General Logistic Model Research Articles

Debt Intolerance: Threshold Level and Composition*

AbstractFiscal vulnerabilities depend on both the level and composition of government debt. This study examines the role of debt thresholds and debt composition in driving the nonlinear behaviour of long‐term interest rates through a novel approach, a panel smooth transition regression with a general logistic model. The main findings are threefold. First, the impact of the expected public debt level on interest rates rises exponentially when the share of foreign private holdings exceeds approximately 20% of government debt denominated in local currency. Second, if the public debt level exceeds a certain level, an increase in foreign private holding of government debt could raise interest rates, offsetting the downward pressure from higher market liquidity. Third, out‐of‐sample forecasts of this novel non‐linear model are more accurate than those of previous methods.

Time-dependent probability density function for general stochastic logistic population model with harvesting effort

We derive and analyze the time-dependent probability density function for the number of individuals in a population at a given time in a general logistic population model with harvesting effort using the Fokker–Planck equation. The time-dependent probability density function (obtained as the unique principal solution of the Fokker–Planck equation corresponding to certain initial value and boundary conditions) is used to describe how the distribution of the population process changes with time. We assume the environment is randomly varying and the population is subject to a continuous spectrum of disturbances, with fluctuations in the intrinsic growth rate and the harvesting effort. The randomness is expressed as independent white noise processes. The effect of changes in the intrinsic growth rate, harvesting effort, and noise intensities on the distribution is investigated. In addition, conditions for the existence of optimal harvesting policy are obtained using properties of the time-dependent probability density function. The results obtained in this work are validated using population and published parameters.

Study of a factored general logistic model of population dynamics with inter- and intraspecific interactions

The logistic equation is the simplest way to limit the growth in population dynamics. When ecological interactions come into play different types of models can be found, e.g. for consumer-resource systems the generalized Lotka–Volterra equation is widely used to model direct competition or predator–prey systems, and for mutualistic systems a functional response that limits the unbounded growth due to the mutual benefit is needed (usually Holling’s type II). Based on a recent general model of population dynamics with intraspecific interactions we present a factored general logistic model of population dynamics with inter- and intraspecific interactions. A major advantage of this model is that it can be used for any type of interspecific ecological interaction and also for beneficial or detrimental intraspecific interaction, and always in a bounded way. In this study we write a general logistic model in a factored way to obtain the stationary solutions by a system of simple linear equations and we formulate the analytical expression for the Jacobian matrix of all the stationary solutions for an arbitrary number of populations. We also show that this simple model can be used to represent complex ecological systems; as an illustration we study some examples such as a stable direct competition with intraspecific cooperation, a predator–prey system with cooperative preys, a mutualism with harmful intraspecific interactions and a real bacterial system with 4 populations.

A General Three-Parameter Logistic Model With Time Effect.

Within the framework of item response theory, a new and flexible general three-parameter logistic model with response time (G3PLT) is proposed. The advantage of this model is that it can combine time effect, ability, and item difficulty to influence the correct-response probability. In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden's model. In addition, the Metropolis–Hastings within Gibbs sampling algorithm is employed to estimate the model parameters. Based on Markov chain Monte Carlo output, two Bayesian model assessment methods are used to assess the goodness of fit between models. Finally, two simulation studies and a real data analysis are performed to further illustrate the advantages of the new model over the traditional three-parameter logistic model.

Development of a general logistic model for disease risk prediction using multiple SNPs

Human diseases are usually linked to multiloci genetic alterations, including single‐nucleotide polymorphisms (SNPs). Methods to use these SNPs for disease risk prediction (DRP) are of clinical interest. DRP algorithms explored by commercial companies to date have tended to be complex and led to controversial prediction results. Here, we present a general approach for establishing a logistic model‐based DRP algorithm, in which multiple SNP risk factors from different publications are directly used. In particular, the coefficient β of each SNP is set as the natural logarithm of the reported odds ratio, and the constant coefficient β0 is comprehensively determined by the coefficient and frequency of each SNP and the average disease risk in populations. Furthermore, homozygous SNP is considered a dummy variable, and the SNPs are updated (addition, deletion and modification) if necessary. Importantly, we validated this algorithm as a proof of concept: two patients with lung cancer were identified as the maximum risk cases from 57 Chinese individuals. Our logistic model‐based DRP algorithm is apparently more intuitive and self‐evident than the algorithms explored by commercial companies, and it may facilitate DRP commercialization in the era of personalized medicine.

Mathematical Model for Malaria Transmission and Chemical Control with Human-Related Activities

In this paper effect of insecticides has been studied for the control of vector-borne diseases, like malaria. A nonlinear SIS mathematical model has been proposed and analyzed for transmission of malaria caused by infected mosquito population on susceptible human population using chemicals to control the disease. It is further assumed that susceptible human population becomes infected by direct contact with vector mosquitoes. The mosquito population density is assumed to be governed by general logistic model. It is found that model exhibits three nonnegative equilibria, namely mosquito and disease-free equilibrium \(E_{0} ,\) mosquito persistence and disease-free equilibrium \(E_{1}\) and endemic equilibrium \(E^{*}\). The model is analyzed by using local and global stability theory of differential equations and numerical simulation.

Fisher information matrix of binary time series

A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for time series with short length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed from the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T. Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that, as T tends to infinity, the exact Fisher information matrix approaches the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to provide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix.

Age, player position and 2 min suspensions were associated with match injuries during the 2017 Men’s Handball World Championship (France)

AimTo study the association between player characteristics, technical components of the game and the risk of match injuries during the 2017 Men’s Handball World Championship.MethodsTeam physicians of the participating teams...

Persistence and extinction in general non-autonomous logistic model with delays and stochastic perturbation

This is a continuation of the paper Liu and Wang (2012) [14]. Firstly, we consider a general non-autonomous logistic model with delays and stochastic perturbation. Then sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Finally, numerical simulations are introduced to support the theoretical analysis results.

Asymptotic properties and simulations of a stochastic logistic model under regime switching

Taking both white noise and colored environmental noise into account, a general stochastic logistic model under regime switching is proposed and studied. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence and global attractivity are established. The critical number between weak persistence and extinction is obtained. Moreover, some simulation figures are introduced to illustrate the main results.

Biometry and sexual maturity in a sample of Colombian schoolchildren from El Yopal

Background: Biometric information obtained from cross-sectional studies works as a mirror of individual and collective life conditions at a given moment and allows assessment of secular trends in growth.Aim: The purpose of this study was to evaluate growth and growth velocity for height and weight, to determine the BMI and the sexual maturation characteristics of a pre-selected urban sample of subjects from El Yopal and to compare the results with those from others countries.Subjects and methods: In 2000–2001, 1039 schoolchildren (517 girls and 522 boys) were evaluated in the age range of 6–18 years. Low, medium and high socio-economic status (SES) were determined from monthly family income. Sexual development (Tanner-Whitehouse scale) and age of menarche (status quo method) were also determined. The LMS method was used to establish biometric centiles and the general logistic model was used to establish the median age for different stages of puberty.Results: Height, Girls: 155.4 cm, at 17.3 years with maximum yearly increment (myi) of 6.24 cm, at 11.10 years. Boys: 166.9 cm, at 18.0 years with myi of 6.48 cm, at 13.60 years. Weight, Girls: 52.5 kg, at 17.3 years with myi of 4.92 kg, at 11.98 years. Boys: 59.2 kg, at 18.0 years with myi of 4.88 kg, at 12.99 years. BMI at 18.0 years, Girls: 22.16 kg/m2, Boys: 21.05 kg/m2. Female puberty by stage of breast B2 began at 10.21 ± 1.16 years (mean ± SD). Male puberty by stage of genitalia G2 began at 11.53 ± 1.07 years.Conclusion: The findings show lower height values and lower weight values, except for the Cuban reference, for both sexes; an early onset of puberty in girls and a prolonged puberty in boys when compared with other Caribbean, Central and South American females and males.

MATHEMATICAL MODELING AND ANALYSIS OF THE SPREAD OF CARRIER DEPENDENT INFECTIOUS DISEASES: EFFECTS OF CUMULATIVE DENSITY OF ENVIRONMENTAL FACTORS

In this paper, a nonlinear mathematical model with immigration for carrier dependent infectious diseases is proposed and analyzed by considering explicitly the cumulative effect of environmental factors, which are conducive to the growth of carrier population. It is assumed that the density of carrier population is governed by a general logistic model. It is assumed further that the growth rate per capita and the modified carrying capacity of carrier population increase as the cumulative density of environmental factors, governed by population density dependent growth equation, increases. It is shown that as the parameters governing environmental factors increase, the number of infectives in the population increases. It is also found that due to immigration, the disease becomes more endemic.

Continuous response functions for quantifying the strength of edge effects

Summary Ecological boundaries are a dominant feature of human‐modified landscapes and have been the subject of numerous empirical studies. Robust statistical methods for determining the strength of edge effects are a vital requirement for the effective management of species that are negatively affected by habitat boundaries in heavily fragmented landscapes, but development of such methods has been slow. We define edge effects as being composed of two complementary, and statistically definable, components: magnitude (the degree of difference in response values between patch and matrix interiors) and extent (the distance over which the difference in response values can be detected). We present a statistical approach to rigorously delineate edge‐effect magnitude and extent. Our approach adapts a form of the general logistic model to describe continuous response functions for any biotic or abiotic variable across ecological boundaries from the landscape matrix into focal patch habitats. The model describes sigmoid and unimodal response functions that have been both theoretically predicted and empirically demonstrated. We use the second derivatives of the functions as an objective means to calculate the magnitude and extent of edge effects, and present a bootstrap technique for calculating confidence intervals around these values. Synthesis and applications. Our results show clearly that edge‐effect magnitude and extent are not necessarily correlated, and therefore provide quantitatively different, and complementary, information about the strength of edge effects. Both effect magnitude and extent can be easily used for cross‐study comparisons, either by directly comparing the absolute values of response variables in the patch and matrix, or by converting those values to a percentage change. Furthermore, this method provides a management tool for more accurately predicting the presence, spatial location and utilization of core habitat by species in fragmented landscapes.

Linkage mapping methods applied to the COGA data set: Presentation Group 4 of Genetic Analysis Workshop 14

Presentation Group 4 participants analyzed the Collaborative Study on the Genetics of Alcoholism data provided for Genetic Analysis Workshop 14. This group examined various aspects of linkage analysis and related issues. Seven papers included linkage analyses, while the eighth calculated identity-by-descent (IBD) probabilities. Six papers analyzed linkage to an alcoholism phenotype: ALDX1 (four papers), ALDX2 (one paper), or a combination both (one paper). Methods used included Bayesian variable selection coupled with Haseman-Elston regression, recursive partitioning to identify phenotype and covariate groupings that interact with evidence for linkage, nonparametric linkage regression modeling, affected sib-pair linkage analysis with discordant sib-pair controls, simulation-based homozygosity mapping in a single pedigree, and application of a propensity score to collapse covariates in a general conditional logistic model. Alcoholism linkage was found with > or =2 of these approaches on chromosomes 2, 4, 6, 7, 9, 14, and 21. The remaining linkage paper compared the utility of several single-nucleotide polymorphism (SNP) and microsatellite marker maps for Monte Carlo Markov chain combined oligogenic segregation and linkage analysis, and analyzed one of the electrophysiological endophenotypes, ttth1, on chromosome 7. Linkage was found with all marker sets. The last paper compared the multipoint IBD information content of several SNP sets and the microsatellite set, and found that while all SNP sets examined contained more information than the microsatellite set, most of the information contained in the SNP sets was captured by a subset of the SNP markers with approximately 1-cM marker spacing. From these papers, we highlight three points: a 1-cM SNP map seems to capture most of the linkage information, so denser maps do not appear necessary; careful and appropriate use of covariates can aid linkage analysis; and sources of increased gene-sharing between relatives should be accounted for in analyses.

A re-examination of the 1966 Kalven-Zeisel study of judge-jury agreements and disagreements and their causes

The classic study, The American Jury, by Kalven and Zeisel showed that trial judges agreed with juries in criminal cases about 75% to 80% of the time. Kalven and Zeisel observed that fewer disagreements occurred in cases where the evidence was clear than when it was close. They found that the juries were more lenient and called these normal disagreements. They also explored the possible factors that determined the normal and other disagreements. Kalven and Zeisel quantified the effect of a factor using a measure now referred to as the population attributable risk. Here, the factor attributable risk (FAP) measure is adopted as it focuses on those cases where that factor is present. The FAP is the measure relied on in product liability and related tort cases to estimate the fraction of cases in the exposed population that are attributable to the exposure under study. The advent of readily available computer packages enables us to use logistic models to reanalyse the data and estimate the effect each factor has on the odds of a disagreement. Thus, while the original authors showed that the presence/absence of a prior record plays a key role in creating a disagreement between the judge and the jury, now one can estimate the increased odds of a disagreement it generates controlling for other variables. From this quite general logistic model it is seen that the strength that ‘absence of a prior record’ had in the original study is partly due to the fact that it is a significant factor in determining whether the jury views the defendant sympathetically. The weight given to the various explanatory variables also depends on the seriousness of the crime. In serious crimes, both a superior defence counsel and a prior record are influential determinants of whether there is a disagreement. For lesser crimes, however, a jury’s sympathetic view of the defendant is the main factor creating a disagreement between the judge and jury. The re-analysis demonstrates the insight that logistic regression and related generalized linear models can provide as well as the importance of utilizing the most appropriate measure of attributable risk to evaluate the role of the various explanatory factors.

Modeling and Analysis of the Spread of Carrier Dependent Infectious Diseases with Environmental Effects

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

The evolution of demand and pricing for internet services

The aim of this paper is to analyse and to estimate the demand for internet dial-up access. The study is both regional and national, giving rise to a static and to a dynamic analysis. The static analysis permits, through a multiple regression model, to analyse the socioeconomic drivers of the demand and to identify potential new market segments. The national analysis has requested the implementation of a general logistic evolution model, subsequently applied to Italian data. The model allows the monthly dial-up traffic values to be forecast, and permits the measurement of both the existing link between internet tariffs and traffic and the influence of different pricing policies on internet traffic and revenues.

Bayesian spatial models for small area estimation of proportions

This article presents a logistic hierarchical model approach for small area prediction of proportions, taking into account both possible spatial and unstructured heterogeneity effects. The posterior distributions of the proportion predictors are obtained via Markov Chain Monte Carlo methods. This automatically takes into account the extra uncertainty associated with the hyperparameters. The procedures are applied to a real data set and comparisons are made under several settings, including a quite general logistic hierarchical model with spatial structure plus unstructured heterogeneity for small area effects. A model selection criterion based on the Expected Prediction Deviance is proposed. Its utility for selecting among competitive models in the small area prediction context is examined.

Generalized Covariance-Adjusted Discriminants: Perspective and Application

When discriminant analysis is used in practice for assessing the usefulness of diagnostic markers, the lack of control over covariates motivates the need for their adjustment in the analysis. This necessity for adjustment arises especially when the researcher's aim is classification based on a set of diagnostic markers and is not based on a set of covariates for which there exists known heterogeneity among the subjects with respect to the groups under consideration. The traditional covariance-adjusted approach is restrictive for such applications in that they assume linear covariates and a normal distribution for the the feature vector. Further, there is no available method for variable selection in using such covariance-adjusted models. In this paper, we generalize the traditional covariance-adjusted model to a general normal and logistic model, where these generalized models not only relax the distributional assumptions on the feature vector but also allow for nonlinear covariates. Exact and asymptotic tests are also derived for the problem of variable selection for these new models. The methodology is illustrated with both simulated data and an actual data set from a psychiatric study on using the Social Rhythm Metric for patients with anxiety disorders.

Multinomial response models

Consider a multinomial response model with (k+1) outcomes and p explanatory variables. The general logistic model for the multinomial probabilities results in a matrix of sufficient statistics having kp elements. The means and variances of the sufficient statistics are derived (under the null hypothesis) and can be written as a Kronecker product. Since the sufficient statistics have asymptotic normal distributions, large sample tests can be derived which uses a chi-square statistic. The conditional test for testing if a single explanatory variable affects the response is derived.