Finite mixture modeling is a useful statistical technique for clustering individuals based on patterns of responses. The fundamental idea of the mixture modeling approach is to assume there are latent clusters of individuals in the population which each generate their own distinct distribution of observations (multivariate or univariate) which are then mixed up together in the full population. Hence, the name mixture comes from the fact that what we observe is a mixture of distributions. The goal of this model-based clustering technique is to identify what the mixture of distributions is so that, given a particular response pattern, individuals can be clustered accordingly. Commonly, finite mixture models, as well as the special case of latent class analysis, are used on data that inherently involve repeated measures. The purpose of this dissertation is to extend the finite mixture model to allow for the number of repeated measures to be incorporated and contribute to the clustering of individuals rather than measures. The dimension of the repeated measures or simply the count of responses is assumed to follow a truncated Poisson distribution and this information can be incorporated into what we call a dimension informative finite mixture model (DIMM). The outline of this dissertation is as follows. Paper 1 is entitled, "Dimension Informative Mixture Modeling (DIMM) for questionnaire data with an informative number of repeated measures." This paper describes the type of data structures considered and introduces the dimension informative mixture model (DIMM). A simulation study is performed to examine how well the DIMM fits the known specified truth. In the first scenario, we specify a mixture of three univariate normal distributions with different means and similar variances with different and similar counts of repeated measurements. We found that the DIMM predicts the true underlying class membership better than the traditional finite mixture model using a predicted value metric score. In the second scenario, we specify a mixture of two univariate normal distributions with the same means and variances with different and similar counts of repeated measurements. We found that that the count-informative finite mixture model predicts the truth much better than the non-informative finite mixture model. Paper 2 is entitled, "Patterns of Physical Activity in the Northern Manhattan Study (NOMAS) Using Multivariate Finite Mixture Modeling (MFMM)." This is a study that applies a multivariate finite mixture modeling approach to examining and elucidating underlying latent clusters of different physical activity profiles based on four dimensions: total frequency of activities, average duration per activity, total energy expenditure and the total count of the number of different activities conducted. We found a five cluster solution to describe the complex patterns of physical activity levels, as measured by fifteen different physical activity items, among a US based elderly cohort. Adding in a class of individuals who were not doing any physical activity, the labels of these six clusters are: no exercise, very inactive, somewhat inactive, slightly under guidelines, meet guidelines and above guidelines. This methodology improves upon previous work which utilized only the total metabolic equivalent (a proxy of energy expenditure) to classify individuals into inactive, active and highly active. Paper 3 is entitled, "Complex Drug Use Patterns and Associated HIV Transmission Risk Behaviors in an Internet Sample of US Men Who Have Sex With Men." This is a study that applies the count-informative information into a latent class analysis on nineteen binary drug items of drugs consumed within the past year before a sexual encounter. In addition to the individual drugs used, the mixture model incorporated a count of the total number of drugs used. We found a six class solution: low drug use, some recreational drug use, nitrite inhalants (poppers) with prescription erectile dysfunction (ED) drug use, poppers with prescription/non-prescription ED drug use and high polydrug use. Compared to participants in the low drug use class, participants in the highest drug use class were 5.5 times more likely to report unprotected anal intercourse (UAI) in their last sexual encounter and approximately 4 times more likely to report a new sexually transmitted infection (STI) in the past year. Younger men were also less likely to report UAI than older men but more likely to report an STI.

In the last few decades as American society and urban life have changed dramatically, public health and urban sociological research have increasingly focused on the effect of residential location on individual well-being. In recent years, social capital has been viewed as an important pathway in understanding the associations between where one lives and health and social outcomes. Although there is not one, single definition of social capital, researchers within public health have often relied on three schools of thought labeled after Pierre Bourdieu, James Coleman, and Robert Putnam to define social capital and hypothesize its relationship with health and behaviors. However, for many years, public health researchers have often relied on Putnam's theory (1993, 1995, 2000) and a communitarian approach to defining social capital and its possible relationship to health and well-being. Many researchers and sociologists have criticized this over-reliance and overuse of Putnam's social capital constructs as they have been criticized for lacking depth and their inability to explain the causal pathways in which social capital and health operate. Additionally, the measures used to operationalize the most widely used Putnam social capital constructs often focus only on a few dimensions of his theory; generalized trust, shared norms and values, reciprocity, and civic engagement. These measures have been criticized for simultaneously being overly theoretically broad and limited in its measurement. In this research, I use a more recent paradigm of social capital theory that conceptualizes social capital as having several dimensions thereby enabling one to examine the possibility that different forms of social capital and cohesion have different impacts (both negative and positive) on health behaviors and well-being. This paper compares a Putnam-based social capital model as measured by the most commonly used variables based on his work against a broader, multi-dimensional model that measures social capital across several constructs and variables. I have evaluated the "expanded" multi-dimensional model and the smaller, Putnam-only model with a different dataset to examine the relationships between these dimensions of social capital and health behaviors and outcomes. Additionally, recent sociological research using this expanded approach has highlighted the important role of individual attachment to the neighborhood as an important mediator in the association between social capital and health outcomes. Using data from the Fragile Families and Child Wellbeing Study (FFCWS), a longitudinal birth cohort study of families in 20 cities with populations of 200,000 or more people, I investigated the role of social capital as measured across four dimensions, social cohesion (the Putnam-based Traditional Model), individual neighborhood attachment, and neighborhood socio-economic conditions on the likelihood of maternal smoking and alcohol use. Moreover, this multi-dimensional model was enhanced by the addition of another feature of social capital that was not extensively addressed in prior research, bridging social capital. Bridging social capital has been defined as relationships among individuals who are not alike in social identity or characteristics. In recent years, bridging social capital at times has been further refined to highlight the relationships within heterogeneous networks who do not share the same power structures and institutions, and economic spheres. This has been referred to as "linking" social capital. Additionally, sociologist Mario Small has extensively documented that importance of both weak ties (an aspect of "bridging" social capital) and organizational embeddedness in the relationship between social capital and health and well- being for residents in poor communities. This underrepresented dimension in the public health literature is addressed in this paper. In this research, I incorporated a measure of bridging social capital and organizational ties to highlight the possible role this form of social capital may play in understanding the association of social capital and health outcomes. This research extends the current literature by applying a recently developed model of social capital to the analysis of health outcomes using a different data set. The goal of this study was not only to explore smoking and alcohol use, neighborhood socioeconomic conditions, indicators of social capital (including social support, social leverage, informal social control, neighborhood organization participation, and bridging social capital), and the role of individual neighborhood attachment but also highlight the importance for public health researchers to use a multidimensional approach rather than rely on utilizing a few social capital constructs retrieved from Putnam's extensive published work. The multi-dimensional approach which broadens the lens in which researchers use to aid them in the understanding the association between social capital and health and well-being is more beneficial than a narrow focus that relies on a few social capital domains to examine this relationship. The association of these different dimensions was statistically tested through multiple logistic regression analyses which examined a hypothesized interaction effect between organizational embeddedness and social capital and its association with health outcomes and behaviors. It is hoped that this research will further advance the public health discourse regarding the association between health outcomes and social capital, measured across several dimensions and conceptualized through an access to resources and networks based lens.