In obesity research, it is assumed that the population is homogeneous. While this approach has yielded important insights, testing this supposition might reveal information that could impact our understanding of the phenomena and its treatment. In this study, data from obese teenagers (N = 248, Mean BMI percentile = 99%; Mean age = 13.9, SD = 1.8) who were predominantly minority (n = 182), female (n = 169), and enrolled in a weight loss intervention were analyzed. Latent profile analysis (LPA) was used to segment patients into groups based on their scores on PedsQL 4.0 scales (physical-, emotional-, social-, and school functioning) and the Coopersmith Self-Esteem Scale. A 3-class solution was parsimonious and demonstrated the best statistical fit (Bayesian information criterion = 10596.96; Lo-Mendell-Rubin-adjusted likelihood ratio test = 73.020, p < .05). The 3 groups were ordinal and composed of respondents with high- (HF; n = 72, 29%), medium- (MF; n = 110, 44%), and low functioning (LF; n = 66, 27%). Further analyses (chi squares and linear regressions) showed that the LF group had a significantly higher proportion of Caucasians and males compared to the HF (referent) group. Also, when controlling for demographics and weight, the LF group had significantly higher blood pressure (diastolic and systolic), lower self-reported physical activity (on two different measures), and a higher total score on a scale of depressed mood. Four groups of ordinal regressions (since the pair of self-reported exercise variables and blood pressure variables were correlated, only one from each pair was included in each set) consistently found that self-reported physical activity and blood pressure improved significantly from the LF to HF groups. However, when depressed mood was included, it became the only significant variable. These findings suggest that LF group members are demographically and clinically distinct and that depressed mood may be the critical factor connecting self-report and metabolic dysfunction. Theory suggests depressed mood is both associated with cognitive schemas that affect responses on self-report measures; skewing them negative, and is also manifested metabolically.

Research has suggested that depression symptoms generally decrease after late adolescence; however, there is increasing attention paid to depression symptoms among college students given the stressors unique to this time period and negative outcomes associated with depression. This study examined latent trajectories of depression symptom severity among college students. Participants were 9,889 college students who participated in the Spit for Science project (Dick et al., 2011). Growth Mixture Modeling was used to identify the presence of four subgroups of individuals with similar patterns of initial level and change in depression severity over four years of college, including Low/Minimal (55.9%), Decreasing (2.8%), Increasing (11.6%), and Chronically Elevated (29.7%) groups. Risk factors of belonging to a depressed mood trajectory include female gender; lesbian, gay, or bisexual orientation; and experiencing a greater number of stressful life events. Higher social support and self-reported resilience were associated with decreased likelihood of belonging to any of the depressed mood trajectories. Overall, it appears that most college students in this sample experience only mild depression symptoms; however, it is important to recognize and intervene early with individuals who report elevated depression symptoms as some are at risk for persistent and increasing depression across college.

The purpose of this study was to assess fear of cancer recurrence (FCR) in breast cancer survivors returning for regularly scheduled follow-up mammograms. FCR was hypothesized to increase prior to the mammogram, decrease from immediately pre- to immediately post-mammogram, and then increase following the mammogram. Based on the cognitive-behavioral model (CBM) of health anxiety, greater perceived risk of recurrence, worse perceived consequences of a recurrence, lower coping self-efficacy, and more engagement in reassurance-seeking behaviors were hypothesized to be associated with greater FCR in each time segment. Finally, exploratory analyses evaluated the various trajectories in FCR over time using growth mixture modeling and the CBM to predict class membership. The sample comprised 161 women who completed treatment for stage 0-IIIA breast cancer between 6 and 36 months previously. Participants completed the following measures at least 31 days prior to the scheduled mammogram: perceived risk and perceived consequences of breast cancer recurrence, treatment efficacy beliefs, coping self-efficacy, and reassurance seeking behaviors. Participants reported FCR at one month, one week, and immediately prior to the mammogram as well as one month, one week, and immediately after the mammogram using visual analogue scales (VAS) to rate anxiety and worry about cancer recurrence, the Cancer Worry Scale (CWS), and the Fear of Cancer Recurrence Inventory (FCRI). State anxiety and reassurance post-mammogram were also assessed. FCR significantly changed over time with increases in CWS scores prior to the mammogram, a significant decline on the VAS observed immediately following receipt of results, and a significant increase on the VAS, and decrease in reassurance during the month following the mammogram. The CBM did not significantly predict change in FCR over time, but certain variables did predict fluctuations including coping-self efficacy and perceived risk in the expected directions. Finally, growth mixture models revealed two classes, high-FCR and low-FCR, which were predicted by the CBM. These study findings support the use of the CBM in predicting which cancer survivors experience greater FCR and indicates that CBM-driven interventions may prove beneficial for reducing distressing FCR.

In this dissertation, we extend several relatively new developments in statistical model selection and data mining in order to improve one of the workhorse statistical tools - mixture modeling (Pearson, 1894). The traditional mixture model assumes data comes from several populations of Gaussian distributions. Thus, what remains is to determine how many distributions, their population parameters, and the mixing proportions. However, real data often do not fit the restrictions of normality very well. It is likely that data from a single population exhibiting either asymmetrical or nonnormal tail behavior could be erroneously modeled as two populations, resulting in suboptimal decisions. To avoid these pitfalls, we develop the mixture model under a broader distributional assumption by fitting a group of multivariate elliptically-contoured distributions (Anderson and Fang, 1990; Fang et al., 1990). Special cases include the multivariate Gaussian and power exponential distributions, as well as the multivariate generalization of the Student’s T. This gives us the flexibility to model nonnormal tail and peak behavior, though the symmetry restriction still exists. The literature has many examples of research generalizing the Gaussian mixture model to other distributions (Farrell and Mersereau, 2004; Hasselblad, 1966; John, 1970a), but our effort is more general. Further, we generalize the mixture model to be non-parametric, by developing two types of kernel mixture model. First, we generalize the mixture model to use the truly multivariate kernel density estimators (Wand and Jones, 1995). Additionally, we develop the power exponential product kernel mixture model, which allows the density to adjust to the shape of each dimension independently. Because kernel density estimators enforce no functional form, both of these methods can adapt to nonnormal asymmetric, kurtotic, and tail characteristics. Over the past two decades or so, evolutionary algorithms have grown in popularity, as they have provided encouraging results in a variety of optimization problems. Several authors have applied the genetic algorithm - a subset of evolutionary algorithms - to mixture modeling, including Bhuyan et al. (1991), Krishna and Murty (1999), and Wicker (2006). These procedures have the benefit that they bypass computational issues that plague the traditional methods. We extend these initialization and optimization methods by combining them with our updated mixture models. Additionally, we “borrow” results from robust estimation theory (Ledoit and Wolf, 2003; Shurygin, 1983; Thomaz, 2004) in order to data-adaptively regularize population covariance matrices. Numerical instability of the covariance matrix can be a significant problem for mixture modeling, since estimation is typically done on a relatively small subset of the observations. We likewise extend various information criteria (Akaike, 1973; Bozdogan, 1994b; Schwarz, 1978) to the elliptically-contoured and kernel mixture models. Information criteria guide model selection and estimation based on various approximations to the Kullback-Liebler divergence. Following Bozdogan (1994a), we use these tools to sequentially select the best mixture model, select the best subset of variables, and detect influential observations - all without making any subjective decisions. Over the course of this research, we developed a full-featured Matlab toolbox (M3) which implements all the new developments in mixture modeling presented in this dissertation. We show results on both simulated and real world datasets. Keywords: mixture modeling, nonparametric estimation, subset selection, influence detection, evidence-based medical diagnostics, unsupervised classification, robust estimation.

Over the past twenty years, the geographical bases of state legislative parties have shifted substantially. In statehouses across the country, legislators from densely-populated districts with large racial minority populations have become a larger presence inside Democratic caucuses while legislators from exurban and sparsely-populated districts have become a larger presence inside Republican caucuses. These changes have had important consequences for roll-call voting and policy outcomes inside legislatures, as new coalitional configurations formed by the intersection of party and geography have replaced older ones. In this dissertation, I examine the causes and consequences of these changes in a new way, one that more closely approximates a legislator's relationship to her "geographical constituency" (to use Richard Fenno's famous term). Unlike traditional studies of the social origins of legislative conflict, which have focused on how the constituency bases of legislative parties can be distinguished by reference to a small set of district-level demographic variables examined independently of each other, my approach views district demographic variables as the empirical manifestations of a wide variety of distinct, if latent, geographical contexts. My efforts to model the geographical constituency are centered upon a technique called Latent Profile Analysis (LPA), which estimates a latent categorical variable (in this case, legislative district categories indicative of distinct socioeconomic contexts) that captures covariation among a set of observed continuous variables (in this case, district-level demographic and geographical variables). The LPA analysis, which incorporates over 3,500 districts from seventeen chambers in the 1990s and 2000s, yields a nine-fold district categorization scheme that serves as the basis for subsequent inquiries of the dissertation. These inquiries examine how demographic and electoral change have interacted to influence trends in partisan representation of the district categories, how party and district category come together to explain patterns of roll-call ideology among state legislators, and how social cleavages over public policy within state electorates are translated into particular voting alignments involving the district categories. The dissertation speaks to a large literature in political science on the constituency-legislator relationship, as well to current debates about geographical sorting, legislative polarization, and the role of policy content in shaping voting coalitions. / text

Obesity, as defined as BMI at or above the 95th percentile on the Centers for Disease Control and Prevention’s growth charts, has increased almost 3-fold among children in the United States since 1980. Overweight in adolescence has been associated with increased fat retention and high blood pressure in adulthood, among other symptoms of metabolic syndrome. However, normative patterns of weight change in childhood have not been developed. Groups of children may follow different trajectory patterns of BMI change over time. If common trajectory patterns could be identified, and their risk factors and outcomes understood, more nuanced intervention with families and children at risk for obesity could be developed. This study used a national dataset of 1,364 children whose weight and length was measured 12 times from birth through 15 ½ years. Testing both latent class growth analysis and growth mixture modeling identified four distinct subgroups, or classes, of BMI growth trajectory from 24 months – 8th grade. These classes were compared on numerous demographic, biological, and psychosocial risk factors identified in previous research as related to obesity. Classes were differentiated primarily on the child’s BMI at 15 months, the mother’s BMI at 15 months, birth weight for age, and percent increase in birth weight. Being male, Black, and lower SES were also related to membership in the higher-BMI trajectory classes. Of the psychosocial factors, maternal sensitivity, maternal depression, and attachment classification were also related to BMI class. Membership in these trajectories strongly predicted weight-related and blood-pressure outcomes at 15 ½ years over and above individual risk factors, demonstrating that patterns of change themselves are highly influential. The best-fitting models of weight-related outcomes at 15 ½ years included change trajectory in combination with biological, psychosocial, and SES risk factors from 0-24 months, with R² ranging from .31 = .50. Characteristics predicting adolescent overweight can be identified in the first years of life and should trigger the development and implementation of early intervention protocols in obstetrics and pediatrics. / text

<p>This thesis develops flexible non- and semiparametric Bayesian models for mixed continuous, ordered and unordered categorical data. These methods have a range of possible applications; the applications considered in this thesis are drawn primarily from the social sciences, where multivariate, heterogeneous datasets with complex dependence and missing observations are the norm. </p><p>The first contribution is an extension of the Gaussian factor model to Gaussian copula factor models, which accommodate continuous and ordinal data with unspecified marginal distributions. I describe how this model is the most natural extension of the Gaussian factor model, preserving its essential dependence structure and the interpretability of factor loadings and the latent variables. I adopt an approximate likelihood for posterior inference and prove that, if the Gaussian copula model is true, the approximate posterior distribution of the copula correlation matrix asymptotically converges to the correct parameter under nearly any marginal distributions. I demonstrate with simulations that this method is both robust and efficient, and illustrate its use in an application from political science.</p><p>The second contribution is a novel nonparametric hierarchical mixture model for continuous, ordered and unordered categorical data. The model includes a hierarchical prior used to couple component indices of two separate models, which are also linked by local multivariate regressions. This structure effectively overcomes the limitations of existing mixture models for mixed data, namely the overly strong local independence assumptions. In the proposed model local independence is replaced by local conditional independence, so that the induced model is able to more readily adapt to structure in the data. I demonstrate the utility of this model as a default engine for multiple imputation of mixed data in a large repeated-sampling study using data from the Survey of Income and Participation. I show that it improves substantially on its most popular competitor, multiple imputation by chained equations (MICE), while enjoying certain theoretical properties that MICE lacks. </p><p>The third contribution is a latent variable model for density regression. Most existing density regression models are quite flexible but somewhat cumbersome to specify and fit, particularly when the regressors are a combination of continuous and categorical variables. The majority of these methods rely on extensions of infinite discrete mixture models to incorporate covariate dependence in mixture weights, atoms or both. I take a fundamentally different approach, introducing a continuous latent variable which depends on covariates through a parametric regression. In turn, the observed response depends on the latent variable through an unknown function. I demonstrate that a spline prior for the unknown function is quite effective relative to Dirichlet Process mixture models in density estimation settings (i.e., without covariates) even though these Dirichlet process mixtures have better theoretical properties asymptotically. The spline formulation enjoys a number of computational advantages over more flexible priors on functions. Finally, I demonstrate the utility of this model in regression applications using a dataset on U.S. wages from the Census Bureau, where I estimate the return to schooling as a smooth function of the quantile index.</p> / Dissertation

Politicians and social marketers considering whether, and how, to implement a national smoking ban in their countries require sound evidence regarding what the causes of support are amongst key stakeholders, how this support will develop over the short to medium term in which they seek to be re-elected, and how support relates to critical outcomes like enforcement. In response to this need, I use structural equation models to develop a model of the antecedents of support, based on theories of self interest and common sense justice, amongst hospitality industry managers. I show that support is determined more by fairness related constructs than self interest constructs, that support for national smoking bans increases consistently over time, and that the initial level of support, and the rate at which support increases, is positively related to subsequent enforcement behaviour by bar managers, in the year after implementation of such a ban, in New Zealand. I use growth mixture modeling to identify two subgroups of bar managers whose support changes at different rates. First, a class of bar managers with a high proportion of smokers who reported fewer instances of respiratory related health problems, showed low initial support, and whose support for the legislation slowly decreased. And second, a class of bar managers comprised of fewer smokers, but reporting more instances of respiratory related health problems. This class began with a high degree support, and steadily increased in support for the national smoking ban. I discuss the implications of these findings for social marketers, health educationalists, and politicians interested in introducing a similar ban in other countries.

Background: Many patients evaluated for acute coronary syndrome (ACS) in emergency departments (EDs) experience ongoing or recurrent symptoms after discharge, regardless of their ultimate medical diagnosis. A comprehensive understanding of post-ED symptom trajectories is lacking. Aims: Aim 1 was to determine trajectories of severity of common symptoms (chest pressure, chest discomfort, unusual fatigue, chest pain, shortness of breath, lightheadedness, upper back pain and shoulder pain) in the six months following an ED visit for potential ACS. Aim 2 was to identify relationships between symptom trajectories and baseline physiologic factors (age, gender, diabetes status, diagnosis, comorbidities, functional status) and situational factors (marital status, insurance status, education level). Aim 3 was to identify relationships between symptom trajectories and health service use (outpatient visits and calls, ED visits, 911 calls, hospitalization) in the six months after the ED visit. Methods: This was a secondary data analysis from a study conducted in five U.S. EDs. Patients (n=1002) who had abnormal electrocardiogram or biomarker testing and were identified by the triage nurse as potentially having ACS were enrolled. Symptom severity was assessed in the hospital and 30 days and six months post-discharge using the 13-item ACS Symptom Checklist. Symptom severity was modeled across the three study time points using growth mixture modeling. Model selection was based on interpretability, theoretical justification, and statistical fit indices. Patient characteristics were used to predict trajectories using logistic regression and differences in health service use were tested using chi-square analysis. Results: Between two and four distinct trajectory classes were identified for each symptom. Identified trajectories were labeled "tapering off," "mild/persistent," "moderate/persistent," "moderate/worsening," "moderate/improving," "late onset," and "severe/improving." Age, sex, diabetes, BMI, functional status, insurance status, and diagnosis significantly predicted symptom trajectories. Clinic visits and phone calls, 911 calls, ED visits, and probability of hospitalization varied significantly among trajectories. Conclusions: Research on the individual nature of symptom trajectories can support patient-centered care. Patients at risk for ongoing symptoms and increased health service use can be targeted for education and follow-up based on clinically observable characteristics. Further research is needed to verify the existence of multiple symptoms trajectories in diverse populations.

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