**follow a logistic**- Under the BBL model, expected responses follow a logistic function which can be made equal to that of the Four Parameter Logistic (4PL) model. (umsystem.edu)
- Most populations do not grow exponentially, rather they follow a logistic model. (wikipedia.org)

**regression model**- Logistic model trees are based on the earlier idea of a model tree: a decision tree that has linear regression models at its leaves to provide a piecewise linear regression model (where ordinary decision trees with constants at their leaves would produce a piecewise constant model). (wikipedia.org)
- Its parameters can be related to covariates such as dose and gender through a regression model. (umsystem.edu)
- The asymptotic normality of maximum likelihood estimators (MLEs) is obtained even though the support of this non-regular regression model depends on unknown parameters. (umsystem.edu)
- For the binary case, a common approach is to apply Platt scaling, which learns a logistic regression model on the scores. (wikipedia.org)

**discrete**- If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic equations. (igi-global.com)
- Each model is a cubic two-dimensional discrete logistic-type equation with its own dynamical properties: stationary regime, periodicity, quasi-periodicity, and chaos. (igi-global.com)
- However, the model is a general one, and can be applied wherever discrete data are obtained with the intention of measuring a quantitative attribute or trait. (wikipedia.org)
- In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. (wikipedia.org)

**sigmoidal**- The logit (/ˈloʊdʒɪt/ LOH-jit) function is the inverse of the sigmoidal "logistic" function or logistic transform used in mathematics, especially in statistics. (wikipedia.org)

**probability**- Not all classification models are naturally probabilistic, and some that are, notably naive Bayes classifiers, decision trees and boosting methods, produce distorted class probability distributions. (wikipedia.org)
- In the Rasch model, the probability of a specified response (e.g. right/wrong answer) is modeled as a function of person and item parameters. (wikipedia.org)
- Specifically, in the original Rasch model, the probability of a correct response is modeled as a logistic function of the difference between the person and item parameter. (wikipedia.org)
- When a person's location on the latent trait is equal to the difficulty of the item, there is by definition a 0.5 probability of a correct response in the Rasch model. (wikipedia.org)
- Multinomial logistic regression is a particular solution to the classification problem that assumes that a linear combination of the observed features and some problem-specific parameters can be used to determine the probability of each particular outcome of the dependent variable. (wikipedia.org)
- Similarly, a model that predicts a probability of making a yes/no choice (a Bernoulli variable) is even less suitable as a linear-response model, since probabilities are bounded on both ends (they must be between 0 and 1). (wikipedia.org)
- For example, the case above of predicted number of beach attendees would typically be modeled with a Poisson distribution and a log link, while the case of predicted probability of beach attendance would typically be modeled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function. (wikipedia.org)
- In a generalized linear model (GLM), each outcome Y of the dependent variables is assumed to be generated from a particular distribution in the exponential family, a large range of probability distributions that includes the normal, binomial, Poisson and gamma distributions, among others. (wikipedia.org)

**Psychometrics**- In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession and market research because of their general applicability. (wikipedia.org)

**LogitBoost**- Specifically, if one considers AdaBoost as a generalized additive model and then applies the cost functional of logistic regression, one can derive the LogitBoost algorithm. (wikipedia.org)
- Specifically, given that we seek an additive model of the form f = ∑ t α t h t {\displaystyle f=\sum _{t}\alpha _{t}h_{t}} the LogitBoost algorithm minimizes the logistic loss: ∑ i log ( 1 + e − y i f ( x i ) ) {\displaystyle \sum _{i}\log \left(1+e^{-y_{i}f(x_{i})}\right)} Jerome Friedman, Trevor Hastie and Robert Tibshirani. (wikipedia.org)

**Rasch**- Linear logistic models with relaxed assumptions (LLRA) are a flexible tool for item-based measurement of change or multidimensional Rasch models. (springer.com)
- Testing the Rasch model. (springer.com)
- A Rasch model for partial credit scoring. (springer.com)
- The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. (wikipedia.org)
- The mathematical theory underlying Rasch models is a special case of item response theory and, more generally, a special case of a generalized linear model. (wikipedia.org)
- However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. (wikipedia.org)
- A central aspect of this divide relates to the role of specific objectivity, a defining property of the Rasch model according to Georg Rasch, as a requirement for successful measurement. (wikipedia.org)
- By requiring measures to remain the same (invariant) across different tests measuring the same thing, Rasch models make it possible to test the hypothesis that the particular challenges posed in a curriculum and on a test coherently represent the infinite population of all possible challenges in that domain. (wikipedia.org)
- A Rasch model is therefore a model in the sense of an ideal or standard that provides a heuristic fiction serving as a useful organizing principle even when it is never actually observed in practice. (wikipedia.org)
- The perspective or paradigm underpinning the Rasch model is distinct from the perspective underpinning statistical modelling. (wikipedia.org)
- The rationale for this perspective is that the Rasch model embodies requirements which must be met in order to obtain measurement, in the sense that measurement is generally understood in the physical sciences. (wikipedia.org)
- This key requirement is embodied within the formal structure of the Rasch model. (wikipedia.org)
- Consequently, the Rasch model is not altered to suit data. (wikipedia.org)
- The logit is also central to the probabilistic Rasch model for measurement, which has applications in psychological and educational assessment, among other areas. (wikipedia.org)

**psychometric model**- The purpose of the present chapter is to introduce a psychometric model for time-limit tests. (springer.com)
- Two approaches are available for the psychometric model of a CCT: classical test theory (CTT) and item response theory (IRT). (wikipedia.org)

**minimizes**- A linear programming model minimizes the sum of all container-related logistic costs throughout the entire network, including customs inspection, handling, and storage costs. (igi-global.com)

**multinomial**- Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit, maximum entropy (MaxEnt) classifier, conditional maximum entropy model. (wikipedia.org)
- Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently categorical, meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. (wikipedia.org)
- The multinomial logistic model also assumes that the dependent variable cannot be perfectly predicted from the independent variables for any case. (wikipedia.org)
- If the multinomial logit is used to model choices, it relies on the assumption of independence of irrelevant alternatives (IIA), which is not always desirable. (wikipedia.org)
- If the multinomial logit is used to model choices, it may in some situations impose too much constraint on the relative preferences between the different alternatives. (wikipedia.org)
- Other models like the nested logit or the multinomial probit may be used in such cases as they allow for violation of the IIA. (wikipedia.org)
- There are multiple equivalent ways to describe the mathematical model underlying multinomial logistic regression. (wikipedia.org)

**logit**- The logit model was introduced by Joseph Berkson in 1944, who coined the term. (wikipedia.org)
- The logit in logistic regression is a special case of a link function in a generalized linear model: it is the canonical link function for the Bernoulli distribution. (wikipedia.org)
- The inverse-logit function (i.e., the logistic function) is also sometimes referred to as the expit function. (wikipedia.org)
- In plant disease epidemiology the logit is used to fit the data to a logistic model. (wikipedia.org)
- Closely related to the logit function (and logit model) are the probit function and probit model. (wikipedia.org)
- In fact, the logit is the quantile function of the logistic distribution, while the probit is the quantile function of the normal distribution. (wikipedia.org)
- As a result, probit models are sometimes used in place of logit models because for certain applications (e.g., in Bayesian statistics) the implementation is easier. (wikipedia.org)

**additive**- But the distribution of responses differs from the classical 4PL model which has additive normal errors. (umsystem.edu)
- Additive logistic regression: a statistical view of boosting. (wikipedia.org)

**algorithm**- In computer science, a logistic model tree (LMT) is a classification model with an associated supervised training algorithm that combines logistic regression (LR) and decision tree learning. (wikipedia.org)

**parameter estimates**- This example creates data sets to contain parameter estimates that are computed by a nominal logistic regression analysis for a set of imputed data sets. (sas.com)
- Following the parameter estimates table, PROC LOGISTIC displays the odds ratio estimates for those variables that are not involved in any interaction terms. (sas.com)

**conditional**- Inference for such models becomes possible within a framework of conditional maximum likelihood estimation. (springer.com)

**mathematical**- The mathematical form of the model is provided later in this article. (wikipedia.org)
- Since George Kingsley Zipf (the well-known "Zipf's Law"), a large number of mathematical models of the relation between rank and frequency has been proposed. (wikipedia.org)

**probabilistic**- Binary probabilistic classifiers are also called binomial regression models in statistics. (wikipedia.org)
- Some classification models, such as naive Bayes, logistic regression and multilayer perceptrons (when trained under an appropriate loss function) are naturally probabilistic. (wikipedia.org)
- Other models such as support vector machines are not, but methods exist to turn them into probabilistic classifiers. (wikipedia.org)
- This situation does not differ from that in the natural sciences, which have since long abandoned the old deterministic and causal views of the world and replaced them by statistical/probabilistic models. (wikipedia.org)

**illustrate**- In this paper we introduce and illustrate new functionality from the R package eRm for fitting, comparing and plotting of LLRA models for dichotomous and polytomous responses with any number of time points, treatment groups and categorical covariates. (springer.com)
- To illustrate this phenomenon, we analyze a real data set using a Lagrange multiplier test for the specification of the model. (springer.com)

**estimates**- These estimates are then combined to generate valid statistical inferences about the model parameters. (sas.com)

**odds**- I am trying to develop a plot a figure in which I would like to show the odds ratios obtained from a logistic model. (ethz.ch)
- Such a model is a log-odds or logistic model. (wikipedia.org)

**Verstralen**- Verhelst N.D., Verstralen H.H.F.M., Jansen M.G.H. (1997) A Logistic Model for Time-Limit Tests. (springer.com)

**covariance**- Equivalent models in covariance structure analysis. (springer.com)
- Specification searches in covariance structure modeling. (springer.com)

**statistical models**- Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. (wikipedia.org)

**Linear**- Linear logistic models for change. (springer.com)
- Rusch T., Maier M.J., Hatzinger R. (2013) Linear Logistic Models with Relaxed Assumptions in R. In: Lausen B., Van den Poel D., Ultsch A. (eds) Algorithms from and for Nature and Life. (springer.com)
- This paper is about the Linear Logistic Test Model (LLTM). (springer.com)
- The linear logistic test model. (springer.com)
- Does any body have any insight or experience running a non-inferiority test based on multiple linear or logistic regression. (talkstats.com)
- The two common way of designing reverse logistics network are the Mixed Integer Linear Programing (MILP) and Mixed Integer Non-Linear Programing (MINLP) methods, where the objective function, decision variables and constraint have to be defined This model is a two-level location problem with three type of facilities, integrated forward and reverse flow of goods. (wikipedia.org)
- Objective function: minimizing linear cost function including fix and variable costs Decision variables: location of manufacturer and distribution centeramount of production demand quantity of returned used products Constraints: satisfaction of the demand opening of facilities This model take into account just reverse flow of goods. (wikipedia.org)
- In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. (wikipedia.org)
- The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. (wikipedia.org)
- This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model). (wikipedia.org)
- Such a model is termed an exponential-response model (or log-linear model, since the logarithm of the response is predicted to vary linearly). (wikipedia.org)
- Generalized linear models cover all these situations by allowing for response variables that have arbitrary distributions (rather than simply normal distributions), and for an arbitrary function of the response variable (the link function) to vary linearly with the predicted values (rather than assuming that the response itself must vary linearly). (wikipedia.org)

**function**- model evaluates the four-parameter logistic function and its gradient. (psu.edu)
- Robust optimization: This method is calibrating the model in that way to minimize the deviation of the values of the objective function at each scenario. (wikipedia.org)
- Imagine, for example, a model that predicts the likelihood of a given person going to the beach as a function of temperature. (wikipedia.org)

**measurement**- The use of cross-classification multilevel logistic models will be illustrated with an educational measurement application. (ed.gov)

**evaluate**- a numeric vector of values at which to evaluate the model. (psu.edu)
- Multi-agent systems modelling approach to evaluate urban motorways for city logistics J.S.E. Teo, E. Taniguchi and A.G. Qureshi 5. (bookdepository.com)

**assumes**- Classical test theory assumes a state model because it is applied by determining item parameters for a sample of examinees determined to be in each category. (wikipedia.org)
- The classification groups will need to be more or less arbitrarily defined along the continuum, such as the use of a cutscore to demarcate masters and nonmasters, but the specification of item parameters assumes a trait model. (wikipedia.org)

**prediction model**- The key question is how best to assess and quantify the improvement in risk prediction offered by new biomarkers or more basically how to assess the performance of a risk prediction model. (diva-portal.org)
- As an example, a prediction model might predict that 10 degree temperature decrease would lead to 1,000 fewer people visiting the beach is unlikely to generalize well over both small beaches (e.g. those where the expected attendance was 50 at a particular temperature) and large beaches (e.g. those where the expected attendance was 10,000 at a low temperature). (wikipedia.org)
- The problem with this kind of prediction model would imply a temperature drop of 10 degrees would lead to 1,000 fewer people visiting the beach, a beach whose expected attendance was 50 at a higher temperature would now be predicted to have the impossible attendance value of −950. (wikipedia.org)

**data**- Beyond data, Rasch's equations model relationships we expect to obtain in the real world. (wikipedia.org)
- Models are most often used with the intention of describing a set of data. (wikipedia.org)
- Data analysed using the model are usually responses to conventional items on tests, such as educational tests with right/wrong answers. (wikipedia.org)
- Statistical Methods for psychology include development and application statistical theory and methods for modeling psychological data. (wikipedia.org)

**classification**- The combination of a multilevel model with random person effects and one with random item effects leads to a cross-classification multilevel model, which can be of interest for IRT applications. (ed.gov)

**latent trait**- The modern test theory is based on latent trait model. (wikipedia.org)

**distribution**- The beta distribution is a simple and flexible model in which responses are naturally confined to the finite interval (0,1). (umsystem.edu)
- A new derivation of the logistic distribution. (springer.com)
- The huge expansion in international trade during the last 50 years (facilitated and propelled by the invention of the standardized container as a medium of transport) has led to overcrowding of port facilities world-wide and growing pains in logistic systems handling the customs examination, storage and distribution of containers. (igi-global.com)
- In this model the products are gathered from the consumers and transferred back to the producers, hence the direction of the flow in the distribution supply chain is reversed and the model is expanded with the recovery center. (wikipedia.org)

**responses**- In contrast, the BBL model naturally has bounded responses and inhomogeneous variance. (umsystem.edu)
- In IRT models, responses are explained on the basis of person and item effects. (ed.gov)

**probabilities**- That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc. (wikipedia.org)

**equivalent ways**- We demonstrate that there are infinitely many equivalent ways to specify a model. (springer.com)

**species**- As three basic relationships between two species are present in nature, namely symbiosis, predator-prey, and competition, three different models are obtained. (igi-global.com)

**method**- They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. (wikipedia.org)

**advantages**- We show the BBL model has advantages over the 4PL model. (umsystem.edu)
- The model highlights the advantages that shippers may enjoy in routing their containers from the seaports to their final hinterland destinations via one or several interports. (igi-global.com)

**criterion**- Regression analysis, Multiple regression analysis, Logistic regression is used as an estimate of criterion validity. (wikipedia.org)

**economics**- In order to modelling reverse logistics network from an economics point of view, the following simplified reverse logistics system has to be set. (wikipedia.org)

**Variable**- In most contexts, the parameters of the model characterize the proficiency of the respondents and the difficulty of the items as locations on a continuous latent variable. (wikipedia.org)

**test**- PROC LOGISTIC displays a table of the Type 3 analysis of effects based on the Wald test ( Output 60.2.2 ). (sas.com)
- This Lagrange multiplier test is similar to the modification index used in structural equation modeling. (springer.com)
- Identifiability of nonlinear logistic test models. (springer.com)

**1987**- Criminologist Lynch (1987), using "domain-specific" models, demonstrates that occupation-related activities generally have a stronger impact on the risk of victimization at work than sociodemographic characteristics. (wikipedia.org)

**population**- This analytic solution is useful in analyzing the behavior of population models. (wikipedia.org)
- The approximation is particularly useful in models with a very large state space, such as stochastic population models. (wikipedia.org)

**Binary**- This allows the choice of K alternatives to be modeled as a set of K-1 independent binary choices, in which one alternative is chosen as a "pivot" and the other K-1 compared against it, one at a time. (wikipedia.org)

**application**- Comparing consumer preferences for color and nutritional quality in maize: Application of a semi-double-bound logistic model on urban consumers in Kenya ," Food Policy , Elsevier, vol. 33(4), pages 362-370, August. (repec.org)
- Application of exact route optimization for the evaluation of a city logistics truck ban scheme Ali Gul Qureshi, Eiichi Taniguchi, Russell G. Thompson and Joel S.E. Teo 3. (bookdepository.com)
- Model of debris collection operation after disasters and its application in urban area Andie Pramudita and Eiichi Taniguchi 9. (bookdepository.com)

**collaboration**- We also propose that these models could be useful for thinking in the different interactions happening in the economic world, as for instance for the competition and the collaboration between corporations. (igi-global.com)
- Collaboration in urban logistics: motivations and barriers Lindawati, Johan van Schagen, Mark Goh and Robert de Souza 12. (bookdepository.com)

**response**- The Ballooned Beta-logistic (BBL) model expands the response boundaries from (0,1) to (L,U), where L and U are unknown parameters. (umsystem.edu)
- An item response model with internal restrictions on item difficulty. (springer.com)
- The Item Response Theory has three models. (wikipedia.org)

**methods**- Discrimination, calibration, and added predictive value have been recently suggested to be used while comparing the predictive performances of the predictive models' with and without novel biomarkers.Objectives: Lack of user-friendly statistical software has restricted implementation of novel model assessment methods while examining novel biomarkers. (diva-portal.org)

**Example**- A reasonable model might predict, for example, that a change in 10 degrees makes a person two times more or less likely to go to the beach. (wikipedia.org)

**analysis**- The overparameterized analysis of variance Model. (springer.com)
- The main objective is to maximize profit by determining the optimal number of facilities in order to: collection point be close to the consumers returning process be simple collection period be appropriate Sensitivity analysis: Through sensitivity analysis it can be tested how the output of the model will be changed if the decision variables such as the returned amount, number of disassembly and cost are varying. (wikipedia.org)

**construct**- Furthermore, these models could be considered as the basic ingredients to construct more complex interactions in the ecological and economic networks. (igi-global.com)

**items**- In a similar way, the effects of the items can be studied as random parameters, yielding multilevel models with a within-item part and a between-item part. (ed.gov)
- It means that the used items are gathered from consumers, transported back to plants and after remanufacturing get into the logistics network of new products. (wikipedia.org)

**partial**- Extending rating scale and partial credit model for assessing change. (springer.com)

**change**- An implication is that there may well be many ways to change the specification of a given LLTM and achieve the same improvement in model fit. (springer.com)

**authors**- Mathematically, the authors identify the "interport model" as an extension of the conventional transshipment problem in a hub-and-spokes configuration with the interport treated as a novel kind of hub. (igi-global.com)