Integrating adoption efficiency and repeat purchase in innovation diffusion modeling

In an era of rapid technological advancement, firms are under increasing pressure to accurately forecast product adoption and consumer engagement. While classical innovation diffusion models like the Bass model provide foundational insights, they often fall short in capturing behavioral dynamics such as repeat purchases and adoption efficiency. In real market scenario, consumer engagement and brand loyalty evolve over time. This study addresses these gaps by introducing four innovation diffusion models that explicitly integrate two behavioral dimensions: the Adoption Efficiency Factor (AEF), which captures how effectively market efforts convert potential adopters into actual adopters, and repeat purchase behavior, which reflects ongoing consumer loyalty and product re-engagement. These models are mathematically formulated using time-dependent adoption rates and solved analytically. Empirical validation is performed using sales data of Samsung smartphones, Acer personal computers, and Apple iPhone. Model parameters are estimated using the least squares technique, and model performance is assessed using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Coefficient of Determination (R2). Among the models, the one incorporating both AEF and repeat purchase demonstrated the best predictive accuracy across all the datasets. It outperformed other models in terms of lower residual errors and higher determination coefficients. This study is among the first to jointly incorporate adoption efficiency and repeat purchase behavior into innovation diffusion models.