Statistical models for the dynamics of brand equity
The purpose of this research is to propose statistical models, develop certain procedures/approaches needed to estimate these models, and when marketing data are available, provide insights about brand equity dynamics in marketing practice, especially firm-based brand equity. In this dissertation, two categories of models are explored. In Chapter II, autoregressive models with exogeneous inputs (ARX) are proposed for brand structural analysis. These models are useful when brand values are known, and the sample size is relatively small. Another category of models, state space models, are proposed when brand values are unavailable. In Chapter III and IV, an approach or a procedure is proposed or designed to guess initial parameter values for a certain iteration algorithm. Moreover, Moreover, mathematical optimization methods are introduced and integrated to estimate unknown parameters of the models for brand equity dynamics. There are at least two important findings. Firstly, the implementation of brand value structure analysis can be realized through the application of an ARX model and the assessment of a firm’s brand management performance is possible. Secondly, innovative approaches must be developed to guess the starting values for iterations and to estimate parameter values of different state space models. These findings are from this innovative and contributive research. Through brand structure analysis, a novel effort in research on brand equity dynamics, brand financial performance outcome is linked with brand equity sources, while long-term brand value is distinguished from short-term performance. The analysis helps brand managers to obtain the insights into the brand performance and the ability to focus on long-term outcomes of marketing campaigns. Moreover, innovative approaches are proposed in applying state space models for brand equity dynamics analysis. Weight least square method is used in guessing the initial parameter values for a state space model with one input series and one state series. For a state space model with two input series and two state series, as well as nonlinear constraints, a procedure is designed to guess the initial parameter values. Moreover, nonlinear mathematical optimization methods are introduced and integrated to estimate the parameter values during the implementation of the expectation-maximization algorithm.