My dissertation investigates multivariate response problems in marketing applying both parametric and non-parametric approaches. In marketing research there are several empirical situations that examine multivariate responses. Examples include predicting customer’s inter-related decision making to transact on multiple channels, multiple firms’ inter-related decision to set prices or enter a market. In my first essay, I examine a multivariate problem on customers’ decision to transact with multiple channels of a firm using a parametric state-space model. I define a customer’s channel engagement as a latent semi-Markovian process conditional upon which she decides her multichannel activities. I model the channel activities of website visits, and online and offline purchases using a parametric specification. My research jointly predicts the customer’s online visitation behavior, and online and offline purchase propensity. Further, the framework recovers the customer’s underlying engagement state with each channel and the expected duration of each state. The second and third essays of my dissertation are motivated by the restrictions imposed by parametric methods. In particular, when the response vector is of higher order (> 3) it becomes difficult to parametrically specify the multivariate distribution. Further, parametric methods are ineffective when the dimensionality (or number of covariates) is large and there are more complex interactions, and the response outcomes are sparse. In my second essay, I use the non-parametric multivariate random forests to develop a variable selection procedure for high dimensional problems. I develop new variable importance measures for dimensionality reduction using a recursive feature elimination strategy. In my empirical application on an ecology dataset with sparse observations I find that the proposed measures have higher prediction accuracy than the extant ones. In my third essay I apply the proposed variable selection method for covariate extraction in a high dimensional marketing application. Here, I examine the inter-related price change decisions of multiple sellers on the Amazon marketplace. I model a series of multivariate regression models using the extracted covariates and compare their predictive performance against the embedded variable selection method of LASSO. I find that the generalized additive model trained on the extracted features outperform LASSO. Further, I provide interpretations of the underlying relationship between the predictors and the multivariate outcome.