Research for Mathematical Methodology

It is common in empirical studies using nonlinear models to estimate the mean response by evaluating the nonlinear response function at the mean value of its argument(s). However, this procedure conceptually is flawed if the response function has significant curvature in the neighborhood of the mean. Ideally, one should evaluate the estimated response function for each of the estimated responses. In general, there will be some nonzero approximation error if one instead simply evaluates the response function at the mean of the independent variable(s). Furthermore, if the variability is significant in the independent variable(s) of interest, the approximation error of using the 'evaluate at the mean' procedure increases. This paper examines the magnitude of the approximation error, and attempts to identify situations in which somewhat more computationally intensive procedures should be used.

The probability of survival can be estimated using a parametric survival model in which a single regression equation is used to summarize the data. For some data, the hazard rate at particular intervals of time differs markedly from the rest of the hazard function. This sharp rise in the hazard rate violates the requirements of the common parametric survival models, and indicates that some alternative modeling approach should be considered. This research contribution outlines a methodology for estimating parametric survival models given non-smooth survival data. As an example of this methodology the procedure is used to estimate the survival pattern of Marine Corps Selected Reservists.

The Family Service Centers (FSCs) present a diverse set of services to Marines and their families. This report presents the results of a study of Marine Corps family programs provided by the FSCs. These services include personal, family, and financial counseling, employment assistance, help for victims of domestic violence, and other services. Data from the 1985 DOD Member and Spouse surveys, USMC exit questionnaires, administrative records, and special purpose surveys of FSC directors and Marine unit commanders are used to assess the success of FSCs in meeting the objectives of serving commanders and Marines and their families and to estimate the impact of family programs on Marine retention.

The Cauchy problem for various types of second order nonlinear elliptic equations is considered. A substitution in the equation leads to a perturbed equation whose solution of an unperturbed second order linear elliptic equation obtained by formally setting Epsilon to zero. In each case a logarithmic convexity argument is used to show that appropriately constrained solutions of the original equation (assumed to exist) are shown to differ from a solution of the associated linear equation in a manner depending continuously on the parameter Epsilon.