Due to its increasing popularity, hierarchical linear modeling (HLM) has been used along with structural equation modeling (SEM) to analyze data with nested structure. In spite of the extensive research on commonly encountered problems such as violation of normality and missing data treatment within the framework of SEM, these areas have been much less explored in HLM. The present study compared HLM and multilevel SEM through a Monte Carlo study from the perspectives of the influence of nonnormality and performance of multiple imputation based on the expectationmaximization (EM) algorithm under various combinations of sample sizes at two levels. The statistical power, parameter estimates, standard errors, and estimation bias for the main effects and cross-level interaction in a two- level model were compared across the four design factors: analysis method, normality condition, missing data proportion, and sample size. HLM and multilevel SEM appeared to have similar power detecting the main effect, while HLM had better power for the cross- level interaction. Neither seemed to be sensitive to violation of the normality assumption. A higher proportion of missing data resulted in larger standard errors and estimation bias. Sample sizes at both the individual and cluster levels played a role in the statistical power for parameter estimates. The two-way interactions for the four factors were generally nonzero. Overall, both HLM and multilevel SEM were quite robust to violation of normality. SEM appears more useful in more complex path models while HLM is superior in detecting main effects. Multiple imputation based on the EM algorithm performed well in producing stable parameter estimates for up to 30% missing data. Sample size design should take into account the level at which the research is most focused.

The three-level multivariate multilevel model (MVMM) is a multivariate extension of the conventional univariate two-level hierarchical linear model (HLM) and is used for estimating and testing the effects of explanatory variables on a set of correlated continuous outcome measures. Two simulation studies were conducted to investigate the sample size requirements for restricted maximum likelihood (REML) estimation of three-level MVMMs, the effects of sample sizes and other design characteristics on estimation, and the performance of the MVMMs compared to corresponding two-level HLMs. The model for the first study was a random-intercept MVMM, and the model for the second study was a fully-conditional MVMM. Study conditions included number of clusters, cluster size, intraclass correlation coefficient, number of outcomes, and correlations between pairs of outcomes. The accuracy and precision of estimates were assessed with parameter bias, relative parameter bias, relative standard error bias, and 95% confidence interval coverage. Empirical power and type I error rates were also calculated. Implications of the results for applied researchers and suggestions for future methodological studies are discussed. / text

The current study proposed a new model, termed the cross-classified multiple membership latent variable regression (CCMM-LVR) model, to be utilized for multiple membership data structures (for example, in the presence of student mobility across schools) that provides an extension to the three-level latent variable regression model (HM3-LVR). The HM3-LVR model is beneficial for testing more flexible, directional hypotheses about growth trajectory parameters and handles pure clustering of participants within higher-level units. However, the HM3-LVR model involves the assumption that students remain in the same cluster (school) throughout the duration of the time period of interest. The CCMM-LVR model, on the other hand, appropriately models the participants’ changing clusters over time. The first purpose of this study was to demonstrate use and interpretation of the CCMM-LVR model and its parameters with a large-scale longitudinal dataset that had a multiple membership data structure (i.e., student mobility). The impact of ignoring mobility in the real data was investigated by comparing parameter estimates, standard error estimates, and model fit indices for the two estimating models (CCMM-LVR and HM3-LVR). The second purpose of the dissertation was to conduct a simulation study to try to understand the source of potential differences between the two estimating models and find out which model’s estimates were closer to the truth given the conditions investigated. The manipulated conditions in the simulation study included the mobility rate, number of clustering units, number of individuals (i.e., students) per cluster (here, school), and number of measurement occasions per individual. The outcomes investigated in the simulation study included relative parameter bias, relative standard error bias, root mean square error, and coverage rates of the 95% credible intervals. Substantial bias was found across conditions for both models, but the CCMM-LVR model resulted in the least amount of relative parameter bias and more efficient estimates of the parameters, especially for larger numbers of clustering units. The results of the real data and simulation studies are discussed, along with the implications for applied researchers for when to consider using the CCMM-LVR model versus the misspecified HM3-LVR model. / text

This study provides a measurable model of the concept of place vulnerability for HIV/AIDS that incorporates both community and structural level effects using data provided at the ZIP code level from the Texas Department of State Health Services. Sociological literature on the effects of place on health has been growing but falls short of providing an operational definition of the effects of place on health. This dissertation looks to the literature in medical/health geography to supplement sociology’s understanding of the effects of place on health, to the end of providing a measurable model. Prior research that has recognized the complexity of the effects of place still have forced data into one scale and emphasized individual-level outcomes. A multilevel model allows for keeping the associated spatial unit data, without aggregating or parsing it out for convenience of model fit. The place vulnerability model proposed examines how exposure, capacity and potentiality variables all influence an area’s HIV/AIDS count. To capture the effects of place vulnerability at multiple levels, this dissertation research uses a multilevel zero-inflated poisson (MLZIP) model to examine how factors measured at the ZIP code and county both affect HIV/AIDS counts per ZIP code as an outcome. Furthermore, empirical Bayes estimates are mapped to display how well the model fits across the state of Texas. Limitations of this research include the need to incorporate time, more specific predictors, and individual level factors. The methodology developed permits a more thorough understanding of place effects on the spatial variation of HIV/AIDS.

Thesis advisor: Sara M. Moorman / I examine how preloss relationship quality with a deceased parent and pre- to post-loss change in relationship quality with a surviving parent influence adult children's marital satisfaction over time. I also test gender interactions. Analyses are based on married or cohabiting adults who experienced the death of a parent (N = 316), drawn from the Longitudinal Study of Generations (LSOG), a longitudinal study of three-plus-generation families from Southern California. Three-level multilevel modeling (MLM) techniques reveal that improved relationship quality with a surviving parent is related to improved marital satisfaction. High preloss relationship quality with a deceased mother is related to improved post-loss marital satisfaction only for sons. These results support theories of linked lives and role context, and suggest that sons who lose mothers are particularly vulnerable relationally and may be especially sensitive to perceived support from their wives. / Thesis (MA) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Sociology.

This simulation study was designed to assess the impact of three ad hoc procedures for handling missing level two (here, school) identifiers in multilevel modeling. A multiple membership data structure was generated and both conventional hierarchical linear modeling (HLM) and multiple membership random effects modeling (MMREM) were employed. HLM models purely hierarchical data structures while MMREM appropriately models multiple membership data structures. Two of the ad hoc procedures investigated involved removing different subsamples of students from the analysis (HLM-Delete and MMREM-Delete) while the other procedure retained all subjects and involved creating a pseudo-identifier for the missing level two identifier (MMREM-Unique). Relative parameter and standard error (SE) bias were calculated for each parameter estimated to assess parameter recovery. Across the conditions and parameters investigated, each procedure had some level of substantial bias. MMREM-Unique and MMREM-Delete resulted in the least amount of relative parameter bias while HLM-Delete resulted in the least amount of relative SE bias. Results and implications for applied researchers are discussed. / text

Mediational analysis quantifies proposed causal mechanisms through which treatments act on outcomes. In the presence of clustered data, conventional multiple regression mediational methods break down, requiring the use of hierarchical linear modeling techniques. As an additional consideration, nonlinear relationships in multilevel mediation models require unique specifications that are ignored if modeled linearly. Improper specification of nonlinear relationships can lead to a consistently overestimated mediated effect. This has direct implications for inferences regarding intervention causality and efficacy. The current investigation examined a specific nonlinear multilevel mediation model parameterization to account for nonlinear relationships in clustered data. A simulation study was conducted to compare linear and nonlinear model specifications in the presence of truly nonlinear data. MacKinnon et al.’s (2007a) empirical-M based PRODCLIN method for estimating the confidence interval surrounding the instantaneous indirect effect was used to compare confidence interval coverage rates surrounding both the linear and nonlinear models’ estimates. Overall, the nonlinear model’s estimates were less biased, more efficient, and produced higher coverage rates than the linear model specification. For conditions containing a true value of zero for the instantaneous indirect effect, bias, efficiency, and coverage rate values were similar for the linear and nonlinear estimators. For conditions with a non-zero value for the instantaneous indirect effect, both the linear and nonlinear models were substantially biased. However, the nonlinear model was always less biased and always produced higher coverage rates than the linear model. The nonlinear model was more efficient than the linear model for all but two design conditions. / text

Past research has confirmed the importance of structural and individual-level factors in predicting voter turnout and citizen trust in the government. In international research particularly, political corruption has been shown to negatively affect citizen trust, though the effect of corruption on voter turnout is mixed. To date, no research has examined the effect of corruption on voting and government trust in the United States over a relatively long period of time. In this dissertation, I aim to answer two primary research questions: how U.S. corruption affects voting and how it affects citizen trust in the government. Using many sources of data for state-level variables, and the American National Election Study (NES) for individual-level variables, I investigate these relationships using multilevel modeling (MLM) of forty-six states and approximately 22,000 individuals in my analysis of voting and forty-one states and about 7,000 individuals in my analysis of political trust. I find that corruption has a small, but significant, negative effect on voting. Surprisingly, I find no effect of corruption on a citizen’s political trust, even after assessing the impact of corruption on four other specifications of trust. I also investigate cross-level interaction effects for each analysis, and find no significant results. I conclude with a discussion of possible explanations for these findings, make policy recommendations with the knowledge gained from this research, and offer suggestions for future investigations.

Research, primarily based out of the United States, has shown that incarceration is related to a variety of negative outcomes for individuals, families, communities, and even broader populations. For example, studies have highlighted primarily negative physical and mental health effects of incarceration at multiple levels. However, we know little about societal consequences of incarceration, even as the global imprisoned population reaches its highest number yet. This dissertation aims to add to the small existing body of cross-national research on nation-level outcomes of imprisonment by examining the effect of incarceration rates on population health. To do so, I have collected, cleaned, and compiled longitudinal data from 1990-2019 from a range of sources, including datasets from the United Nations’ Office on Drugs and Crime and the World Bank. Using multilevel models with repeated measures within countries, this dissertation examines the overall relationship between incarceration and five population health outcomes – life expectancy, infant mortality, suicide rate, HIV prevalence, and TB incidence – for over 100 nations. In addition, models explore factors suggested by the literature to moderate or mediate these relationships, including prison conditions, welfare support, and racial diversity for the former and social capital for the latter.The findings from this research partially support hypotheses that incarceration levels relate to negative health outcomes at the population level. Bivariate and simple multivariate analyses of around 200 countries show that incarceration can be protective, especially at lower levels of country wealth, but high-income countries are often negatively affected by high levels of incarceration. When looking at a smaller sample of around 130 countries with available data for a range of relevant variables in this 30-year time period, most of these overarching relationships between incarceration and health do show negative effects – the one consistent outlier is infant mortality rate. Moderation analyses showed many of the direct effects to be moderated by country contexts such as racial diversity and exclusion, social protection expenditure, and prison conditions. Adding in these interactions revealed some relationships that were obscured in the direct effect models; sometimes, these were relationships that supported the narrative suggested by the literature, such as infectious disease outcomes being exacerbated by high racial diversity (HIV prevalence) or harsh prison conditions (TB incidence), but other times these were in the opposite, or an unexpected, direction. Subsample analyses allowed examination of subgroups of countries that were driving overall effects. For example, the negative effect of incarceration on life expectancy over time was found to be present only in the subsample of countries with above average racial diversity and/or exclusion, below average social protection expenditure, and worse than average prison conditions. Mediation analyses within a smaller sample of countries and years (2007-19) showed some evidence of partial mediation through civic participation and social networks, but also evidence of a suppressive effect of social capital variables on the relationship between incarceration and both infant mortality rates and HIV prevalence. While there are limitations to this research due mainly to characteristics and availability of comparative international data, there are also implications for theory, research, policy, and practice. Hopefully this work will promote more theory and research on the effects of incarceration at the country level, as negative consequences are not confined to the U.S., and encourage policymakers and practitioners to better understand how incarceration levels are affecting the health of the whole population. / Criminal Justice

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