176,916 research outputs found
Categorical variables in DEA.
If a DEA model has a mix of categorical and continuous variables a standard LP formulation can still be used by entering all combinations of categorical and continuous variables as different types of inputs and/or outputs. Most units will then not have positive levels of all variables. The implications for selection of peers are investigated. Peers can have the same or fewer types of inputs than the unit under investigation, but either fewer or more types of outputs. There is a basic asymmetry between number of positive inputs and outputs of the peer units due to more of inputs reducing efficiency while more of outputs improving efficiency. The special cases of imposing a hierarchical structure on the categorical variables dealt with in the literature can easily be incorporated.Categorical variable; DEA; efficiency; linear programming; peer
Covariance and PCA for Categorical Variables
Covariances from categorical variables are defined using a regular simplex
expression for categories. The method follows the variance definition by Gini,
and it gives the covariance as a solution of simultaneous equations. The
calculated results give reasonable values for test data. A method of principal
component analysis (RS-PCA) is also proposed using regular simplex expressions,
which allows easy interpretation of the principal components. The proposed
methods apply to variable selection problem of categorical data USCensus1990
data. The proposed methods give appropriate criterion for the variable
selection problem of categoricalComment: 12 pages, 5 figure
Clustering of categorical variables around latent variables
In the framework of clustering, the usual aim is to cluster observations and not variables. However the issue of variable clustering clearly appears for dimension reduction, selection of variables or in some case studies (sensory analysis, biochemistry, marketing, etc.). Clustering of variables is then studied as a way to arrange variables into homogeneous clusters, thereby organizing data into meaningful structures. Once the variables are clustered into groups such that variables are similar to the other variables belonging to their cluster, the selection of a subset of variables is possible. Several specific methods have been developed for the clustering of numerical variables. However concerning categorical variables, much less methods have been proposed. In this paper we extend the criterion used by Vigneau and Qannari (2003) in their Clustering around Latent Variables approach for numerical variables to the case of categorical data. The homogeneity criterion of a cluster of categorical variables is defined as the sum of the correlation ratio between the categorical variables and a latent variable, which is in this case a numerical variable. We show that the latent variable maximizing the homogeneity of a cluster can be obtained with Multiple Correspondence Analysis. Different algorithms for the clustering of categorical variables are proposed: iterative relocation algorithm, ascendant and divisive hierarchical clustering. The proposed methodology is illustrated by a real data application to satisfaction of pleasure craft operators.clustering of categorical variables, correlation ratio, iterative relocation algorithm, hierarchical clustering
Testing for Network and Spatial Autocorrelation
Testing for dependence has been a well-established component of spatial
statistical analyses for decades. In particular, several popular test
statistics have desirable properties for testing for the presence of spatial
autocorrelation in continuous variables. In this paper we propose two
contributions to the literature on tests for autocorrelation. First, we propose
a new test for autocorrelation in categorical variables. While some methods
currently exist for assessing spatial autocorrelation in categorical variables,
the most popular method is unwieldy, somewhat ad hoc, and fails to provide
grounds for a single omnibus test. Second, we discuss the importance of testing
for autocorrelation in data sampled from the nodes of a network, motivated by
social network applications. We demonstrate that our proposed statistic for
categorical variables can both be used in the spatial and network setting
Consumer Profile Identification and Allocation
We propose an easy-to-use methodology to allocate one of the groups which
have been previously built from a complete learning data base, to new
individuals. The learning data base contains continuous and categorical
variables for each individual. The groups (clusters) are built by using only
the continuous variables and described with the help of the categorical ones.
For the new individuals, only the categorical variables are available, and it
is necessary to define a model which computes the probabilities to belong to
each of the clusters, by using only the categorical variables. Then this model
provides a decision rule to assign the new individuals and gives an efficient
tool to decision-makers. This tool is shown to be very efficient for customers
allocation in consumer clusters for marketing purposes, for example.Comment: Accepted in the IWANN 07 conference San Sebastian, June 2007
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