model selection, Akaike's information criterion, AIC, CAIC, CAICF, asymptotic properties,

In this paper we briefly study the basic idea of Akaike's (1973) information criterion (AIC). Then, we present some recent developments on a new entropic or information complexity (ICOMP) criterion of Bozdogan (1988aBozdogan ( , 1988bBozdogan ( , 1990Bozdogan ( , 1994dBozdogan ( , 1996Bozdogan ( , 1998aBozdogan ( , 1998b for model selection. A rationale for ICOMP as a model selection criterion is that it combines a badness-of-fit term (such as minus twice the maximum log likelihood) with a measure of complexity of a model differently than AIC, or its variants, by taking into account the interdependencies of the parameter estimates as well as the dependencies of the model residuals. We operationalize the general form of ICOMP based on the quantification of the concept of overall model complexity in terms of the estimated inverse-Fisher information matrix. This approach results in an approximation to the sum of two Kullback Leibler distances. Using the correlational form of the complexity, we further provide yet another form of ICOMP to take into account the interdependencies (i.e., correlations) among the parameter estimates of the model. Later, we illustrate the practical utility and the importance of this new model selection criterion by providing several real as well as Monte Carlo simulation examples and compare its performance against AIC, or its variants.

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$7ill~~(J)65~(J)iJ;:i: 13 ~t5? L -C (Dedicated to Professor Akaike on the occasion of his 65th birthday celebration.) . IntroductionAnalysis of clusters by means of mixture distributions, called mixture-model cluster analysis, has been one of the most difficult problems in statistics. But theoretical work, coupled with the development of new computational tools in the past ten years, has made it possible to overcome some of the intractable technical and numerical issues that have limited the widespread applicability of mixture-model cluster analysis to complex real-word problems. The development of new objective analysis techniques had to wait the emergence of information-based model selection procedures to overcome difficulties with conventional techniques within the context of the mixture-model cluster analysis. See, e.g., Bozdogan (1992), Windham and Cutler (1992), Cutler and Windham (1993) (in this volume), and Rissanen and Ristad (1993) (in this volume).This paper is based on the extended work of Bozdogan (1981Bozdogan ( , 1983, where the information-theoretic approach via Akaike's (1973) Information Criterion (AIC) was first introduced and proposed in choosing the number of component clusters in the mixturemodel cluster analysis. Therefore, this paper considers the problem of choosing the number of component clusters of individuals within the context of the standard mixture of multivariate normal distributions, and presents some new results.A common problem in all clustering techniques is the difficulty of deciding on the number of clusters present in a given data set, cluster validity, and the identification of the approximate number of clusters. How do we determine what variables best discriminate between the clusters as we simultaneously estimate the number of component clusters? How do we determine the outliers or extreme observations across the clustering alternatives? These are some fundamental questions confronting practitioners and research workers in classification and clustering. The importance and the difficulty of these problems have been noted by many authors such as Beale (1969), Marriott (1971, Calinski and Harabasz (1974), Maronna and Jacovkis (1974), Hartigan (1977), Matusita and Ohsurni (1980). It is reasonable for an investigator to discover whether there is any structure in the data, or whether they indicate just a single cluster or group. If there is only one group, that is, no cluster structure, then most investigators conclude that clustering techniques are not

A s stakeholders continue to increasingly hold firms accountable for environmental and social performance in their supply chains, the importance of understanding how firms can be more sustainable becomes more prescient. Based on the underlying premise of stakeholder theory that business and ethics decisions are intertwined, the current research introduces the concept of supply chain integrity (SCI) to explore how the interdependence of business and ethics decisions can lead to improvements in sustainable supply chain management (SSCM) practices. Exploratory analysis employing secondary data sources in an elastic net (EN) logistic regression provides support for the proposed construct, by providing preliminary empirical evidence that SCI, measured through two subdimensions of structural and moral SCI, can be linked to firm sustainability. The research contributes to the supply chain management literature by: (1) introducing the concept of SCI; (2) performing an exploratory econometric analysis to provide initial validity of the SCI construct; and (3) providing a research agenda to guide further research on the concept of SCI and its role in SSCM.