This is a website of Gary Horlacher of Long Beach, California who is currently doing a postdoctoral fellowship at the University of Southern California (USC) in Gerontology. This website has changed several times as my goals and ambitions in academics have been evolving. Although I have a grand theory behind my work, I have decided it is much too broad and ambitious. Instead, I decided to try to limit myself to two goals which seem to be pushing me towards becoming an applied statistician interested in developmental processes. I call these my two MAD goals:
Modeling Ambivalence and Dissonance. [This type of statistical modeling provides multi-dimensional analysis which can broaden more strict linear assumptions.]
Modeling Asymmetrical Distributions. [This provides a way of statistically modeling a broader family of continuous distributions, including but not restricted to the normal distribution.]
Statistics provides a gold standard for scientific work. It provides a way of distinguishing between whether an idea that seems reasonable actually proves to be true or not. It has been widely validated by the rapid advancement of technology in modern society. Yet science has made much more advances in physics and engineering than it has in the life sciences. Because much more complex interactions and dynamics are involved in life sciences phenomena, the statistical methods require a much higher level of sophistication. Although much progress is being made by applying methods that have worked in physics and engineering to the life sciences, biology and social life processes generally do not fit the simplified assumptions that these statistics require. Four main assumptions underlie statistical methods as they are currently being used: linearity, normality, homoscedasticity, and independence. Recent advancements (i.e. hierarchical linear models) have provided ways to adapt statistics to deal with the latter two of these assumptions, especially independence. In an introduction to a book that presents these innovations, Jan de Leeuw qualifies the significance of these advancements,
Hierarchical linear models, or multilevel models, are certainly not a solution to all the data analysis problems of the social sciences. For this they are far too limited, because they are still based on the assumptions of linearity and normality.. Nevertheless, technically they are a big step ahead... (Raudenbush & Bryk, 2002, p.xxi)
Now that there are methods to better deal with homoscedasticity and independence, what about assumptions of linearity and normality which are overly restrictive to biology and the social sciences? Linearity and normality can be considered special cases of more complex possibilities that are less restrictive. Ideas and methods for expanding statistical science to better deal with both of these areas have been put forward, but further development of these ideas and methods are needed before they will be adopted as core statistical methods. This is where MAD comes in. The first MAD goal deals with the linearity assumption. Moving beyond a two-dimensional framework allows for modeling overlapping pressures which can result in accelerated growth and discontinuities. The second MAD goal deals with non-normal distributions. A number of renown statisticians have worked with a family continuous distributions of which the normal distribution is a special case, known as the exponential family of distributions. In the late 1970s and early 80s, Loren Cobb advanced a new field of statistics known as statistical catastrophe theory which provided a plan for integrating multi-dimensional statistics and the exponential family of distributions. I believe the methods for resolving the current impediment to statistical modeling of social science phenomena lie in the further development of the methods suggested by Cobb. These two challenges to statistical modeling lie at the heart of developmental processes and are core to understanding the greater complexity found in the life sciences.
Once the methodologies have been sufficiently established to deal with these complexities, they could then be used to advance understanding of variety of important developmental processes involving biological and social life (i.e. stress-coping with irresolvable stressor situations). I would like my life work to be focused on establishing the methodology needed to extend modern statistics in these two directions. All of the various social and biological developmental applications that are part of my grand theory could then benefit from these additions to statistical methodology. I believe that these two goals can be reached by continuing to build on the work of Loren Cobb in statistical catastrophe theory and its use of the exponential family of distributions in modeling social phenomena.
Last Updated: 05/22/2008