A Recursive Partitioning Approach for Dynamic Discrete Choice Modeling in High Dimensional Settings

Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive and/or infeasible in high-dimensional settings. Indeed, even specifying the structure for how the utilities/state transitions enter the agent's decision is challenging in high-dimensional settings when we have no guiding theory. In this paper, we present a semi-parametric formulation of dynamic discrete choice models that incorporates a high-dimensional set of state variables, in addition to the standard variables used in a parametric utility function. The high-dimensional variable can include all the variables that are not the main variables of interest but may potentially affect people's choices and must be included in the estimation procedure, i.e., control variables. We present a data-driven recursive partitioning algorithm that reduces the dimensionality of the high-dimensional state space by taking the variation in choices and state transition into account. Researchers can then use the method of their choice to estimate the problem using the discretized state space from the first stage. Our approach can reduce the estimation bias and make estimation feasible at the same time. We present Monte Carlo simulations to demonstrate the performance of our method compared to standard estimation methods where we ignore the high-dimensional explanatory variable set

Short-term and long-term mate preference in men and women in an Iranian population.

Mate preference in short-term relationships and long-term ones may depend on many physical, psychological, and socio-cultural factors. In this study, 178 students (81 females) in sports and 153 engineering students (64 females) answered the systemizing quotient (SQ) and empathizing quotient (EQ) questionnaires and had their digit ratio measured. They rated their preferred mate on 12 black-line drawing body figures varying in body mass index (BMI) and waist to hip ratio (WHR) for short-term and long-term relationships. Men relative to women preferred lower WHR and BMI for mate selection for both short-term and long-term relationships. BMI and WHR preference in men is independent of each other, but has a negative correlation in women. For men, digit ratio was inversely associated with BMI (p = 0.039, B = - 0.154) preference in a short-term relationship, and EQ was inversely associated with WHR preference in a long-term relationship (p = 0.045, B = - 0.164). Furthermore, men and women in sports, compared to engineering students, preferred higher (p = 0.009, B = 0.201) and lower BMI (p = 0.034, B = - 0.182) for short-term relationships, respectively. Women were more consistent in their preferences for short-term and long-term relationships relative to men. Both biological factors and social/experiential factors contribute to mate preferences in men while in women, mostly social/experiential factors contribute to them

Essays on Algorithms for Customer Acquisition and Retention in SaaS Business Model

Thesis (Ph.D.)--University of Washington, 2021In recent years, software firms have migrated from the traditional licensing business model to the ``Software as a Service'' (SaaS) model, where consumers subscribe to the software on monthly, quarterly, or annual contracts. This change has created new opportunities and challenges in the domain of customer acquisition and retention for firms. SaaS firms have access to an unprecedented amount of data since offering software as a service enables them to capture users' behavioral and contextual data at a granular level. Nevertheless, utilizing this amount of data requires a set of high-dimensional friendly tools and methodologies that may not be available. In this dissertation, I try to address the challenge of high-dimensionality in modeling customer acquisition and retention in the SaaS business model. The first chapter, following the introduction, outlines high-dimensional data algorithms available to design and evaluate optimal free trials, the most commonly used customer acquisition strategy in SaaS. Using data from a field experiment, I showcase how companies can design optimal trial policies and understand the underlying mechanism for the effect of trial length on customer acquisition. In the second chapter, I discuss the problem of modeling customer retention as a dynamic discrete choice model. I offer a new algorithm that let researchers incorporate the high-dimensional usage data when modeling users' subscription decision. I run several simulations using the canonical bus engine replacement problem to show the performance of the proposed algorithm. Then, I discuss the limitations of the new algorithm and explain how researchers can use it to model customer retention in SaaS. The algorithm's source code is available on Github to be used and further developed for other applications