Novel Modeling of Parameters Related to Intra-Firm Diffusion Innovation

In this paper, we present a novel intra-firm diffusion model to predict the variation of Penetration Level (PL) with the Intensity of Use (IU) and Speed of Adoption (SA) with respect to information and communication technologies (I.C.T) within Tunisian Small Medium Enterprises (SMEs). The study was motivated by the work of Youssef et al., (2014), and its inspired data scope/range. The method of modeling focuses on optimization and non-linear regression. The first model has the capacity to compute the variation of PL with IU. However, this first model was modified to a second model through transformation in order to derive physical meaning to the parameters. The modified second model shows a quasi-vertical curvature which approximates the reciprocal of hyperbolic tangent. The Variation of PL with the SA was computed using the second model which estimated the parameters with the variables explaining about 62% variation in PL with SA χ2=0.0655, R2=0.61651 . We further formulated a third model to predict correlation of SA with PL, while imposing boundary assumptions to avoid problems of divergence; with the final model having a PL as the only adjustable parameter. The model exhibited a plateau effect at points (0.9933,0.4373) and (0,0) between two steeply vertical asymptotes at -0.06105 and 1.0013, respectively. The developed model can be useful for eliciting information when data from different countries (or surveys) are compared for same or different span time through examining the behavior of the parameters, especially after Covid-19 era.