Outliers and Robustness for Ordinal Data

Riani, Marco; Torti, Francesca; Zani, Sergio

doi:10.1002/9781119961154.ch9

Cited by 8 publications

(12 citation statements)

References 18 publications

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“…We contaminate the original data set with a 5 percent of outliers in order to study the robustness of both MDS configurations. We consider 22 individuals either from P2 or P5 profiles and modify some of their characteristics in a contradictory way (in concordance with the definition of outlier for multivariate ordinal variables given in Riani et al 2012), simulating individuals that would rarely be participants of the social programs described in Description of the Data Set subsection. In this way, the four contaminated data sets are constructed according to multivariate contamination patterns.…”

Section: Contaminating the Data Setmentioning

confidence: 99%

“…This topic has been scarcely addressed in the framework of mixed-type data. In this sense, Solaro (2010) and Riani, Torti, and Zani (2012) present interesting applications of the forward search (FS) procedure (Atkinson and Riani 2000;Riani, Atkinson, and Ceroli 2009) in the context of customer satisfaction analysis. As far as we know, the FS is still not extended to mixed-type data, hence it requires to assume an MDS configuration as the starting data matrix.…”

Section: Introductionmentioning

confidence: 99%

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On Visualizing Mixed-Type Data

Grané

Romera

2016

Sociological Methods & Research

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Survey data are usually of mixed type (quantitative, multistate categorical, and/or binary variables). Multidimensional scaling (MDS) is one of the most extended methodologies to visualize the profile structure of the data. Since the past 60s, MDS methods have been introduced in the literature, initially in publications in the psychometrics area. Nevertheless, sensitivity and robustness of MDS configurations have been topics scarcely addressed in the specialized literature. In this work, we are interested in the construction of robust profiles for mixed-type data using a proper MDS configuration. To this end, we propose to compare different MDS configurations (coming from different metrics) through a combination of sensitivity and robust analysis. In particular, as an alternative to classical Gower's metric, we propose a robust joint metric combining different distance matrices, avoiding redundant information, via related metric scaling. The search for robustness and identification of outliers is done through a distance-based procedure related to geometric variability notions. In this sense, we propose a statistic for detecting multivariate outliers in the context of mixed-type data and evaluate its performance through a simulation study. Finally, we apply these Downloaded from techniques to a real data set provided by the largest humanitarian organization involved in social programs in Spain, where we are able to find in a robust way the most relevant factors defining the profiles of people that were under risk of being socially excluded in the beginning of the 2008 economic crisis.

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Section: Contaminating the Data Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Visualizing Mixed-Type Data

Grané

Romera

2016

Sociological Methods & Research

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“…Another extension of COM‐Poisson can be obtained by considering the (scarce) literature on multivariate outliers for ordinal data. Riani et al define bivariate and multivariate outliers for ordinal variables as units presenting an unusual combination of the categories (or values) of the variables. To identify outliers in ordinal data, they evoke the ordinal regression model:

italiclink (γ_{italicij}) MathClass-rel= α_{j} MathClass-bin- ([], b_{1} x_{i 1} MathClass-bin+ b_{2} x_{i 2} MathClass-bin+ MathClass-rel\dots MathClass-bin+ b_{p} x_{ip}) MathClass-punc, j MathClass-rel= 1 MathClass-punc, MathClass-op\dots k MathClass-bin- 1 MathClass-punc, and i MathClass-rel= 1 MathClass-punc, MathClass-op\dots MathClass-punc, n MathClass-punc,

where γ ij is the cumulative distribution function for the j ‐th category of the i ‐th case and link ( γ ij ) is the ‘link function’, which is a transformation of the cumulative probabilities of the ordered dependent variable that allows for estimation of the model .…”

Section: Outliers In Contingency Tablesmentioning

confidence: 99%

“…In order to evaluate the goodness of fit of a model, the indexes that are typically used are the Cox and Snell R 2 ,

R_{CS}^{2}

, and the pseudo Nagelkerke R 2 ,

R_{N}^{2}

, expressed as

R_{CS}^{2} MathClass-rel= 1 MathClass-bin- {((), \frac{l (0)}{l (\overset{β}{true})})}^{\frac{2}{n}} and R_{N}^{2} MathClass-rel= \frac{R_{CS}^{2}}{normalmax ({falsefalse}_{R}^{CS})}

where

l (\overset{β}{true})

is the likelihood of the tested model and l (0) is the likelihood of the initial model that does not contain explanatory variables (null model), and

normalmax ({falsefalse}_{R}^{CS}) MathClass-rel= 1 MathClass-bin- {({}, l (0))}^{\frac{2}{n}}

. For more details and examples from a customer satisfaction survey, see Atkinson and Riani and Riani et al .…”

Section: Outliers In Contingency Tablesmentioning

confidence: 99%

“…Another extension of COM-Poisson can be obtained by considering the (scarce) literature on multivariate outliers for ordinal data. Riani et al [10] define bivariate and multivariate outliers for ordinal variables as units presenting an unusual combination of the categories (or values) of the variables. To identify outliers in ordinal data, they evoke the ordinal regression model: where ij is the cumulative distribution function for the j -th category of the i-th case and link.…”

Section: Statistical Models Versus Phenomenological or Mechanistic Momentioning

confidence: 99%

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‘The COM‐Poisson model for count data: a survey of methods and applications’ by K. Sellers, S. Borle and G. Shmueli

Kenett¹

2012

Appl Stoch Models Bus & Ind

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Robustness of the one‐class Peeling method to the Gaussian Kernel Bandwidth

Lee

Weese

Martinez

et al. 2021

Quality & Reliability Eng

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The One Class Peeling (OCP) method is an outlier detection method for Phase I analysis of large multivariate samples. The two stage OCP method is based on support vector data description and employs the Gaussian kernel function to create sequential flexible boundaries to peel away observations to estimate the center of a data set. Subsequently the distance from that estimated center is used as the monitoring statistic. In this work we study the effect of the bandwidth parameter for the Gaussian Kernel on the performance of the OCP method. We find that the OCP method is robust to the value of the bandwidth parameter in terms of in‐control and out‐of‐control simulation performance. We verify these results on example data. The result is a recommendation for a small value of the bandwidth value, providing a computational advantage to the OCP method.

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Outliers and Robustness for Ordinal Data

Cited by 8 publications

References 18 publications

On Visualizing Mixed-Type Data

On Visualizing Mixed-Type Data

‘The COM‐Poisson model for count data: a survey of methods and applications’ by K. Sellers, S. Borle and G. Shmueli

Robustness of the one‐class Peeling method to the Gaussian Kernel Bandwidth

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