The development of the digital economy is driving a comprehensive digital transformation of the Chinese economy. Digital marketing pinpoints customer needs in terms of both technology and interaction, enhances the interactive experience, and influences consumers' willingness to buy. Digital marketing can increase customer acquisition, improve user experience, increase sales viscosity and expand sales segments at a lower cost. Under the wave of digital technology empowering the traditional industry, the marketing approach of the auto show industry has changed from being based on traditional media promotional tools to being based on new media matrices in an attempt to maximize the matching of customer needs and increase the sales conversion rate of potential customers. This paper attempts to answer the following two questions: first, whether the level of digital marketing in auto shows can effectively increase car sales; second, if the level of digital marketing in auto shows has a significant positive impact on increasing car sales in auto shows, what is the intrinsic impact mechanism. Company X is one of the first leading exhibition companies in the exhibition industry to embrace the Internet economy and seek digital transformation. This paper utilizes Company X's auto show sales data and rating data on auto show digital marketing to construct a panel regression model and a moderated utility model for empirical testing, and the results show that the level of digital marketing at auto shows can effectively enhance car sales, attract more customers and improve sales conversion rates, but with regional heterogeneity. Next, for the intrinsic influence mechanism, this paper utilizes the evaluation data of consumers' interactive experience and perceived value of auto shows collected by questionnaires to construct the Tobit regression model for empirical testing, and the results show that the online interactive features of digital marketing of auto shows enhance the customers' purchasing intention by enhancing the users' perceived value, which ultimately translates into the enhancement of auto sales in auto shows. With the gradual penetration of digital technology into all aspects of people's lives, digital marketing for auto shows may give rise to new forms in the future.

Many longitudinal studies, especially in clinical trials, suffer from missing data issues. Most estimation procedures assume that the missing values are ignorable or missing at random (MAR). However, this assumption leads to unrealistic simplification and is implausible for many cases. For example, an investigator is examining the effect of treatment on depression. Subjects are scheduled with doctors on a regular basis and asked questions about recent emotional situations. Patients who are experiencing severe depression are more likely to miss an appointment and leave the data missing for that particular visit. Data that are not missing at random may produce bias in results if the missing mechanism is not taken into account. In other words, the missing mechanism is related to the unobserved responses. Data are said to be non-ignorable missing if the probabilities of missingness depend on quantities that might not be included in the model. Classical pattern-mixture models for non-ignorable missing values are widely used for longitudinal data analysis because they do not require explicit specification of the missing mechanism, with the data stratified according to a variety of missing patterns and a model specified for each stratum. However, this usually results in under-identifiability, because of the need to estimate many stratum-specific parameters even though the eventual interest is usually on the marginal parameters. Pattern mixture models have the drawback that a large sample is usually required. In this thesis, two studies are presented. The first study is motivated by an open problem from pattern mixture models. Simulation studies from this part show that information in the missing data indicators can be well summarized by a simple continuous latent structure, indicating that a large number of missing data patterns may be accounted by a simple latent factor. Simulation findings that are obtained in the first study lead to a novel model, a continuous latent factor model (CLFM). The second study develops CLFM which is utilized for modeling the joint distribution of missing values and longitudinal outcomes. The proposed CLFM model is feasible even for small sample size applications. The detailed estimation theory, including estimating techniques from both frequentist and Bayesian perspectives is presented. Model performance and evaluation are studied through designed simulations and three applications. Simulation and application settings change from correctly-specified missing data mechanism to mis-specified mechanism and include different sample sizes from longitudinal studies. Among three applications, an AIDS study includes non-ignorable missing values; the Peabody Picture Vocabulary Test data have no indication on missing data mechanism and it will be applied to a sensitivity analysis; the Growth of Language and Early Literacy Skills in Preschoolers with Developmental Speech and Language Impairment study, however, has full complete data and will be used to conduct a robust analysis. The CLFM model is shown to provide more precise estimators, specifically on intercept and slope related parameters, compared with Roy's latent class model and the classic linear mixed model. This advantage will be more obvious when a small sample size is the case, where Roy's model experiences challenges on estimation convergence. The proposed CLFM model is also robust when missing data are ignorable as demonstrated through a study on Growth of Language and Early Literacy Skills in Preschoolers.