The development and testing of a multivariate model of differentiation of self among Hispanics

Individuals of Hispanic origin are the nation's largest minority (13.4%). Therefore, there is a need for models and methods that are culturally appropriate for mental health research with this burgeoning population. This is an especially salient issue when applying family systems theories to Hispanics, who are heavily influenced by family bonds in a way that appears to be different from the more individualistic non-Hispanic White culture. Bowen asserted that his family systems' concept of differentiation of self, which values both individuality and connectedness, could be universally applied. However, there is a paucity of research systematically assessing the applicability of the differentiation of self construct in ethnic minority populations. ^ This dissertation tested a multivariate model of differentiation of self with a Hispanic sample. The manner in which the construct of differentiation of self was being assessed and how accurately it represented this particular ethnic minority group's functioning was examined. Additionally, the proposed model included key contextual variables (e.g., anxiety, relationship satisfaction, attachment and acculturation related variables) which have been shown to be related to the differentiation process. ^ The results from structural equation modeling (SEM) analyses confirmed and extended previous research, and helped to illuminate the complex relationships between key factors that need to be considered in order to better understand individuals with this cultural background. Overall results indicated that the manner in which Hispanic individuals negotiate the boundaries of interconnectedness with a sense of individual expression appears to be different from their non-Hispanic White counterparts in some important ways. These findings illustrate the need for research on Hispanic individuals that provides a more culturally sensitive framework. ^

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.