variants: the Transmuted Laplace (TL), Alternative Laplace (AL), and Asymmetric Laplace (ASL) distributions. While these extensions introduce additional parameters to enhance flexibility, their empirical performance remains a subject of interest. Using three datasets Rent prices, Voltage Drop, and Nigeria’s Unemployment Rate, this study assessed model fit based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Squared Error (MSE). Findings revealed that the standard Laplace (L) distribution consistently outperforms its counterparts. In the Rent dataset, it achieves the lowest AIC (613.636), BIC (609.2266), and a reasonable MSE (2343.761), whereas the TL and AL distributions yield significantly higher AIC and BIC values, and the ASL distribution demonstrates an extremely high MSE (9.34 × 10¹²), indicating poor fit. A similar trend is observed in the Voltage Drop dataset, where the L distribution records the lowest AIC (201.1564), BIC (197.7293), and MSE (132.7978), while TL and ASL show excessive model instability. In the Unemployment Rate dataset, the L distribution again provides the best fit, with an AIC of 349.7985, a BIC of 345.896, and a moderate MSE of 186.4666. On average, across all datasets, the L distribution remains the most robust model, with the lowest AIC (388.197), BIC (384.284), and MSE (887.6751). The AL distribution follows closely with an MSE of 888.9518 but exhibits significantly higher AIC (2426.027) and BIC (2424.071). The ASL distribution, while demonstrating moderate AIC (1443.016) and BIC (1448.885), suffers from poor predictive accuracy with an extremely high MSE (3.19E+12). The TL distribution performs the worst, with the highest AIC (34,686.77), BIC (20,112.08), and an MSE of 76,038.22, highlighting its instability. In conclusion, this study established that the standard Laplace (L) distribution provides the most reliable and accurate fit across diverse datasets. While alternative forms introduce additional flexibility, their increased complexity does not necessarily yield superior model performance. Future research should explore modifications to improve the parameter stability of Laplace extensions and investigate alternative estimation techniques to enhance predictive accuracy in real-world applications.

Information criteria provide an attractive basis for model selection. However, little is understood about their relative performance in asymmetric price transmission modelling framework. To explore this issue, this research evaluated the performance of the two commonly used model selection criteria, Akaike information criteria (AIC) and Bayesian information criteria (BIC) in discriminating between asymmetric price transmission models under various conditions. Monte Carlo experimentation indicated that the performance of the different model selection criteria are affected by the size of the data, the level of asymmetry and the amount of noise in the model used in the application. The Bayesian information criterion is consistent and outperforms AIC in selecting the suitable asymmetric price relationship in large samples. Key words: Model selection, Akaike’s information criteria (AIC), Bayesian information criteria (BIC), asymmetry, Monte Carlo.