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A hybrid decision support framework for generating & selecting causal explanatory regression splines models for information systems research

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Abstract

Much of Information Systems research is of the behavioral science category that involves the analysis of quantitative data. Typically a confirmatory approach is taken where only unconditional hypotheses are specified based on existing theory and evaluated using techniques such as regression analysis. In this paper we present a knowledge discovery via data mining (KDDM) process model based multi-criteria framework for selecting the most appropriate causal explanatory model based on the researchers subjective preferences including accuracy, simplicity, the relative importance of variables in his/her tentative research model, relative preferences for inclusion of some causal relationships.

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Authors and Affiliations

  1. Department of Information Systems, Virginia Commonwealth University, Richmond, VA, 23284, USA

    Kweku-Muata Osei-Bryson

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  1. Kweku-Muata Osei-Bryson
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Correspondence to Kweku-Muata Osei-Bryson.

Appendices

Appendix A: Overview on pairwise comparisons based

1.1 Weight generation techniques

Pairwise comparison (PC) information may be used to elicit preference information from the decision maker and to indirectly produce a corresponding weight vector (w). The preference information is represented numerically using a positive reciprocal PC matrix A = {aij} with aij = 1/aji, where aij is a rational number that is the numeric equivalent of the relative importance of between object “i” compared to object “j”. The weight vector w may then be obtained from the pairwise comparisons matrix A using a variety of techniques, including the right eigenvector method (EM), the logarithmic least squares method (e.g. De Jong 1984), and the logarithmic goal programming method (Bryson 1995). Choo and Wedley (2004) presented an overview of the major weight vector generation techniques.

Right Eigenvector Method

Aw = λMaxw

where λMax is the largest eigenvalue of A

Logarithmic Least Squares Method

Min ∑i∑j (aij - (wi/w)j)2

subject to ∑i wi = 1; wi ≥ 0.

Logarithmic Goal Programming Method

Min ∑i∑j |aij - (wi/wj) |

subject to ∑i wi = 1; wi ≥ 0.

The pairwise comparison matrix A is said to be consistent if for each triple of objects (i, j, k) the equality aij = (aik*akj) holds; otherwise it is said to be inconsistent. As noted by Obata et al. (1999), “When a pairwise comparison matrix contains seriously inconsistent comparisons, the priority weights calculated from such a wrong matrix are not reliable”. Now because the matrix A is often inconsistent, it is necessary to measure the level of inconsistency in order to determine if the resulting weight vector w will be meaningful.

Consistency indicators have been proposed by various researchers (e.g. Saaty 1980; Salo and Hämäläinen 1997; Aguaron and Moreno-Jimenez 2003; Osei-Bryson 2006) have proposed consistency indicators. The most popular of the Consistency indicators is Saaty’s Consistency Ratio (CR) which is defined as CR = CI/RI, where CI = (λMax - N), λMax is the largest eigenvalue of A, and RI. is similar to CI but based on random matrices, each with the same dimension as A, and using Saaty’s ‘rule of thumb’ the pairwise comparison matrix is deemed to be inconsistent only if CR > 0.10. Osei-Bryson (2006) also proposed interpretable consistency indicators.

Appendix B: Description of variables of the illustrative example

Table 8 Description of variables
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Osei-Bryson, KM. A hybrid decision support framework for generating & selecting causal explanatory regression splines models for information systems research. Inf Syst Front 17, 845–856 (2015). https://doi.org/10.1007/s10796-013-9469-y

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