Uncertainties in spatially aggregated predictions from a logistic regression model

USING A MULTIVARIABLE MODEL FOR PREDICTION AND DIAGNOSIS

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.

In epidemiology, one approach to investigating the dependence of disease risk on an explanatory variable in the presence of several confounding variables is by fitting a binary regression using a conditional likelihood, thus eliminating the nuisance parameters. When the explanatory variable is measured with error, the estimated regression coefficient is biased usually towards zero. Motivated by the need to correct for this bias in analyses that combine data from a number of case-control studies of lung cancer risk associated with exposure to residential radon, two approaches are investigated. Both employ the conditional distribution of the true explanatory variable given the measured one. The method of regression calibration uses the expected value of the true given measured variable as the covariate. The second approach integrates the conditional likelihood numerically by sampling from the distribution of the true given measured explanatory variable. The two approaches give very similar point estimates and confidence intervals not only for the motivating example but also for an artificial data set with known properties. These results and some further simulations that demonstrate correct coverage for the confidence intervals suggest that for studies of residential radon and lung cancer the regression calibration approach will perform very well, so that nothing more sophisticated is needed to correct for measurement error.

پتانسیل تجاری اتحادیه اکو: کاربردی از رگرسیون فضایی پویا با در نظرگرفتن اثرات سرریز فضایی

Accurate and reliable forecasting of monthly runoff considering several years of rehabilitation helps in planning and managing the water resources system of bauxite mining areas. A combination of linear regression models and artificial intelligence was proposed and applied to predict runoff from mined areas. The ideal number of input variables was chosen considering a correction threshold (correlation above 95%), stepwise selection, and according to the recursive feature elimination (RFE). The linear regression equations were divided into explanatory and predictive, with the predictive ones being trained and validated with all possible combinations of annual data periods. Five machine learning models (linear model (LM), K-nearest neighbor regression (KNN), support vector machine (SVM), random forest (RF), and Cubist) were trained and used as a prediction instrument on the test set of each subsequent year. Precipitation, accumulated precipitation duration, maximum precipitation intensity, and number of events were the most explanatory variables in most linear regression and machine learning equations. The linear regression model approach presented satisfactory performance indices in predicting surface runoff in a mined bauxite area. The Cubist and RF models were the best predictors for the greatest number of years of rehabilitation, with a coefficient of determination varying with maximum values between 0.52 and 0.88 in validation. There was no best model that consistently presented the best result in all years of rehabilitation, and it is recommended to use the annual model for the respective year of rehabilitation. The linear regression equations and algorithms were useful tools in predicting runoff series and, therefore, promising monthly runoff prediction. The presented approach becomes a starting point in the search to optimize the hydrological planning of surface bauxite mines.

Logistic regression models used to predict tree mortality are critical to post-fire management, planning prescribed burns and understanding disturbance ecology. We review literature concerning post-fire mortality prediction using logistic regression models for coniferous tree species in the western USA. We include synthesis and review of: methods to develop, evaluate and interpret logistic regression models; explanatory variables in logistic regression models; factors influencing scope of inference and model limitations; model validation; and management applications. Logistic regression is currently the most widely used and available technique for predicting post-fire tree mortality. Over 100 logistic regression models have been developed to predict post-fire tree mortality for 19 coniferous species following wild and prescribed fires. The most widely used explanatory variables in post-fire tree mortality logistic regression models have been measurements of crown (e.g. crown scorch) and stem (e.g. bole char) injury. Prediction of post-fire tree mortality improves when crown and stem variables are used collectively. Logistic regression models that predict post-fire tree mortality are the basis of simple field tools and contribute to larger fire-effects models. Future post-fire tree mortality prediction models should include consistent definition of model variables, model validation and direct incorporation of physiological responses that link to process modelling efforts.

SUMMARY Suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case. We apply the local influence method of Cook (1986) to assess the effect of small perturbations of the data, including the vector of responses, case weights, explanatory variables, and the components of one case. The resulting diagnostics allow one to check for different kinds of influence, and may give insight into its workings. Two examples illustrate some of the diagnostics.

Two-stage logistic regression model

Boosted Regression Trees. Excellent for data-poor spatial management but hard to useMarine resource managers and scientists often advocate spatial approaches to manage data-poor species. Existing spatial prediction and management techniques are either insufficiently robust, struggle with sparse input data, or make suboptimal use of multiple explanatory variables. Boosted Regression Trees feature excellent performance and are well suited to modelling the distribution of data-limited species, but are extremely complicated and time-consuming to learn and use, hindering access for a wide potential user base and therefore limiting uptake and usage.BRTs automated and simplified for accessible general use with rich feature setWe have built a software suite in R which integrates pre-existing functions with new tailor-made functions to automate the processing and predictive mapping of species abundance data: by automating and greatly simplifying Boosted Regression Tree spatial modelling, the gbm.auto R package suite makes this powerful statistical modelling technique more accessible to potential users in the ecological and modelling communities. The package and its documentation allow the user to generate maps of predicted abundance, visualise the representativeness of those abundance maps and to plot the relative influence of explanatory variables and their relationship to the response variables. Databases of the processed model objects and a report explaining all the steps taken within the model are also generated. The package includes a previously unavailable Decision Support Tool which combines estimated escapement biomass (the percentage of an exploited population which must be retained each year to conserve it) with the predicted abundance maps to generate maps showing the location and size of habitat that should be protected to conserve the target stocks (candidate MPAs), based on stakeholder priorities, such as the minimisation of fishing effort displacement.Gbm.auto for management in various settingsBy bridging the gap between advanced statistical methods for species distribution modelling and conservation science, management and policy, these tools can allow improved spatial abundance predictions, and therefore better management, decision-making, and conservation. Although this package was built to support spatial management of a data-limited marine elasmobranch fishery, it should be equally applicable to spatial abundance modelling, area protection, and stakeholder engagement in various scenarios.

The partially linear varying coefficient spatial autoregressive model is a recently proposed semi-parametric spatial autoregressive model, in which some of the explanatory variables have varying coefficients while the remained explanatory variables possess constant ones. Although some estimation methods have been proposed for the partially linear varying coefficient spatial autoregressive model, the problem of selecting important explanatory variables in the parametric component of such model has not been addressed to date. In this paper, we propose a penalized profile least squares method to address this problem. Different from the existing estimation methods, the proposed method can simultaneously select the significant explanatory variables in the parametric component and estimate the corresponding nonzero regression coefficients. Furthermore, we provide a computationally feasible algorithm to obtain the penalized profile least squares estimator. The finite sample performance of the proposed variable selection method is evaluated through some simulation studies and illustrated by a real data example.

The Poisson regression model (PRM) is a widely used statistical technique for analyzing count data. However, when explanatory variables in the model are correlated, the estimation of regression coefficients using the maximum likelihood estimator (MLE) can be compromised by multicollinearity. This phenomenon leads to inaccurate parameter estimates, inflated variance, and increased mean squared error (MSE). To address multicollinearity in PRM, we propose a novel Kibria–Lukman hybrid estimator. We evaluate the performance of our estimator through extensive Monte Carlo simulations, assessing its accuracy using mean absolute percentage errors (MAPE) and MSE. Furthermore, we provide empirical applications to illustrate the practical relevance of our proposed method. Our simulation results and empirical applications demonstrate the superiority of the proposed estimator.

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A cost-minimizing diagnostic methodology for discrimination between neoplastic and non-neoplastic brain lesions: utilizing a genetic algorithm 1 scientific reports

In Multiple regression analysis, it is assumed that the independent variables are uncorrelated with one another, when such happen, the problem of multicollinearity occurs. Multicollinearity can create inaccurate estimates of the regression coefficients, inflate the standard errors of the regression coefficients, deflate the partial t-tests for the regression coefficients, give false p-values and degrade the predictability of the model. There are several methods to get rid of this problem and one of the most famous one is the ridge regression. The purpose of this research is to study the performance of some popular ridge regression estimators based on the effects of sample sizes and correlation levels on their Average Mean Square Error (AMSE) for Poisson Regression models in the presence of multicollinearity. As performance criteria, average MSE of k was used. A Monte Carlo simulation study was conducted to compare performance of Fifty (50) k estimators under four experimental conditions namely: correlation, Number of explanatory variables, sample size and intercept. From the results of the analysis as summarized in the Tables, the MSE of the estimators performed better in a lower explanatory variables <i>p</i> and an increased intercept value. It was also observed that some estimators performed better on the average at all correlation levels, sample sizes, intercept values and explanatory variables than others.

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature and on possible extensions and limitations of the estimation approach. Finally, the numerical performance and usefulness of the estimator are illustrated by the results of Monte Carlo experiments and two empirical examples, demand for fish and returns to schooling.