Modeling the growth curve in ducks: a sinusoidal model as an alternative to classical nonlinear models.

The present study aimed to apply a sinusoidal model to duck body weight records in order to introduce it to the field of poultry science. Using 8 traditional growth functions as a guide (Bridges, Janoschek, logistic, Gompertz, Von Bertalanffy, Richards, Schumacher, and Morgan), this study looked at how well the sinusoidal equation described the growth patterns of ducks. By evaluating statistical performance and examining model behavior during nonlinear regression curve fitting, models were compared. The data used in this study came from 3 published articles reporting 1) body weight records of Kuzi ducks aged 1 to 70 d, 2) body weight records for Polish Peking ducks aged 1 to 70 d, and 3) average body weight of Peking ducks aged 1 to 42 d belonging to 5 different breeds. The general goodness-of-fit of each model to the various data profiles was assessed using the adjusted coefficient of determination, root mean square error, Akaike's information criterion (AIC), and Bayesian information criterion. All of the models had adjusted coefficient of determination values that were generally high, indicating that the models generally fit the data well. Duck growth dynamics are accurately described by the chosen sinusoidal equation. The sinusoidal equation was found to be one of the best functions for describing the age-related changes in body weight in ducks when the growth functions were compared using the goodness-of-fit criteria. To date, no research has been conducted on the use of sinusoidal equations to describe duck growth development. To describe the growth curves for a variety of duck strains/lines, the sinusoidal function employed in this study serves as a suitable substitute for conventional growth functions.

A Bayesian Measure of Model Accuracy.

Ensuring that the proposed probabilistic model accurately represents the problem is a critical step in statistical modeling, as choosing a poorly fitting model can have significant repercussions on the decision-making process. The primary objective of statistical modeling often revolves around predicting new observations, highlighting the importance of assessing the model's accuracy. However, current methods for evaluating predictive ability typically involve model comparison, which may not guarantee a good model selection. This work presents an accuracy measure designed for evaluating a model's predictive capability. This measure, which is straightforward and easy to understand, includes a decision criterion for model rejection. The development of this proposal adopts a Bayesian perspective of inference, elucidating the underlying concepts and outlining the necessary procedures for application. To illustrate its utility, the proposed methodology was applied to real-world data, facilitating an assessment of its practicality in real-world scenarios.

Improving the Hosmer-Lemeshow goodness-of-fit test in large models with replicated Bernoulli trials.

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type I error rate (and hence power) of the HL test decreases as model complexity grows, provided that the sample size remains fixed and binary replicates (multiple Bernoulli trials) are present in the data. We demonstrate that a generalized version of the HL test (GHL) presented in previous work can offer some protection against this power loss. These results are also supported by application of both the HL and GHL test to a real-life data set. We conclude with a brief discussion explaining the behavior of the HL test, along with some guidance on how to choose between the two tests. In particular, we suggest the GHL test to be used when there are binary replicates or clusters in the covariate space, provided that the sample size is sufficiently large.

A mutual information measure of phase-amplitude coupling using gamma generalized linear models.

Introduction: Cross frequency coupling (CFC) between electrophysiological signals in the brain is a long-studied phenomenon and its abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling, specifically phase-amplitude coupling (PAC), do not attempt to capture the phase and amplitude statistical relationships. Methods: In this paper, we first demonstrate a method of modeling these joint statistics with a flexible parametric approach, where we model the conditional distribution of amplitude given phase using a gamma distributed generalized linear model (GLM) with a Fourier basis of regressors. We perform model selection with minimum description length (MDL) principle, demonstrate a method for assessing goodness-of-fit (GOF), and showcase the efficacy of this approach in multiple electroencephalography (EEG) datasets. Secondly, we showcase how we can utilize the mutual information, which operates on the joint distribution, as a canonical measure of coupling, as it is non-zero and non-negative if and only if the phase and amplitude are not statistically independent. In addition, we build off of previous work by Martinez-Cancino et al., and Voytek et al., and show that the information density, evaluated using our method along the given sample path, is a promising measure of time-resolved PAC. Results: Using synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase-amplitude coupling through receiver operating characteristic (ROC) curve analysis. To validate our method, we test on invasive EEG recordings by generating comodulograms, and compare our method to the gold standard PAC measure, Modulation Index, demonstrating comparable performance in exploratory analysis. Furthermore, to showcase its use in joint gut-brain electrophysiology data, we generate topoplots of simultaneous high-density EEG and electrgastrography recordings and reproduce seminal work by Richter et al. that demonstrated the existence of gut-brain PAC. Using simulated data, we validate our method for different types of time-varying coupling and then demonstrate its performance to track time-varying PAC in sleep spindle EEG and mismatch negativity (MMN) datasets. Conclusions: Our new measure of PAC using Gamma GLMs and mutual information demonstrates a promising new way to compute PAC values using the full joint distribution on amplitude and phase. Our measure outperforms the most common existing measures of PAC, and show promising results in identifying time varying PAC in electrophysiological datasets. In addition, we provide for using our method with multiple comparisons and show that our measure potentially has more statistical power in electrophysiologic recordings using simultaneous gut-brain datasets.

A generalized Hosmer-Lemeshow goodness-of-fit test for a family of generalized linear models.

Generalized linear models (GLMs) are very widely used, but formal goodness-of-fit (GOF) tests for the overall fit of the model seem to be in wide use only for certain classes of GLMs. We develop and apply a new goodness-of-fit test, similar to the well-known and commonly used Hosmer-Lemeshow (HL) test, that can be used with a wide variety of GLMs. The test statistic is a variant of the HL statistic, but we rigorously derive an asymptotically correct sampling distribution using methods of Stute and Zhu (Scand J Stat 29(3):535-545, 2002) and demonstrate its consistency. We compare the performance of our new test with other GOF tests for GLMs, including a naive direct application of the HL test to the Poisson problem. Our test provides competitive or comparable power in various simulation settings and we identify a situation where a naive version of the test fails to hold its size. Our generalized HL test is straightforward to implement and interpret and an R package is publicly available. Supplementary Information: The online version contains supplementary material available at 10.1007/s11749-023-00912-8.

Goodness-of-fit tests for modified Poisson regression possibly producing fitted values exceeding one in binary outcome analysis.

Modified Poisson regression, which estimates the regression parameters in the log-binomial regression model using the Poisson quasi-likelihood estimating equation and robust variance, is a useful tool for estimating the adjusted risk and prevalence ratio in binary outcome analysis. Although several goodness-of-fit tests have been developed for other binary regressions, few goodness-of-fit tests are available for modified Poisson regression. In this study, we proposed several goodness-of-fit tests for modified Poisson regression, including the modified Hosmer-Lemeshow test with empirical variance, Tsiatis test, normalized Pearson chi-square tests with binomial variance and Poisson variance, and normalized residual sum of squares test. The original Hosmer-Lemeshow test and normalized Pearson chi-square test with binomial variance are inappropriate for the modified Poisson regression, which can produce a fitted value exceeding 1 owing to the unconstrained parameter space. A simulation study revealed that the normalized residual sum of squares test performed well regarding the type I error probability and the power for a wrong link function. We applied the proposed goodness-of-fit tests to the analysis of cross-sectional data of patients with cancer. We recommend the normalized residual sum of squares test as a goodness-of-fit test in the modified Poisson regression.

Quantifying regional low flows under data scarce conditions.

Estimating low flow quantiles is essential for regulating minimum flow requirements and ensuring water availability, ecological health, and overall system sustainability. This study aims to quantify regional low flows by analyzing low-flow time series in data-limited environments. We utilized annual minimum 7-day instantaneous streamflow data collected from gaging stations. Discordancy measure assessments revealed that all sites were homogeneous, forming a single region. We employed Easy-Fit Statistical Software to select the best-fit probability distribution model and determine estimation parameter values. Through goodness-of-fit tests (GOFs), the Generalized Pareto model emerged as the most suitable, predicting low flow quantiles for 100-year returns. Rigorous application of GOFs ensures the statistical soundness of the model, capturing underlying data patterns. A correlation coefficient determination (R2) of 0.989 demonstrates the high satisfaction of the selected distribution model. The developed regression line for the region exhibited strong agreement between predicted low flows and catchment area. Thus, accurate estimation proves valuable in environmental and human-influenced decision-making processes, providing insights into low-flow behavior and mitigating drought effects on aquatic ecosystems.

Uncertainty Analysis of Time-Integrated Activity Coefficient in Single-Time-Point Dosimetry Using Bayesian Fitting Method.

Purpose: Calculation of the uncertainty of the individual time-integrated activity coefficient (TIACs) is desirable in molecular radiotherapy. However, the calculation of TIAC's uncertainty in single-time-point (STP) method has never been reported in the literature. This study presents a method based on the Bayesian fitting (BF) to calculate the standard deviation (SD) of individual TIACs in the STP dosimetry. Methods: Biokinetic data of 177Lu-DOTATATE in kidneys were obtained from PMID33443063. BF methods with extended objective function, which optimize the fitting using prior knowledge of the function's parameters, were used. Reference TIACs (rTIACs) were calculated by fitting a mono-exponential function to the all-time-point data. The goodness of fit was checked based on the visual inspection and the coefficient of variations (CV) of the fitted parameters < 0.5. BF with relative (BFr) and absolute-based (BFa) variance methods were used to obtain the calculated TIACs (cTIACs) from the STP dosimetry. Performance of the STP method was obtained by calculating the relative deviation (RD) between cTIACs and rTIACs. Results: Visual inspection showed a good fit for all patients with CV of fitted parameters less than 50%. The mean ± SD of cTIAC's %RD were 7.0 ± 25.2 for BFr and 2.6 ± 8.9 for BFa. The range of %CV of the individual cTIAC's SD for BFr and BFa methods was 36-78% and 22-33%, respectively, while the %CV of the rTIAC SD was 0.8-49%. Conclusion: We introduce the BF method to calculate the SD of individual TIACs in STP dosimetry. The presented method might be used as an alternative method for uncertainty analysis in STP dosimetry. Supplementary Information: The online version contains supplementary material available at 10.1007/s13139-024-00851-8.

Good Fit Is Weak Evidence of Replication: Increasing Rigor Through Prior Predictive Similarity Checking.

Replication provides a confrontation of psychological theory, not only in experimental research, but also in model-based research. Goodness of fit (GOF) of the original model to the replication data is routinely provided as meaningful evidence of replication. We demonstrate, however, that GOF obscures important differences between the original and replication studies. As an alternative, we present Bayesian prior predictive similarity checking: a tool for rigorously evaluating the degree to which the data patterns and parameter estimates of a model replication study resemble those of the original study. We apply this method to original and replication data from the National Comorbidity Survey. Both data sets yielded excellent GOF, but the similarity checks often failed to support close or approximate empirical replication, especially when examining covariance patterns and indicator thresholds. We conclude with recommendations for applied research, including registered reports of model-based research, and provide extensive annotated R code to facilitate future applications of prior predictive similarity checking.

Diagnostics for regression models with semicontinuous outcomes.

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (eg, deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that is applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey.

Numerical investigation of louver edges effect on the performances of louvered fin compact heat exchanger.

The rectangular channel louvered-fin compact heat exchanger (LFCHE) is the most efficient type that has been served in a radiator. However, with this type of heat exchanger, the pressure drop rises by three to four times as the heat transfer increases, which results in decreasing performance. This research is aimed to numerically investigate the louver edges (vertical, inclined, and horizontal) effect on LFCHE performance at different louver angle (θ) with air inlet velocities ranging from 1 to 30 m/s. A total of twelve models are made and simulated. The result revealed that the horizontal edge decreases the pressure drop up to 24.2% with a 1.01% increase in outlet air temperature over the base model (inclined edge). Thus, louver edge has design which results in higher and lower effect on pressure drop and temperature change, respectively. The research investigated the effects of louver edges using different performance evaluation criteria. At 10 m/s (Relp = 972.33) the horizontal edge increases the volume goodness (jf) factor up to 21.49% over the base model. Similarly, the horizontal edged fins resulted in maximum increment of jf-factor by 22% and 25% as compared with inclined edge for louver angles θ of 24 ° (at low Relp) and 20 ° (at high Relp), respectively. Generally, the horizontally edged LFCHE is proven to have higher performance in cooling the coolant with a minimum air side pressure drop.

Comparison of four performance models in quantifying the inequality of leaf and fruit size distribution.

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t-tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution.

The quest for psychological symmetry through figural goodness, randomness, and complexity: A selective review.

Of the four interrelated concepts in the title, only symmetry has an exact mathematical definition. In mathematical development, symmetry is a graded variable-in marked contrast with the popular binary conception of symmetry in and out of the laboratory (i.e. an object is either symmetrical or nonsymmetrical). Because the notion does not have a direct graded perceptual counterpart (experimental participants are not asked about the amount of symmetry of an object), students of symmetry have taken various detours to characterize the perceptual effects of symmetry. Current approaches have been informed by information theory, mathematical group theory, randomness research, and complexity. Apart from reviewing the development of the main approaches, for the first time we calculated associations between figural goodness as measured in the Garner tradition and measures of algorithmic complexity and randomness developed in recent research. We offer novel ideas and analyses by way of integrating the various approaches.

Construction of a geographically weighted nonparametric regression model fit test.

One of the approach of Geographically Weighted Regression (GWR) models is the Geographically Weighted Nonparametric Regression (GWNR) has more parameters than the GWR model. Models with more parameters usually have better match values, which is an advantage, while models with fewer parameters have the advantage of being easier to use and interpret. However, a model with more parameters should be used if it is proven to be significantly superior. Therefore, the purpose of this study was to develop a hypothesis test of goodness of fit test for GWNR model. The goodness of fit test was performed for the real data. We found that the GWNR model was more suitable than the mixed nonparametric regression model. Some highlights of the proposed method are:•A new model for GWR to overcome the unknown regression function by using mixed estimator spline truncated and fourier series at nonparametric regression•Goodness of fit for GWNR to testing the model fit between the mixed nonparametric regression model and GWNR•Applied goodness of fit test to poverty data in Sulawesi Island and infant mortality in East Java.

Assessment of nonlinear dose-response relationships via nonparametric regression.

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose-response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study.

Generalized exponentiated unit Gompertz distribution for modeling arthritic pain relief times data: classical approach to statistical inference.

Arthritis is the tenderness and swelling of one or more of the joints. Arthritis therapies are directed mainly at reducing symptoms and improving quality of life. In this article, we introduced a novel four parametric model known as generalized exponentiated unit Gompertz (GEUG) for modeling a clinical trial data which represent the relief or relaxing times of arthritic patients receiving a fixed dosage of certain medication. The key feature of such novel model is the addition of new tuning parameters to unit Gompertz (UG) with the intention of increasing versatility of the UG model. We have derived and studied different statistical and reliable attributes, along with moments and associated measures, uncertainty measures, moments generating functions, complete/incomplete moments, quantile function, survival and hazard functions. A comprehensive simulation analysis is implemented to evaluate the effectiveness of estimation of distribution parameters using numerous well-known classical approaches, like maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson Darling estimation (ADE), right tail Anderson darling estimation (RTADE), and Cramer-Von Mises estimation (CVME). Finally, using a relief time's data on arthritis pain show adaptability of suggested model. The results revealed that it might fit better than other relative models.

The analysis of randomized response "ever" and "last year" questions: A non-saturated Multinomial model.

Randomized response (RR) is a well-known interview technique designed to eliminate evasive response bias that arises from asking sensitive questions. The most frequently asked questions in RR are either whether respondents were "ever" carriers of the sensitive characteristic, or whether they were carriers in a recent period, for instance, "last year". The present paper proposes a design in which both questions are asked, and derives a multinomial model for the joint analysis of these two questions. Compared to the separate analyses with the binomial model, the model makes a useful distinction between last year and former carriers of the sensitive characteristic, it is more efficient in estimating the prevalence of last year carriers, and it has a degree of freedom that allows for a goodness-of-fit test. Furthermore, it is easily extended to a multinomial logistic regression model to investigate the effects of covariates on the prevalence estimates. These benefits are illustrated in two studies on the use of anabolic androgenic steroids in the Netherlands, one using Kuk and one using both the Kuk and forced response. A salient result of our analyses is that the multinomial model provided ample evidence of response biases in the forced response condition.

Coping strategy-situation fit vs. present control: relations with perceived stress in U.S. college students.

BACKGROUND: According to the strategy-situation fit hypothesis, it is adaptive to match coping strategies to the controllability of stressors. Although early research generally supported this hypothesis, recent findings have been inconsistent. The goals of this study were to test the strategy-situation fit hypothesis, addressing limitations of past research, and compare it to an alternative hypothesis from the temporal model of control (i.e., to focus on what one can control rather than matching coping strategies to control appraisals). DESIGN AND METHODS: College students (n = 159) completed measures assessing their stressors, coping strategies, stressor controllability, perceived control over present aspects of stressors, and perceived stress. Data were collected via online surveys in Fall 2020. RESULTS: Consistent with the strategy-situation fit hypothesis, using a higher ratio of problem-solving coping for more controllable stressors was associated with less stress. However, using more emotion-focused coping for less controllable stressors was not associated with less stress. In addition, focusing on what one could control in the present was associated with less stress, above and beyond strategy-situation fit. CONCLUSIONS: It may be more adaptive to focus on what one can control in the present than to match coping styles to stressor controllability.

Estimation of In Vitro True Digestibility and Fiber Degradation from Feedstuff Fiber Composition When Incubated in Equine Fecal Inoculum.

Neutral detergent fiber (NDF) and acid detergent fiber (ADF) composition have been shown to predict in vitro true digestibility (IVTD), in vitro NDF digestibility (IVNDFD), and in vitro ADF digestibility (IVADFD) in ruminants. This study's objective was to estimate in vitro digestibility measures within the DaisyII incubator using equine fecal inoculum from feedstuff NDF and ADF composition. Analyzed feedstuffs included alfalfa hay (Medicago sativa), Coastal Bermudagrass hay, soybean meal, rice bran, hempseed meal, and Bluebonnet® Equilene® Pellets. Data were analyzed using Akaike's information criterion (AIC) within the R Statistical Program©. The highest ranked model for IVTD was the interaction of NDF and ADF: 10003.32 - 0.2904 × NDF - 0.4220 × ADF - 0.0010 × NDF × ADF (Adjusted R2 = 0.959 and AICc = 474.97). Sample IVNDFD was moderately predicted by ADF: 855.15 - 1.5183 × ADF (Adjusted R2 = 0.749 and AICc = 560.82). Feedstuff ADF produced the highest ranked model for IVNDFD: 881.91 - 1.5952 × ADF (Adj. R2 = 0.835 and AICc = 541.33). These results indicate the effectiveness of using feedstuff NDF and ADF composition to predict IVTD, IVNDFD, and IVADFD within equine fecal inoculum. The findings of this study provide better understanding of feedstuff digestibility using equine fecal inoculum, but more research is warranted for validation of the models and the potential impact in vivo.

The type II exponentiated half logistic-odd Burr X-G power series class of distributions with applications.

A new distribution, the type II exponentiated half logistic-odd Burr X-G power series (TII-EHL-OBX-GPS), is introduced in this study. This distribution combines the type II exponentiated half logistic-odd Burr X-G family of distributions with power series distributions. We discuss its mathematical characteristics, maximum likelihood estimates and simulation experiments, along with practical applications in the type II exponentiated half logistic-odd Burr X-log-logistic Poisson distribution.