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The network of suppliers and, in particular, the allocation of a buyer’s procurement volumes is one of the key issues in supply chain management when following a multiple-sourcing strategy. This paper proposes a buyer–supplier model which considers a supplier quantity–quality trade-off reflecting the responsiveness of quality to changes in volume. The trade-off is based on the assumption that suppliers are not able to maintain the same level of quality, if quantity increases and vice versa. In order to model the relation between quantity and quality, a generalized logistic function is used. Considering heterogeneous suppliers in terms of the quantity–quality trade-off, we analyze, how different procurement volumes for a product affect the supplier structure of a buyer in a multiple-sourcing buyer–supplier network. An agent-based simulation is applied which is an appropriate approach to study systems of heterogeneous and interacting agents (e.g., buyer and suppliers, interactions between suppliers, mutual effects of parameters). The results show that in such a network not only the procurement volume remarkably shapes the supplier structure and, eventually, may lead to instability. Moreover, the results suggest that less advanced quality management systems on the buyer’s side may increase the stability of the supplier structure.

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena.

We examine a new form of smooth approximation to the zero one loss in which learning is performed using a reformulation of the widely used logistic function. Our approach is based on using the posterior mean of a novel generalized Beta-Bernoulli formulation. This leads to a generalized logistic function that approximates the zero one loss, but retains a probabilistic formulation conferring a number of useful properties. The approach is easily generalized to kernel logistic regression and easily integrated into methods for structured prediction. We present experiments in which we learn such models using an optimization method consisting of a combination of gradient descent and coordinate descent using localized grid search so as to escape from local minima. Our experiments indicate that optimization quality is improved when learning metaparameters are themselves optimized using a validation set. Our experiments show improved performance relative to widely used logistic and hinge loss methods on a wide variety of problems ranging from standard UC Irvine and libSVM evaluation datasets to product review predictions and a visual information extraction task. We observe that the approach is as follows: (1) more robust to outliers compared to the logistic and hinge losses; (2) outperforms comparable logistic and max margin models on larger scale benchmark problems; (3) when combined with Gaussian–Laplacian mixture prior on parameters the kernelized version of our formulation yields sparser solutions than Support Vector Machine classifiers; and (4) when integrated into a probabilistic structured prediction technique our approach provides more accurate probabilities yielding improved inference and increasing information extraction performance.

The rapid spread of the COVID-19 pandemic has raised huge concerns about the prospect of a major health disaster that would result in a huge number of deaths. This anxiety was largely fueled by the fact that the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), responsible for the disease, was so far unknown, and therefore an accurate prediction of the number of deaths was particularly difficult. However, this prediction is of the utmost importance for public health authorities to make the most reliable decisions and establish the necessary precautions to protect people’s lives. In this paper, we present an approach for predicting the number of deaths from COVID-19. This approach requires modeling the number of infected cases using a generalized logistic function and using this function for inferring the number of deaths. An estimate of the parameters of the proposed model is obtained using a Particle Swarm Optimization algorithm (PSO) that requires iteratively solving a quadratic programming problem. In addition to the total number of deaths and number of infected cases, the model enables the estimation of the infection fatality rate (IFR). Furthermore, using some mild assumptions, we derive estimates of the number of active cases. The proposed approach was empirically assessed on official data provided by the State of Qatar. The results of our computational study show a good accuracy of the predicted number of deaths.

Logistic regressions are subject to high uncertainty when the data are not past the inflection point. For example, for logistic regressions estimated with data up to or before inflection point, uncertainties in the upper asymptotic value $K$ can be of the same order of magnitude of the population under analysis. This paper presents a method for uncertainty reduction in logistic regression using data from a surrogate logistic process. We illustrate the procedure using the Richards' growth function (Generalized Logistic Function) to make predictions for COVID-19 evolution in Brazilian cities at stages before and during their epidemic inflection points. We constrain the logistic function regression with $K$ calculated from selected surrogate international cities where the epidemic is clearly past its inflection point. Information gained with this constraint stabilizes the logistic regression, reducing the uncertainty in the curves' parameters, including the rate of growth at the inflection point. The uncertainty is reduced even when the actual surrogate $K$ is used just as an anchor to simulate different epidemic scenarios. Results predicted for COVID-19 trajectories within Brazil agree with actual data. These results suggest that in the absence of big data, a simple logistic regression may provide low uncertainty if surrogate cities have been identified for estimates of $K$, even if the specifics of the evolution in the surrogate cities are different. The method may be used for other logistic models and for other logistic processes in other areas such as economics and biology, if surrogate processes can be identified.

The standard growth model of epidemic evolution such as the Richards generalized logistic function is remarkably successful because it agrees with almost all previous epidemic data. Yet, it fails to explain intervention measures for mitigations of the ongoing coronavirus 2019 disease (COVID-19) pandemic. It also fails to replicate an endemic phase that occurs in many countries epidemic curves (time series data of daily new cases). These discrepancies demonstrate that new epidemic laws are required to understand, predict and mitigate the COVID-19 pandemic. Here we show that almost all COVID-19 evolution can be modeled by three innovative epidemic laws. Specifically, based on the world COVID-19 data, we first divide an epidemic curve into three phases: an exponential growth phase, an exponential decay phase, and a constant endemic phase. We next integrate the growth and the decay phases into the first epidemic law with interventions as a model parameter. This law is completely opposite to the Richards generalized logistic function in terms of intervention measures. We then combine the first epidemic law with the endemic phase to form the second epidemic law, which makes the curve of cumulative cases increase linearly as time tends to infinity. The third epidemic law states if an epidemic is composed of multiple epidemic waves, the superposition principle applies. These laws were confirmed by the COVID-19 data from 18 countries including undeveloped, developing and developed countries. Finally, we pave the way for future research to incorporate the proposed theory into the classic SIR model. We anticipate that the results from this research can provide a scientific base for governments to mitigate the COVID-19 and other epidemic disasters.

COVID-19 was declared as a pandemic by the World Health Organization on March 11, 2020. Here, the dynamics of this epidemic is studied by using a generalized logistic function model and extended compartmental models with and without delays. For a chosen population, it is shown as to how forecasting may be done on the spreading of the infection by using a generalized logistic function model, which can be interpreted as a basic compartmental model. In an extended compartmental model, which is a modified form of the SEIQR model, the population is divided into susceptible, exposed, infectious, quarantined, and removed (recovered or dead) compartments, and a set of delay integral equations is used to describe the system dynamics. Time-varying infection rates are allowed in the model to capture the responses to control measures taken, and distributed delay distributions are used to capture variability in individual responses to an infection. The constructed extended compartmental model is a nonlinear dynamical system with distributed delays and time-varying parameters. The critical role of data is elucidated, and it is discussed as to how the compartmental model can be used to capture responses to various measures including quarantining. Data for different parts of the world are considered, and comparisons are also made in terms of the reproductive number. The obtained results can be useful for furthering the understanding of disease dynamics as well as for planning purposes.

Many analytical approaches to single-case data assume either linear effects (regression-based methods) or instant effects (mean-based methods). Neither assumption is realistic; therefore, these approaches’ assumptions are often violated. In this article, we propose modeling curvilinear effects to appropriately parametrize the characteristics of singe-case data. Specifically, we introduce the generalized logistic function as adequate function for this situation. The merits of the proposed procedure are demonstrated using data previously used in single case research that represent typical single case data. We provide the function with auxiliary graphical options to demonstrate the model parameters. The function is freely available in the R package “userfriendlyscience.” The proposed procedure is a new way to analyze single case data, which may provide applied single case researchers with a new tool to better understand their data and avoid applying methods with violated assumptions.

This paper proposes a new color fringe correction method that preserves the object color well by the color difference prediction using the logistic function. We observe two characteristics between normal edge (NE) and degraded edge (DE) due to color fringe: 1) the DE has relatively smaller R-G and B-G correlations than the NE and 2) the color difference in the NE can be fitted by the logistic function. The proposed method adjusts the color difference of the DE to the logistic function by maximizing the R-G and B-G correlations in the corrected color fringe image. The generalized logistic function with four parameters requires a high computational load to select the optimal parameters. In experiments, a one-parameter optimization can correct color fringe gracefully with a reduced computational load. Experimental results show that the proposed method restores well the original object color in the DE, whereas existing methods give monochromatic or distorted color.

A generalization of the fractional logistic equation by using k-Caputo derivative is introduced. Also a solution that can be expressed en terms of the k-Mittag-Le er function is obtained. The development of this paper has been done on the basis what has been done by Camargo and Bruno-Alfonso. Fil: Cerutti, Rubén A. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.

In this article, I present three commands that perform adjacent-category logistic regression (adjcatlogit), constrained continuation-ratio logistic regression (ccrlogit), and unconstrained continuation-ratio logistic regression (ucrlogit) for ordered response data.

A logistic regression method can be applied to regressing the [Formula: see text]-year survival probability to covariates, if there are no censored observations before time [Formula: see text]. But if some observations are incomplete due to censoring before time [Formula: see text], then the logistic regression cannot be applied. Jung (1996) proposed to modify the score function for logistic regression to accommodate the right-censored observations. His modified score function, motivated for a consistent estimation of regression parameters, becomes a regular logistic score function if no observations are censored before time [Formula: see text]. In this article, we propose a modification of Jung's estimating function for an optimal estimation for the regression parameters in addition to consistency. We prove that the optimal estimator is more efficient than Jung's estimator. This theoretical comparison is illustrated with a real example data analysis and simulations.

In the present paper, we propose a new approach to investigate the logistic function, which is commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some characteristic points corresponding to zeroes of successive derivatives of the logistic function. We also give examples of application of this method.

We modeled binary count data with categorical predictors, using logistic regression to develop a statistical method. We found that ANOVA-type analyses often performed unsatisfactorily, even when using different transformations. The logistic transformation of fraction data could be an alternative, but it is not desirable in the statistical sense. We concluded that such methods are not appropriate, especially in cases where the fractions were close to 0 or 1. The major purpose of this paper is to demonstrate that logistic regression with an ANOVA-model like parameterization aids our understanding and provides a somewhat different, but sound, statistical background. We examined a simple real world example to show that we can efficiently test the significance of regression parameters, look for interactions, estimate related confidence intervals, and calculate the difference between the mean values of the referent and experimental subgroups. This paper demonstrates that precise confidence interval estimates can be obtained using the proposed ANOVA-model like approach. The method discussed here can be extended to any type of experimental fraction data analysis, particularly for experimental design.

In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.

In the paper an experiment is described, that was designed and conducted to verify hypothesis that artificial neuron with sigmoidal activation function can efficiently solve the task of logistic regression in the case when the explaining variable is one-dimensional, and the explained variable is binomial. Computations were performed with 12 sets of statistical parameters, assumed for the generation of 65356 sets of data in each case. Comparative analysis of the obtained results with use of the reference values for the regression coefficients indicated that the investigated neuron can satisfactory perform the task, with efficiency similar to that obtained with classical logistic regression algorithm, when the teaching sets of input data, corresponding with output values 0 and 1, do not allow for simple separation. Moreover, it has been discovered that the simple formulas estimating the statistical distributions parameters from the samples, offer statistically superior assessment of the regression coefficient parameters.

Fuzzy Cognitive Maps is an important representation tool that has the ability to model complicated systems. Based on linear influence relations between concepts, FCMs can be trained to lead a system to a desired state. This work proposes a generalized flexible nonlinear function as an alternative way of estimating that influence. Its adjustable character offers the ability to lead a FCM into a large set of different equilibrium states, where the conventional approach constitutes only one instance. Experimental studies present the properties of the proposed methodology in two benchmarks and other synthetic data. The examination of a system under different considerations of influence offers a more complete understanding of a system behavior.

This paper discusses the Bayesian approach as an alternative to the classical analysis of nonlinear models for growth curve data in Japanese quail. A Bayesian nonlinear modeling method is introduced and compared with the classical nonlinear least squares (NLS) method using three non-linear models that are widely used in modeling the growth data of poultry. The Gompertz, Richards and Logistic models were fitted to 499 Japanese quail weekly averaged body weight data. Normal prior was assumed for all growth curve parameters of the models with assuming Jeffreys' non-informative prior for residual variances. Models were compared based on the Bayesian measure of fit, deviance information criterion (DIC), and our results indicated the better fit of Gompertz and Richards models than the Logistic model to our data. Moreover, the parameter estimates of the models fitted by both approaches showed only small differences. Akdeniz University Scientific Research Projects Management UnitAkdeniz University [2005.02.0121.005] We would like to express our gratitude to Dr. Tulin Aksoy (Akdeniz University, Faculty of Agriculture, Department of Animal Science, Antalya-TURKEY) for supplying the data, which was collected as part of a research project supported by Akdeniz University Scientific Research Projects Management Unit (project number: 2005.02.0121.005).

Background/Objectives: Different methods can be applied to create predictive models for the clinical data with binary outcome variable. This research aims to explore the process of constructing the modified predictive model of Logistic Regression (LR). Method/Statistical Analysis: To improve the accuracy of prediction, the Distance based Outlier Detection (DBOD) is used for pre-processing and Bipolar Sigmoid Function calculated using Neuro based Weight Activation Function is used in Logistic Regression instead of Sigmoid Function. Datasets were collected from clinical laboratory of AR Hospital in Madurai for the three years 2012, 2013 and 2014 are used for analysis. Data pre-processing is done to avoid the existence of insignificant data in the dataset. The detected outliers, using DBOD method are treated using a method closest to the normal range. A comparative study among different distance measures likes Euclidean and Manhattan etc. are done for DBOD method. The pre-processed data finally is fed as input to the Logistic Regression model. Maximum likelihood estimation is used to fit the model. Logistic Model is built from the Sigmoid Function using the Regression Coefficients. The accuracy of the model is evaluated by 10 fold cross validation. Findings: Logistic Model is built from the Sigmoid Function using the Regression Coefficients, produces the accuracy of 79%. The Sigmoid Function calculated using Random Weight Function provides the prediction accuracy of 84.2% and the Bipolar Sigmoid Function calculated using Neuro based Weight Activation function provides the prediction accuracy of 90.4%. On comparison, Bipolar Sigmoid Function calculated using Neuro weight activation function outperforms well than the Sigmoid Function calculated using regression coefficients. Improvements/Applications: The accuracy of Logistic Regression is improved from 79% to 90.4%. The most important factors: Erythrocyte Sedimentation Rate (ESR) and Estimation of Mean blood Glucose are identified from positive subjects of Diabetes Mellitus. The analysis is done for the 31 Diabetes Disease attributes of three years dataset.

In this article, we will describe how to analyze binary data from matched studies in orthodontics. We have previously discussed matched analysis for paired binary data (McNemar test), but now we will focus on the use of regression methods to model our data.1 The idea is the same as with simple logistic regression models for binary data2,3; however, we must remember that the observations are not independent, and participants in different treatment groups have been matched for at least 1 characteristic, and this must be taken into account in the analysis.

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence–absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this multilevel framework. An advantage of the multilevel framework is that it allows relating person fit to explanatory variables for person misfit/fit. We critically discuss Reise's approach. First, we argue that often the interpretation of the PRF slope as an indicator of person misfit is incorrect. Second, we show that the multilevel logistic regression model and the logistic PRF model are incompatible, resulting in a multilevel person-fit framework, which grossly violates the bivariate normality assumption for residuals in the multilevel model. Third, we use a Monte Carlo study to show that in the multilevel logistic regression framework estimates of distribution parameters of PRF intercepts and slopes are biased. Finally, we discuss the implications of these results and suggest an alternative multilevel regression approach to explanatory person-fit analysis. We illustrate the alternative approach using empirical data on repeated anxiety measurements of cardiac arrhythmia patients who had a cardioverter-defibrillator implanted.

The logistic regression model is a powerful method for modeling the relationship between a categorical variable and a set of explanatory variables. In practice, however, the existence of maximum likelihood estimates is known to be dependent on the data configuration. In fact, the Maximum Likelihood Estimators (MLE) of unknown parameters exists if, and only if, there is data overlapping. The Hidden Logistic Regression (HLR) is an alternative model under which the observed response is related to the unobservable response. The Maximum Estimated Likelihood (MEL) method is also proposed, once it is immune to the complete or quasi-complete separation of data. The Principal Component Logistic Regression (PCLR) model is useful to reduce the number of dimensions of a logistic regression model with continuous covariates avoiding multicollinearity. In this paper we present an extension of the HLR and PCLR models as means for the solution of problems with polytomous responses. The main purpose is to compare the classificatory performance obtained by the models mentioned above with those of the Classical Logistic Regression (CLR) and Individualized Logistic regression (ILR) models, in the case of polytomous responses. The purpose is to propose an alternative approach for the parameter estimation problem in polytomous logistic models when the data groups are completely separated. Simulations results resulting from databases taken from the literature show that the proposed approach is feasible.

An open-ended form of the logistic equation was recently proposed, using a model comprising two differential equations [Thornley, J.H.M., France, J., 2005. An open-ended logistic-based growth function. Ecol. Model. 184, 257–261]. The equations represent the two processes of growth and development, and are coupled. In this note, an analytical solution is developed for constant parameters. The solution can be expressed as a targetted single-differential-equation model, the θ-logistic or power-law logistic model, which is a well-known empirical growth equation in ecology and elsewhere. The analysis may facilitate mechanistic interpretation and application of the power-law logistic model as well as the original open two-differential-equation model.

ロジスティック回帰モデルを利用する際,最尤法によりパラメータ推定を行うのが一般的である.しかし,最尤推定量は完全分離または準完全分離の場合に存在しないことが知られている.また,発現確率が極端に小さい(または大きい)場合やパラメータ数に比べて標本サイズが小さい場合も妥当でないことが知られている.このような状況において,精確ロジスティック回帰推定法が有用であると言われている.しかし,すべての統計ソフトで精確ロジスティック回帰推定法を実施できるわけではない.Firth(1993)は最尤推定量のバイアスを取り除く方法を提案したが,完全分離または準完全分離に近い状態での検証は十分行われていない.本報告の目的は,完全分離または準完全分離に近い状態において,最尤推定値またはFirth法推定値を精確ロジスティック回帰推定値に近似する方法を検討することである.また,パラメータ推定の改善のためのデータ構造に関する近似法をシミュレーションにより検討する.尤度関数をTaylor展開することにより,最尤推定値またはFirth法推定値を精確ロジスティック回帰推定値に近似することが可能であることが分かった.さらに,最尤推定値はデータ構造を考慮することにより,近似の精度の改善が可能であることを示した.

We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued В step function is В discussed В using В Hausdorff metric. В Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA.

RESUMOObjetivou-se neste estudo analisar a aplicação da função logística generalizada para a descrição da estrutura diamétrica de povoamentos de eucalipto, bem como propor um modelo de distribuição diamétrica utilizando a função. Realizou-se também a modelagem da distribuição diamétrica utilizando a função Weibull para fins comparativos. Utilizaram-se dados de parcelas permanentes de um inventário florestal contínuo nas idades de 28, 40, 52, 64, 76 e 84 meses. Ajustou-se a função logística generalizada e Weibull para todas as parcelas e medições. A aderência das funções aos dados foi verificada pela aplicação do teste Kolmogorov- Smirnov. A função logística generalizada apresentou resultados satisfatórios para a modelagem da distribuição diamétrica de povoamentos de eucalipto. ABSTRACTThe objective of this study was to examine the generalized logistic function to describe the diameter structure of eucalypt plantations, and propose a model of diameter distribution using the function. There was also modeling the diameter distribution using the Weibull function for comparative purposes. We used data from permanent of a continuous forest inventory measured at ages 28, 40, 52, 64, 76 and 84 months. The generalized logistics and Weibull function were set for all plots and measurements. The adherence of the functions to the data was verified by applying the Kolmogorov-Smirnov test. The generalized logistic function showed good results for modeling the diameter distribution of eucalypt.

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

Results from Genome-Wide Association Studies (GWAS) have shown that the genetic basis of complex traits often include many genetic variants with small to moderate effects whose identification remains a challenging problem. In this context multi-marker analysis at the gene and pathway level can complement traditional point-wise approaches that treat the genetic markers individually. In this paper we propose a novel statistical approach for multi-marker analysis based on the Rasch model. The method summarizes the categorical genotypes of SNPs by a generalized logistic function into a genetic score that can be used for association analysis. Through different sets of simulations, the false-positive rate and power of the proposed approach are compared to a set of existing methods, and shows good performances. The application of the Rasch model on Alzheimer’s Disease (AD) ADNI GWAS dataset also allows a coherent interpretation of the results. Our analysis supports the idea that APOE is a major susceptibility gene for AD. In the top genes selected by proposed method, several could be functionally linked to AD. In particular, a pathway analysis of these genes also highlights the metabolism of cholesterol, that is known to play a key role in AD pathogenesis. Interestingly, many of these top genes can be integrated in a hypothetic signalling network.

SUMMARY The multivariate logistic transform is a reparameterisation of cell probabilities in terms of marginal logistic contrasts. It is known that an arbitrary set of logistic contrasts may not correspond to a valid joint distribution. In this paper we present an efficient algorithm for detecting whether or not the inverse transform exists, and for computing it if it does.

In this paper, we discuss suppression for logistic regression model. Suppression for linear regression model was defined as the relationship among sums of squared for regression as well as correlation coefficients of. variables. Since it is not common to obtain simple correlation coefficient for binary response variable of logistic model, we consider cumulative logistic models with multinomial and ordinal response variables rather than usual logistic model. As number of category of a response variable for the cumulative logistic model gets collapsed into binary, it is found that suppressions for these logistic models are changed. These suppression results for cumulative logistic models are discussed and compared with those of linear model.

The logistic equation as usually formulated and applied to organism growth has a prescribed asymptote. Some applications require an asymptote depending on conditions during growth such as nutrition, temperature or irradiance. A logistic-based growth equation which fulfils this requirement has not, to-date, been available. A direct dependence of asymptote on growth conditions would be ineffective as well as scientifically incorrect. An indirect method of achieving the objective is suggested. The usual logistic asymptote becomes a state variable which can decrease, depending on degree of growth limitation, current organism mass and an additional parameter, D, representing development or differentiation. Early limitation has greater effect than late limitation. Duration of limitation is also important. The proposed modification of the logistic also moves mass at the inflexion point closer to asymptotic final mass; this could be valuable for many applications. An open-ended logistic-like growth model extends the range of applications of this valuable equation in the animal, plant and ecological sciences.

A generalized logistic distribution is proposed, based on the fact that the difference of two independent Gumbel-distributed random variables has the standard logistic distribution.

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Logistic regression is a powerful technique for fitting models to data with a binary response variable, but the models are difficult to interpret if collinearity, nonlinearity, or interactions are present. Besides, it is hard to judge model adequacy because there are few diagnostics for choosing variable transformations and no true goodness-of-fit test. To overcome these problems, this article proposes to fit a piecewise (multiple or simple) linear logistic regression model by recursively partitioning the data and fitting a different logistic regression in each partition. This allows nonlinear features of the data to be modeled without requiring variable transformations. The binary tree that results from the partitioning process is pruned to minimize a cross-validation estimate of the predicted deviance. This obviates the need for a formal goodness-of-fit test. The resulting model is especially easy to interpret if a simple linear logistic regression is fitted to each partition, because the tree structure...

We consider a form of generalized logistic distribution which is called extended type I generalized logistic distribution. Some theorems that relate the distribution to some other statistical distributions are established. A possible application of one of the theorems is included.

We can use the logistic model for categorical data when the response variables are binary data. In this paper we consider the problem of constructing the confidence intervals for logistic model in IJ2 contingency table. These constructions are simplified by applying logit transformation. This transforms the problem to consider linear form which called the logit model. After obtaining the confidence intervals for the logit model, the reverse transform is applied to obtain the confidence intervals for the logistic model.

We propose modified exact inferential methods in logistic regression model. Exact conditional distribution in logistic regression model is often highly discrete, and ordinary exact inference in logistic regression is conservative, because of the discreteness of the distribution. For the exact inference in logistic regression model we utilize the modified P-value. The modified P-value can not exceed the ordinary P-value, so the test of size based on the modified P-value is less conservative. The modified exact confidence interval maintains at least a fixed confidence level but tends to be much narrower. The approach inverts results of a test with a modified P-value utilizing the test statistic and table probabilities in logistic regression model.

Loop mediated isothermal amplification (LAMP) is a highly efficient, selective and rapid DNA amplification technique for genetic screening of pathogens. However, despite its popularity, there is yet no mathematical model to quantify the outcome and no well-defined metric for comparing results that are available. LAMP is intrinsically complex and involves multiple pathways for gene replication, making fundamental modelling nearly intractable. To circumvent this difficulty, an alternate, empirical model is introduced that will allow one to extract a set of parameters from the concentration versus time curves. A simple recipe to deduce the time to positive, Tp - a parameter analogous to the threshold cycling time in polymerase chain reaction (PCR), is also provided. These parameters can be regarded as objective and unambiguous indicators of LAMP amplification. The model is exemplified on Escherichia coli strains by using the two gene fragments responsible for vero-toxin (VT) production and tested against VT-producing (O157 and O45) and non-VT producing (DH5 alpha) strains. Selective amplification of appropriate target sequences was made using well established LAMP primers and protocols, and the concentrations of the amplicons were measured using a Qubit 2.0 fluorometer at specific intervals of time. The data is fitted to a generalized logistic function. Apart from providing precise screening indicators, representing the data with a small set of numbers offers significant advantages. It facilitates comparisons of LAMP reactions independently of the sampling technique. It also eliminates subjectivity in interpretation, simplifies data analysis, and allows easy data archival, retrieval and statistical analysis for large sample populations. To our knowledge this work represents a first attempt to quantitatively model LAMP and offer a standard method that could pave the way towards high throughput automated screening.

For a correctly assumed logistic dose–response curve, a number of authors have considered the various interval estimation methods for the median effective dose (ED 50 ). In this paper, we look at the performance of four large sample parametric methods and four bootstrap resampling approaches for the problem of constructing a confidence interval of the ED 50 and investigate the robustness of these methods when a logistic dose–response curve is incorrectly assumed. The underlying true dose–response curve studied is, respectively, either the probit model, the cubic logistic model or the asymmetric Aranda-Ordaz model.

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.

SUMMARY We test the logistic regression assumption under a case-control sampling plan. After reparameterisation, the assumed logistic regression model is equivalent to a two-sample semiparametric model in which the log ratio of two density functions is linear in data. By identifying this model with a biased sampling model, we propose a Kolmogorov-Smirnovtype statistic to test the validity of the logistic link function. Moreover, we point out that this test statistic can also be used in mixture sampling. We present a bootstrap procedure along with some results on simulation and on analysis of two real datasets.