Introduction: In Iran’s dynamic and competitive Fast-Moving Consumer Goods (FMCG) market, particularly in the dairy sector, the effectiveness of advertising has become a pressing concern for both private companies and policymakers. Despite the essential role of dairy consumption in public health and nutrition, per capita dairy consumption in Iran has declined over the past decade, falling below WHO-recommended levels. This trend has been attributed, in part, to ineffective advertising strategies and the misallocation of promotional resources. Therefore, this study addressed this gap by proposing a data-driven, Bayesian-based framework to evaluate the effectiveness of multimedia advertising across various stages of the consumer decision-making process, modeled as a sales funnel (awareness, interest, desire, and action). Unlike conventional linear advertising models, this research accounted for saturation, delayed effects, and the varying impact of different media channels at each funnel stage. The key objective was to quantify the contribution of each media type (television, digital media, and radio) on dairy product sales, while also identifying the most efficient media mix strategy. The study drew upon recent advances in Media Mix Modeling (MMM) and Bayesian inference to analyze the nuanced relationship between advertising and consumer response, offering practical insights for optimizing advertising expenditure.
Materials and Methods: The study employed a Bayesian MMM framework to capture the nonlinear, multi-stage, and time-dependent nature of advertising effectiveness. The analytical model was based on a decomposition of total sales into baseline sales and cumulative effects of advertisements across four funnel stages. A nonlinear Michaelis-Menten function was used to model advertising saturation, while ad carryover effects were represented using exponential decay (Adstock) functions. Weekly sales data were collected from six major Iranian dairy brands including Pegah, Kaleh, Mimas, Damdaran, Sabah, and Ramak, covering a 24-week period from July to December 2024, totaling 144 observations. Advertising expenditures were disaggregated into three channels: television, digital media, and radio. Control variables included raw milk prices, seasonal dummies, national holidays, and competitor advertising intensity. The parameters of the model (e.g. baseline sales, media effectiveness weights, saturation point, and carryover coefficients) were estimated via Bayesian inference using Markov Chain Monte Carlo (MCMC) techniques— specifically, Gibbs sampling and the Metropolis-Hastings algorithm. Posterior distributions were derived for each parameter, and convergence was assessed using the R-hat statistic and trace plots. Model accuracy was validated using predictive checks, WAIC, and leave-one-out cross-validation (LOO-CV).
 
Results and Discussion: The Bayesian analysis yielded critical insights into how different media channels contribute to sales across the consumer decision-making funnel. The baseline weekly sales, absent any advertising, were estimated at 12,300 units (95 percent CI: 10,050-14,500), serving as a benchmark for evaluating media effectiveness. Among the media channels, television had the greatest influence at the awareness stage, with a posterior coefficient of 0.48, indicating a strong but short-lived impact. Digital advertising was more effective in the desire and action stages, with a coefficient of 0.35, offering longer-lasting effects on purchasing behavior. The impact of radio was limited and statistically insignificant. The analysis also captured the saturation effect of advertising, modeled using the Michaelis-Menten function, indicating that returns began to diminish sharply after 8 million IRR per week in ad spending. Moreover, the carryover coefficient of 0.82 reflected the gradual and persistent nature of advertising effects, which decay over time but remain significant across several weeks. Breaking down the sales funnel revealed that awareness accounted for 35 percent of the total impact, while interest (25 percent), desire (20 percent), and action (20 percent) comprised the remaining 65 percent. These findings stress the importance of allocating more resources to media like digital platforms that influence deeper stages of the funnel. Scenario-based simulations using Monte Carlo methods explored various budget allocation strategies. Increasing the share of TV advertising from 50 to 70 percent yielded only an 8 percent sales growth due to rapid saturation. Conversely, raising digital ad share from 30 to 50 percent resulted in a 14 percent increase in sales. The optimal mix— 45 percent TV, 40 percent digital, and 15 percent radio— produced the highest gain at 18 percent, highlighting the need for a balanced, stage-specific media strategy. Control variables also played significant roles. Higher raw milk prices negatively affected sales (−0.27 coefficient), while national holidays led to a 12 percent decline. Seasonal changes showed a +0.08 uplift in spring and summer, and competitor advertising had a −0.19 crowding-out effect. In sum, the Bayesian funnel model effectively captured the complex, nonlinear nature of advertising response and provides a valuable framework for data-driven planning in the dairy industry.
Conclusion and Suggestions: This study provides a robust quantitative framework for evaluating multimedia advertising effectiveness in the Iranian dairy sector. By integrating the sales funnel structure with Bayesian inference and nonlinear modeling techniques, the research captures both immediate and long-term impacts of different advertising channels while accounting for saturation and media interaction effects. The findings underscore that effective advertising is not merely a function of budget volume, but of strategic allocation based on media roles within the consumer journey. Digital media, despite its slower initial uptake, delivers more durable influence, particularly at the purchase stage. Television, while useful for brand awareness, quickly reaches its saturation point. In sum, the proposed framework can guide data-driven advertising strategy formulation, maximize return on investment, and support national policy design in other consumer industries facing similar market dynamics