Top Research Papers on Logistic Regression

Applied Logistic Regression, Third Edition provides an easily accessible introduction to the logistic regression model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables.

The purpose of this investigation was to illustrate, using a substantive example, the potential increase in power gained from an ordinal instead of a dichotomous specification for an inherently continuous response.

Although logistic regression models are widely used in multivariable analyses with dichotomous outcomes, many of their features, which can be very helpful tools in better understanding the data, are often underutilized. In addition to the widely used and reported odds ratios and p-values, PROC LOGISTIC generates a plethora of statistics from which one can gain further insight, make stronger analytical inferences, and more easily identify errors in the model construction. Model options will be explored, and resulting outputs from real-world examples will be explained in detail. Topics covered i...

Linear regression modeling is well suited to predicting continuous data where the outcome y is a real number (i.e., y ∈ ℝ). Logistic regression is a modeling technique for binary outcomes (i.e., yes/no, true/false, 1/0). Such outcomes are needed in many domains: public health officials might want to know the likelihood that a person will contract COVID-19 if she is a doctor in Ontario;a hospital would like to know if a discharged patient is more likely to be readmitted or not;a company would like to know if a customer visiting its website is more likely to order;a bank would like to know if a ...

This technical note presents the reason for using a binomial logic regression in marketing applications and a consumer-utility-based behavioral rationale is presented for the applicability of the binomial logistic regression for modeling dummy variables.

Logistic regression has probably been underutilized in clinical investigations of personality because of its relatively recent development (dictated by the need for computer programs to obtain maximum likelihood estimates), and the fact that use has been largely confined to the fields of biostatistics, epidemiology, and economics Its use should be given serious consideration when the outcome of interest is dichotomous (or polychotomous) in nature and the predictors of interest may be categorical or continuous. The logit transformation is quite tractable mathematically, and it embodies the noti...

It was commented that reoperation was nearly twice as likely when the tumour had a carcinoma in situ component recorded, and the association between breast reoperation and patients’ characteristics was examined.

Predicting dichotomous outcomes is central to epidemiologic science and clinical care and is used to describe and test the relationship between a dichotomyous outcome and one or more potentially predictive variables.

Like contingency table analyses and 2 tests, logistic regression allows the analysis of dichotomous or binary outcomes with 2 mutually exclusive levels.1 However, logistic regression permits the use of continuous or categorical predictors and provides the ability to adjust for multiple predictors. This makes logistic regression especially useful for analysis of observational data when adjustment is needed to reduce the potential bias resulting from differences in the groups being compared.2 Use of standard linear regression for a 2-level outcome can produce very unsatisfactory results. Predict...

1 Many statistical tests require the dependent (response) variable to be continuous so a different set of tests are needed when the dependent variable is categorical. One of the most commonly used tests for categorical variables is the Chi-squared test which looks at whether or not there is a relationship between two categorical variables but this doesn’t make an allowance for the potential influence of other explanatory variables on that relationship. For continuous outcome variables, Multiple regression can be used for

The risks of two kinds of project management are compared and the goal of this research is to model the project success in case of different types of projects and project management approaches.

In many ways, binomial logistic regression is similar to linear regression, with the exception of the measurement type of the dependent variable (i.e., linear regression uses a continuous dependent variable rather than a dichotomous one). However, unlike linear regression, you are not attempting to determine the predicted value of the dependent variable, but the probability of being in a particular category of the dependent variable given the independent variables. An observation is assigned to whichever category is predicted as most likely. As with other types of regression, binomial logistic...

Multiple Logistic Regression Just as in OLS regression, logistic models can include more than one predictor. The analysis options are similar to regression. One can choose to select variables, as with a stepwise procedure, or one can enter the predictors simultaneously, or they can be entered in blocks. Variations of the likelihood ratio test can be conducted in which the chi-square test (G) is computed for any two models that are nested. Nested models are models in which only a subset of predictors from the full model are included. A chi-square test is not valid unless the two models compared...

A new regression method called Kappa regression is introduced to model conditional probabilities and is based on Dombi’s Kappa function, which is well known in statistics.

Abstract Classification procedures are useful for the prediction of a response (or outcome) as a result of knowledge of the levels of one or more independent (or predictor) variables. The procedure is said to classify the (possibly multivariate) observation to a level of the response variable. An example might be the prediction of whether an individual will be well, suffer a nonfatal heart attack, or suffer a fatal heart attack. This prediction might be made on the basis of the levels of various independent variables, such as weight, blood pressure, and serum cholesterol, to name a few. The th...

Methods of estimating the coefficients in the model and procedures for hypothesis testing are considered, and the correspondence of the coefficients of the logistic regression model to the odds ratio is noted along with methods for computing point estimates and confidence intervals for the odds ratios.

This book discusses the normal model foundation of the Binomial Model, the nature and Scope of Overdispersion, and how to model and estimate these phenomena.

The focus of this document is on situations in which the outcome variable is dichotomous, although extension of the techniques of LRA to outcomes with three or more categories is possible.

It is shown how periodic logistic regression models can be fitted simultaneously to several groups of data, taking into account that the groups may exhibit similar (but not identical) cyclic patterns.

A review is given of the development of logistic regression as a multi-purpose statistical tool. A historical introduction shows several lines culminating in the unifying paper of Cox (1966), in which theory as developed in the field of bio-assay is shown to be applicable to designs as discriminant-analysis and case-control study. A review is given of several designs all leading to the same analysis. The link is made with epidemiological literature. Several optimization criteria are discussed that can be used in the case of more observations per cell, namely maximum likelihood, m...

Logistic regression has, in recent years, become the analytic technique of choice for the multivariate modeling of categorical dependent variables. Nevertheless, for many potentird users this procedure is still relatively arcane. This artile is therefore designed to render this technique more accessible to practicing researchers by comparing it, where possible, to linear regression. I will begin by discussing the modeling of a binary dependent variable. Then I will show the modeling of polytomous dependent variables, considering cases in which the values are alternately unordered, then ordered...

An algorithm for training a logistic regression model on nonstationary classification problems based on maximising the evidence of updated predictions is described and illustrated on a number of synthetic problems.

The method, which is based on the use of grayscale graphics to visualize contributions to a likelihood function, provides an analog of a scatterplot for logistic regression, as well as probit analysis.

A negative result is shown, namely, that no strongly sublinear sized coresets exist for logistic regression, and to deal with intractable worst-case instances, a complexity measure $\mu(X)$ is introduced, which quantifies the hardness of compressing a data set for Logistic regression.

Simple and multiple linear regression models study the relationship between a single continuous dependent variable Y and one or multiple independent variables X, respectively, using the logistic model and the probit model.

An efficient optimization method using non-linear conjugate gradient (CG) descent is proposed, which employs the optimized step size without exhaustive line search, which significantly reduces the number of iterations, making the whole optimization process fast.

This work uses a different approach called the logistic regression that does not require computing the p-value and still be able to localize the regions of brain network differences and performs the classification at each edge level.

In this paper a review will be given of some methods available for modelling relationships between categorical response variables and explanatory variables. These methods are all classed under the name polytomous logistic regression (PLR). Models for PLR will be presented and compared; model parameters will be tested and estimated by weighted least squares and by likelihood. Usually, software is needed for computation, and available statistical software is reported. An industrial problem is solved to some extent as an example to illustrate the use of PLR. The paper is concluded by a discuss...

Stochastic Gradient Descent and 2-Norm Regularization techniques are implemented and a new trick of modifying Sigmoid transfer function in the training stage is described and implemented, which is shown could help reducing overfitting as well.

Multinomial logistic regression is used to predict categorical placement in or the probability of category membership on a dependent variable based on multiple independent variables. The independent variables can be either dichotomous (i.e., binary) or continuous (i.e., interval or ratio in scale). Multinomial logistic regression is a simple extension of binary logistic regression that allows for more than two categories of the dependent or outcome variable. Like binary logistic regression, multinomial logistic regression uses maximum likelihood estimation to evaluate the probability of catego...

Multinomial logistic regression (often just called 'multinomial regression') is used to predict a nominal dependent variable given one or more independent variables. It is sometimes considered an extension of binomial logistic regression to allow for a dependent variable with more than two categories. As with other types of regression, multinomial logistic regression can have nominal and/or continuous independent variables and can have interactions between independent variables to predict the dependent variable.

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Multinomial logistic regression is an extension of this approach to situations where the response variable is categorical and has more than two possible values.

Response is a Bernoulli random variable with parameter denoting the ] 1 probability of " success ". We have the model ] oe  oe 3 3 3 3

In this paper, we consider the logistic regression model with an integrated regressor driven by a general linear process. In particular, we derive the limit distributions of the nonlinear least squares (NLS) estimators and their t-ratios of the parameters in the model. It is shown that the NLS estimators are generally not efficient. Moreover, the t-ratios for the level parameters have limit distributions that are nonnormal and dependent upon nuisance parameters, due to the asymptotic correlation between the innovations of the regressor and the regression errors. We propose an efficient NLS pro...

As a consultant, I am always on the lookout for new books that help me do my job better. Iwould recommend practitioners of regression, that is, probably most of us, to read and use this book. Anthony Atkinson and Marco Riani develop a novel methodology for examining the effect each observation has on the Ž tted regression model. Robust Ž tting procedures are combined with regression diagnostics, graphics, and a “forward” processing through the observations to provide a new way of identifying in uential and/or outlier observations while simultaneously determining the best Ž tting model. The me...

This paper describes the origins of the logistic function, its adoption in bio-assay, and its wider acceptance in statistics. Its roots spread far back to the early 19th century; the survival of the term logistic and the wide application of the device have been determined decisively by the personal histories and individual actions of a few scholars.

One feature of the usual polychotomous logistic regression model for categorical outcomes is that a covariate must be included in all the regression equations. If a covariate is not important in all of them, the procedure will estimate unnecessary parameters. More flexible approaches allow different subsets of covariates in different regressions. One alternative uses individualized regressions which express the polychotomous model as a series of dichotomous models. Another uses a model in which a reduced set of parameters is simultaneously estimated for all the regressions. Large-sample effici...

A novel methodology for examining the effect each observation has on the Ž tted regression model is developed, initially introduced for simple linear regression, but individual chapters are devoted to applying the methodology to nonlinear models in general and generalized linear models in particular.

Multinomial logistic regression is the extension for the (binary) logistic regression when the categorical dependent outcome has more than two levels. For example, instead of predicting only dead or alive, we may have three groups, namely: dead, lost to follow-up, and alive. In the analysis to follow, a reference group has to be chosen for comparison, the appropriate group would be the alive, i.e. dead compared to alive and lost to follow-up compared to alive. The predictors used are two categorical (gender and race) and four quantitative variables (x1 – x4). In SPSS, go to Analyse, Regression...

Many procedures in SAS/STAT can be used to perform logistic regression analysis: CATMOD, GENMOD,LOGISTIC, and PROBIT. Each procedure has special features that make it useful for certain applications. For most applications, PROC LOGISTIC is the preferred choice. It fits binary response or proportional odds models, provides various model-selection methods to identify important prognostic variables from a large number of candidate variables, and computes regression diagnostic statistics. This tutorial discusses some of the problems users encountered when they used the LOGISTIC procedure. INTRODU...

The multinomial logit model (MLM) that uses maximum likelihood estimator and its application in nursing research is understood and can handle situations with several categories.

As a quick review, the logistic regression model gives the probability of a binary label given a feature vector: P(y=1 | x, w) = σ(w>x) = 1/(1 + e−wx). (1) We usually add a bias parameter b to the model, making the probability σ(w>x+b). Although the bias is often dropped from the presentation, to reduce clutter. We can always work out how to add a bias back in, by including a constant element in the input features x.

The fact that the maximum likelihood estimate in a logistic regression model may not exist is a well-known phenomenon and a number of recent papers have explored its underlying geometrical basis. [9], [12] and [7] point out that existence, and non-existence, of the estimate can be fully characterised by considering the closure of the model as an exponential family. In this formulation it becomes clear that the maximum is always well-defined, but can lie on the boundary rather than in the relative interior. Furthermore, the boundary can be considered as a polytope characterised by a finite numb...

The 4th printing enhances Stata code to use version 11 rather than version 9-10 code. The book was completed before Stata version 11 was published. For example, when constructing synthetic data, the book now uses the new Stata pseudo-random number generators rather than the ones I created back in 1995 – the suite of rnd* commands -or Roberto Gutierrez’s unpublished genbinomial command. No more corrections to the text are planned for future printings. A second edition is planned to be published in 2013 and will include nested logistic regression, and chapters on latent class models and on Bayes...

The center’s initial PCEA regimens were based on a review by D’Angelo, and the clinical difference was small, but it was statistically significant.

This paper contains discussions of issues associated with logistic regression where the issues are easier to understand when presented graphically than when they are presented using formulas. The topics discussed are: odds are not probabilities or percents; why use 1 / (1 + exp(-x)); complete and partial separation; why do we use the logit (What do the estimates in SAS printouts mean); the effect of beta values on the percent curve; oversampling – why and how; the ROC curve; the C statistic.

Two regression techniques that can be used for truncated binary data are compared and it is shown that only truncated logistic regression requires a knowledge of group level covariates and allows estimation of grouplevel effects.

Many measures to detect multicollinearity in linear regression have been proposed in statistics and numerical analysis literature. Among them, condition number and variance inflation factor(VIF) are most popular. In this study, we give new interpretations of condition number and VIF in linear regression, using geometry on the explanatory space. In the same line, we derive natural measures of condition number and VIF for logistic regression. These computer intensive measures can be easily extended to evaluate multicollinearity in generalized linear models.

I am very glad I was asked to read the new edition of the book, and I found it to be a useful resource that belongs on the required book lists for personnel preparation programs.