Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Regularized logistic regression and multi-objective variable selection for classifying MEG data

This paper addresses the question of maximizing classifier accuracy for classifying task-related mental activity from Magnetoencelophalography (MEG) data. We propose the use of different sources of information and introduce an automatic channel selection procedure. To determine an informative set of channels, our approach combines a variety of machine learning algorithms: feature subset selection methods, classifiers based on regularized logistic regression, information fusion, and multiobjective optimization based on probabilistic modeling of the search space. The experimental results show that our proposal is able to improve classification accuracy compared to approaches whose classifiers use only one type of MEG information or for which the set of channels is fixed a priori.

System failure prediction through rare-events elastic-net logistic regression

Predicting failures in a distributed system based on previous events through logistic regression is a standard approach in literature. This technique is not reliable, though, in two situations: in the prediction of rare events, which do not appear in enough proportion for the algorithm to capture, and in environments where there are too many variables, as logistic regression tends to overfit on this situations; while manually selecting a subset of variables to create the model is error- prone. On this paper, we solve an industrial research case that presented this situation with a combination of elastic net logistic regression, a method that allows us to automatically select useful variables, a process of cross-validation on top of it and the application of a rare events prediction technique to reduce computation time. This process provides two layers of cross- validation that automatically obtain the optimal model complexity and the optimal mode l parameters values, while ensuring even rare events will be correctly predicted with a low amount of training instances. We tested this method against real industrial data, obtaining a total of 60 out of 80 possible models with a 90% average model accuracy.

LOGITCPRPLOT: Stata module to graph component-plus-residual plot for logistic regression

logitcprplot can be used after logistic regression for graphing a component-plus-residual plot (a.k.a. partial residual plot) for a given predictor, including a lowess, local polynomial, restricted cubic spline, fractional polynomial, penalized spline, regression spline, running line, or adaptive variable span running line smooth

RRLOGIT: Stata module to estimate logistic regression for randomized response data

rrlogit fits a maximum-likelihood logistic regression for randomized response data.

A review of two journals found that articles using multivariable logistic regression frequently did not report commonly recommended assumptions

Background and Objective: To examine if commonly recommended assumptions for multivariable logistic regression are addressed in two major epidemiological journals. Methods: Ninety-nine articles from the Journal of Clinical Epidemiology and the American Journal of Epidemiology were surveyed for 10 criteria: six dealing with computation and four with reporting multivariable logistic regression results. Results: Three of the 10 criteria were addressed in 50% or more of the articles. Statistical significance testing or confidence intervals were reported in all articles. Methods for selecting independent variables were described in 82%, and specific procedures used to generate the models were discussed in 65%. Fewer than 50% of the articles indicated if interactions were tested or met the recommended events per independent variable ratio of 10: 1. Fewer than 20% of the articles described conformity to a linear gradient, examined collinearity, reported information on validation procedures, goodness-of-fit, discrimination statistics, or provided complete information on variable coding. There was no significant difference (P >.05) in the proportion of articles meeting the criteria across the two journals. Conclusion: Articles reviewed frequently did not report commonly recommended assumptions for using multivariable logistic regression. (C) 2004 Elsevier Inc. All rights reserved.

Optimal crossover designs for logistic regression models in pharmacodynamics

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Logistic Regression in Modelling Data for CVC - Related Infection

2000 Mathematics Subject Classification: 62J12, 62P10.

Modeling Data for Complications in Diabetics Using Logistic Regression

2010 Mathematics Subject Classification: 62P10.

Sequential Logistic Regression: A Method to Reveal Subtlety in Self-Efficacy

This paper uses self-efficacy to predict the success of women in introductory physics. We show how sequential logistic regression demonstrates the predictive ability of self-efficacy, and reveals variations with type of physics course. Also discussed are the sources of self-efficacy that have the largest impact on predictive ability.

Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Obtaining environmental favourability functions from logistic regression

Logistic regression is a statistical tool widely used for predicting species’ potential distributions starting from presence/absence data and a set of independent variables. However, logistic regression equations compute probability values based not only on the values of the predictor variables but also on the relative proportion of presences and absences in the dataset, which does not adequately describe the environmental favourability for or against species presence. A few strategies have been used to circumvent this, but they usually imply an alteration of the original data or the discarding of potentially valuable information. We propose a way to obtain from logistic regression an environmental favourability function whose results are not affected by an uneven proportion of presences and absences. We tested the method on the distribution of virtual species in an imaginary territory. The favourability models yielded similar values regardless of the variation in the presence/absence ratio. We also illustrate with the example of the Pyrenean desman’s (Galemys pyrenaicus) distribution in Spain. The favourability model yielded more realistic potential distribution maps than the logistic regression model. Favourability values can be regarded as the degree of membership of the fuzzy set of sites whose environmental conditions are favourable to the species, which enables applying the rules of fuzzy logic to distribution modelling. They also allow for direct comparisons between models for species with different presence/absence ratios in the study area. This makes themmore useful to estimate the conservation value of areas, to design ecological corridors, or to select appropriate areas for species reintroductions.

Bayesian Linear Regression for estimation of the Fractal Dimension of the Cerebral Cortex

The cerebral cortex presents self-similarity in a proper interval of spatial scales, a property typical of natural objects exhibiting fractal geometry. Its complexity therefore can be characterized by the value of its fractal dimension (FD). In the computation of this metric, it has usually been employed a frequentist approach to probability, with point estimator methods yielding only the optimal values of the FD. In our study, we aimed at retrieving a more complete evaluation of the FD by utilizing a Bayesian model for the linear regression analysis of the box-counting algorithm. We used T1-weighted MRI data of 86 healthy subjects (age 44.2 ± 17.1 years, mean ± standard deviation, 48% males) in order to gain insights into the confidence of our measure and investigate the relationship between mean Bayesian FD and age. Our approach yielded a stronger and significant (P < .001) correlation between mean Bayesian FD and age as compared to the previous implementation. Thus, our results make us suppose that the Bayesian FD is a more truthful estimation for the fractal dimension of the cerebral cortex compared to the frequentist FD.