Regression Diagnostics for Binomial Data from the Forward Search

Atkinson, Anthony C.; Riani, Marco

doi:10.1111/1467-9884.00261

Cited by 13 publications

(12 citation statements)

References 27 publications

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“…According to his method, the objective function takes into account all observations, but model parameters are estimated from a subset of the data. Atkinson and Riani (2001) use a similar approach for extracting the initial subset for generalized models. Similarly here, we use a procedure for choosing the initial subset that resembles the Least Median of Squares Regression.…”

Section: Choosing the Initial Subset For The Forward Searchmentioning

confidence: 99%

Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

Mavridis

Moustaki

2008

Multivariate Behavioral Research

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In this article we extend and implement the forward search algorithm for identifying atypical subjects/observations in factor analysis models. The forward search has been mainly developed for detecting aberrant observations in regression models ( Atkinson, 1994 ) and in multivariate methods such as cluster and discriminant analysis ( Atkinson, Riani, & Cerioli, 2004 ). Three data sets and a simulation study are used to illustrate the performance of the forward search algorithm in detecting atypical and influential cases in factor analysis models. The first data set has been discussed in the literature for the detection of outliers and influential cases and refers to the grades of students on 5 exams. The second data set is artificially constructed to include a cluster of contaminated observations. The third data set measures car's characteristics and is used to illustrate the performance of the forward search when the wrong model is specified. Finally, a simulation study is conducted to assess various aspects of the forward search algorithm.

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Section: Choosing the Initial Subset For The Forward Searchmentioning

confidence: 99%

Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

Mavridis

Moustaki

2008

Multivariate Behavioral Research

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“…The problem with these methods was that they can be misled by masking, where a set of observations are influential and hence could not be detected by individual-case deletions. Atkinson and Riani (2001) extended a method called the forward search (Atkinson 1994) to binomial regression models where the goal was first to identify a relatively small set of observations that does not contain outlier or influential data points and to sequentially add data points so that individual or sets of influential data points can be identified. In their approach, an initial subset of p observations was found by (typically) taking a sample of subsets of size p and selecting the subset such that median squared deviance residual was minimized.…”

Section: Assessment Of Stability Of the Cluster Groupingsmentioning

confidence: 99%

“…Motivated by the forward-search criterion of Atkinson and Riani (2001), we selected a subset size p and took a sample of subsets of this size. For each sampled subset, we recorded the median squared deviance residual for each model.…”

Section: Stability and Visualization Of The Idaho Landbird Cluster Grmentioning

confidence: 99%

A method for assigning species into groups based on generalized Mahalanobis distance between habitat model coefficients

Williams

Heglund

2008

Environ Ecol Stat

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Habitat association models are commonly developed for individual animal species using generalized linear modeling methods such as logistic regression. We considered the issue of grouping species based on their habitat use so that management decisions can be based on sets of species rather than individual species. This research was motivated by a study of western landbirds in northern Idaho forests. The method we examined was to separately fit models to each species and to use a generalized Mahalanobis distance between coefficient vectors to create a distance matrix among species. Clustering methods were used to group species from the distance matrix, and multidimensional scaling methods were used to visualize the relations among species groups. Methods were also discussed for evaluating the sensitivity of the conclusions because of outliers or influential data points. We illustrate these methods with data from the landbird study conducted in northern Idaho. Simulation results are presented to compare the success of this method to alternative methods using Euclidean distance between coefficient vectors and to methods that do not use habitat association models. These simulations demonstrate that our Mahalanobis-distance-based method was nearly always better than Euclidean-distance-based methods or methods not based on habitat association models. The methods used to develop candidate species groups are easily explained to other scientists and resource managers since they mainly rely on classical multivariate statistical methods.

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“…Although methods and applications that take outliers into account are well known when the dependent variables are continuous [22,24] , few have conducted empirical studies when the dependent variable is binary. Atkinson and Riani [3] , Flores and Garrido [12] have developed the theoretical foundations as well as the algorithm to obtain consistent estimator in logit model with outliers, but they do not provide applied studies.…”

Section: Introductionmentioning

confidence: 99%

“…The second aim of this study is to predict bankruptcy probability with the consideration of outliers. We developed the method used by Atkinson and Riani [3] . According to literature, present study is the first one that using the Robust logit model for financial data and bankruptcy predictions.…”

Section: Introductionmentioning

confidence: 99%

Robust Logistic Regression to Static Geometric Representation of Ratios

Bahiraie¹,

Ibrahim²,

Azhar³

et al. 2009

J. of Mathematics and Statistics

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Problem statement: Some methodological problems concerning financial ratios such as nonproportionality, non-asymetricity, non-salacity were solved in this study and we presented a complementary technique for empirical analysis of financial ratios and bankruptcy risk. This new method would be a general methodological guideline associated with financial data and bankruptcy risk. Approach: We proposed the use of a new measure of risk, the Share Risk (SR) measure. We provided evidence of the extent to which changes in values of this index are associated with changes in each axis values and how this may alter our economic interpretation of changes in the patterns and directions. Our simple methodology provided a geometric illustration of the new proposed risk measure and transformation behavior. This study also employed Robust logit method, which extends the logit model by considering outlier. Results: Results showed new SR method obtained better numerical results in compare to common ratios approach. With respect to accuracy results, Logistic and Robust Logistic Regression Analysis illustrated that this new transformation (SR) produced more accurate prediction statistically and can be used as an alternative for common ratios. Additionally, robust logit model outperforms logit model in both approaches and was substantially superior to the logit method in predictions to assess sample forecast performances and regressions. Conclusion/Recommendations: This study presented a new perspective on the study of firm financial statement and bankruptcy. In this study, a new dimension to risk measurement and data representation with the advent of the Share Risk method (SR) was proposed. With respect to forecast results, robust loigt method was substantially superior to the logit method. It was strongly suggested the use of SR methodology for ratio analysis, which provided a conceptual and complimentary methodological solution to many problems associated with the use of ratios. Respectively, robust logit regression can be employed as a tool of regression in providing regression for studies associated with financial data.

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Regression Diagnostics for Binomial Data from the Forward Search

Cited by 13 publications

References 27 publications

Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

A method for assigning species into groups based on generalized Mahalanobis distance between habitat model coefficients

Robust Logistic Regression to Static Geometric Representation of Ratios

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