A re-examination of the algebraic properties of the AHP as a ratio-scaling technique

The Analytic Hierarchy Process (AHP) ratio-scaling approach is re-examined in view of the recent developments in mathematical psychology based on the so-called separable representations. The study highlights the distortions in the estimates based on the maximum eigenvalue method used in the AHP distinguishing the contributions due to random noises from the effects due to the nonlinearity of the subjective weighting function of separable representations. The analysis is based on the second order expansion of the Perron eigenvector and Perron eigenvalue in reciprocally symmetric matrices with perturbations. The asymptotic distributions of the Perron eigenvector and Perron eigenvalue are derived and related to the eigenvalue-based index of cardinal consistency used in the AHP. The results show the limits of using the latter index as a rule to assess the quality of the estimates of a ratio scale. The AHP method to estimate the ratio scales is compared with the classical ratio magnitude approach used in psychophysics.Separable representations, reciprocally symmetric matrices, consistency indexes.

Estimation in Discrete Parameter Models

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points. In this case, we speak of discrete parameter models. Even though the problem is quite old and has interesting connections with testing and model selection, asymptotic theory for these models has hardly ever been studied. Therefore, we discuss consistency, asymptotic distribution theory, information inequalities and their relations with efficiency and superefficiency for a general class of m-estimators

On the quest for defining organisational plasticity: a community modelling experiment

Purpose: This viewpoint article is concerned with an attempt to advance organisational plasticity (OP) modelling concepts by using a novel community modelling framework (PhiloLab) from the social simulation community to drive the process of idea generation. In addition, the authors want to feed back their experience with PhiloLab as they believe that this way of idea generation could also be of interest to the wider evidence-based human resource management (EBHRM) community. Design/methodology/approach: The authors used some workshop sessions to brainstorm new conceptual ideas in a structured and efficient way with a multidisciplinary group of 14 (mainly academic) participants using PhiloLab. This is a tool from the social simulation community, which stimulates and formally supports discussions about philosophical questions of future societal models by means of developing conceptual agent-based simulation models. This was followed by an analysis of the qualitative data gathered during the PhiloLab sessions, feeding into the definition of a set of primary axioms of a plastic organisation. Findings: The PhiloLab experiment helped with defining a set of primary axioms of a plastic organisation, which are presented in this viewpoint article. The results indicated that the problem was rather complex, but it also showed good potential for an agent-based simulation model to tackle some of the key issues related to OP. The experiment also showed that PhiloLab was very useful in terms of knowledge and idea gathering. Originality/value: Through information gathering and open debates on how to create an agent-based simulation model of a plastic organisation, the authors could identify some of the characteristics of OP and start structuring some of the parameters for a computational simulation. With the outcome of the PhiloLab experiment, the authors are paving the way towards future exploratory computational simulation studies of OP

Creative destruction in science

Drawing on the concept of a gale of creative destruction in a capitalistic economy, we argue that initiatives to assess the robustness of findings in the organizational literature should aim to simultaneously test competing ideas operating in the same theoretical space. In other words, replication efforts should seek not just to support or question the original findings, but also to replace them with revised, stronger theories with greater explanatory power. Achieving this will typically require adding new measures, conditions, and subject populations to research designs, in order to carry out conceptual tests of multiple theories in addition to directly replicating the original findings. To illustrate the value of the creative destruction approach for theory pruning in organizational scholarship, we describe recent replication initiatives re-examining culture and work morality, working parents\u2019 reasoning about day care options, and gender discrimination in hiring decisions. Significance statement It is becoming increasingly clear that many, if not most, published research findings across scientific fields are not readily replicable when the same method is repeated. Although extremely valuable, failed replications risk leaving a theoretical void\u2014 reducing confidence the original theoretical prediction is true, but not replacing it with positive evidence in favor of an alternative theory. We introduce the creative destruction approach to replication, which combines theory pruning methods from the field of management with emerging best practices from the open science movement, with the aim of making replications as generative as possible. In effect, we advocate for a Replication 2.0 movement in which the goal shifts from checking on the reliability of past findings to actively engaging in competitive theory testing and theory building. Scientific transparency statement The materials, code, and data for this article are posted publicly on the Open Science Framework, with links provided in the article

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

A Tight Bound on the Distance Between a Noncentral Chi Square and a Normal Distribution

We provide a nonasymptotic bound on the distance between a noncentral chi square distribution and a normal approximation. It improves on both the classical Berry-Esseen bound and previous distances derived specifically for this situation. First, the bound is nonasymptotic and provides an upper limit for the real distance. Second, the bound has the correct rate of decrease and even the correct leading constant when either the number of degrees of freedom or the noncentrality parameter (or both) diverge to infinity. The bound is applied to some probabilities arising in energy detection and Rician fading