Academic literature on the topic 'Forward Stepwise Regression'

Stepwise fitting of nonlinear nested regression models is considered in this chapter. The forward stepwise method of linear model building is used as far as possible. With linear models this is straightforward as there is in principle a free choice of the order that individual terms or factors are selected for inclusion. The only real issue is that sufficient submodels are examined to ensure that those finally selected really are amongst the best. The nonlinear case is not so straightforward, as embeddedness and parameter indeterminacy issues impose restrictions on the order in which steps can be taken to build a valid model, as certain parameters can only be meaningfully included if other specific parameters are definitely present. A systematic way of building valid nonlinear models of increasing complexity is described and illustrated by two examples using real data. A brief review of non-nested model building is also given.

Regression model (RM) is an important tool for modeling and analyzing data. It is one of the popular predictive modeling techniques which explore the relationship between a dependent (target) and independent (predictor) variables. The variable selection method is used to form a good and effective regression model. Many variable selection methods existing for regression model such as filter method, wrapper method, embedded methods, forward selection method, Backward Elimination methods, stepwise methods, and so on. In this chapter, computational intelligence-based variable selection method is discussed with respect to the regression model in cybersecurity. Generally, these regression models depend on the set of (predictor) variables. Therefore, variable selection methods are used to select the best subset of predictors from the entire set of variables. Genetic algorithm-based quick-reduct method is proposed to extract optimal predictor subset from the given data to form an optimal regression model.

Regression model (RM) is an important tool for modeling and analyzing data. It is one of the popular predictive modeling techniques which explore the relationship between a dependent (target) and independent (predictor) variables. The variable selection method is used to form a good and effective regression model. Many variable selection methods existing for regression model such as filter method, wrapper method, embedded methods, forward selection method, Backward Elimination methods, stepwise methods, and so on. In this chapter, computational intelligence-based variable selection method is discussed with respect to the regression model in cybersecurity. Generally, these regression models depend on the set of (predictor) variables. Therefore, variable selection methods are used to select the best subset of predictors from the entire set of variables. Genetic algorithm-based quick-reduct method is proposed to extract optimal predictor subset from the given data to form an optimal regression model.

The fashion industry is subject to recurring cycles of popularity that are regular enough to be dubbed the “20-year rule.” Activewear clothing that is suitable for the gym and the street was fashionable in the 1990s and, 20 years later, in the 2010s. Intellectually, the British economist Dennis Robertson once wrote, “Now, as I have often pointed out to my students, some of whom have been brought up in sporting circles, high-brow opinion is like a hunted hare; if you stand in the same place, or nearly the same place, it can be relied upon to come round to you in a circle.” In the same way, today’s data miners have rediscovered several statistical tools that were once fashionable. These tools have been given new life because they are mathematically complex, indeed beautifully complex, and many data miners are easily seduced by mathematical beauty. Too few think about whether the underlying assumptions make sense and if the conclusions are reasonable. Consider data mining with multiple regression models. Rummaging through a large data base looking for the combination of explanatory variables that gives the best fit can be daunting. With 100 variables to choose from, there are more than 17 trillion possible combinations of 10 explanatory variables. With 1,000 possible explanatory variables, there are nearly a trillion trillion possible combinations of 10 explanatory variables. With 1 million possible explanatory variables, the number of 10-variable combinations grows to nearly a million trillion trillion trillion trillion (if we were to write it out, there would be 54 zeros). Stepwise regression was born back when computers were much slower than today, but it has become a popular data-mining tool because it is less computationally demanding than a full search over all possible combinations of explanatory variables but, it is hoped, will still give a reasonable approximation to the results of a full search. The stepwise label comes from the fact that the calculations go through a number of steps, considering potential explanatory variables one by one. There are three main stepwise procedures. A forward-selection rule starts with the one explanatory variable that has the highest correlation with the variable being predicted. Then the procedure adds a second variable, the variable that improves the fit the most.

Architectural distortion is a subtle but important early sign of breast cancer. The purpose of this study is to develop methods for the detection of sites of architectural distortion in prior mammograms of interval-cancer cases. Screening mammograms obtained prior to the detection of cancer could contain subtle signs of early stages of breast cancer, in particular architectural distortion. The methods for the detection of architectural distortion are based upon Gabor filters, phase portrait analysis, a novel method for the analysis of the angular spread of power, fractal analysis via Fractal Dimension (FD), structural analysis of texture via Laws’ texture energy measures derived from geometrically transformed regions of interest (ROIs), and statistical analysis of texture using Haralick’s 14 texture features. The application of Gabor filters and linear phase portrait modeling was used to detect initial candidates of sites of architectural distortion; 4,224 ROIs, including 301 true-positive ROIs related to architectural distortion, were automatically obtained from 106 prior mammograms of 56 interval-cancer cases and from 52 mammograms of 13 normal cases. For each ROI, the FD, three measures of angular spread of power, 10 Laws’ measures, and 14 Haralick’s features were computed. The areas under the receiver operating characteristic curves obtained using the features selected by stepwise logistic regression and the leave-one-ROI-out method are 0.76 with the Bayesian classifier, 0.75 with Fisher linear discriminate analysis, and 0.78 with a single-layer feed forward neural network. Free-response receiver operating characteristics indicated sensitivities of 0.80 and 0.90 at 5.8 and 8.1 false positives per image, respectively, with the Bayesian classifier and the leave-one-image-out method. The methods have shown good potential in detecting architectural distortion in mammograms of interval-cancer cases.

<em>Abstract.</em>—Forest harvests have been shown to have negative effects on stream fish and habitat; however, the relationship between these factors, and the magnitude of these effects, has received little study. We investigated the influence that various land-cover types (including recent forest harvest) have on fish assemblages at multiple spatial scales and compared these results to the influences of local instream habitat variables. Satellite land-cover data and land management harvest maps were used to characterize the land-cover types throughout the Knife River basin in northeast Minnesota. Eleven spatial scales (with 30-m and 100-m buffer widths), including site, reach, stream corridor, and catchment, were evaluated. Forward stepwise regression was used to relate land cover to coldwater index of biotic integrity scores and metrics. Land-cover relationships varied with spatial scale, but land cover at the catchment and corridor scales explained the most variation in fish and habitat variables. Generally, increases in forest cover and decreases in water/wetland were associated with higher quality fish assemblages and instream habitat. No negative effects of forest harvest were found at the site or reach scales. Forest harvest 5–8 years old was negatively related to fish assemblage quality at the stream corridor and catchment scales, possibly related to changes in temperature and substrate at the corridor scale, and increases in fine sediments and unstable banks at the catchment scale. The cumulative effect of increasing forest harvest from 0 to 8 years old throughout the catchment was associated with lower quality fish assemblages and instream habitat, indicating that large increases in similar timed forest harvests throughout a catchment (not just in the riparian zone) can have negative effects on stream fish and habitat.