Nonlinear Regression

It is often thought that regression data should be mean-centered before being diagnosed for collinearity (ill conditioning). This view is shown not generally to be correct. Such centering can mask elements of ill conditioning and produce meaningless and misleading collinearity diagnostics. In order to assess conditioning meaningfully, the data must be in a form that possesses structural interpretability.     

On unification of the asymptotic theory of nonlinear econometric models

After reading a few articles in the nonlinear econonetric literature one begins to notice that each discussion follows roughly the same lines as the classical treatment of maximum likelihood estimation. There are some technical problems having to do with simultaneously conditioning on the exogenous variables and subjecting the true parameter to a Pittman drift which prevent the use of the classical methods of proof but the basic impression of similarity is correct . An estimator – be it nonlinear least squares, three – stage nonlinear least squares, or whatever – is the solution of an optimization problem. And the objective function of the optimization problem can be treated as if it were the likelihood to derive the Wald test statistic, the likelihood ratio test statistic , and Rao's efficient score statistic. Their asymptotic null and non – null distributions can be found using arguments fairly similar to the classical maximum likelihood arguments. In this article we exploit these observations and unify much of the nonlinear econometric literature. That which escapes this unificationis that which has an objective function which is not twice continuously differentiable with respect to the parameters – minimum absolute deviations regression for example.

The model which generates the data need not bethe same as the model which was presumed to define the optimization problem. Thus, these results can be used to obtain the asymptotic behavior of inference procedures under specification error We think that this will prove to be the nost useful feature of the paper. For example, it i s not necessary toresortto Monte Carlo simulat ionto determine i f a Translog estimate of an elasticity of sub stitution obtained by nonlinear three-stage least squares is robust against a CES truestate of nature. The asymptotic approximations we give here w ill provide an analytic answer to the question, sufficiently accurate for most purposes.     

On choosing between two nonlinear models estimated robustly. Some Monte Carlo evidence

The article considers the problem of choosing between two (possibly) nonlinear models that have been fitted to the same data using M-estimation methods. An asymptotically normally distributed test statistic that takes into account the fact that the models are fitted robustly is given. The new procedure is compared with other test statistics using a Monte Carlo study. We found that the presence of a competitive model either in the null or the alternative hipothesis affects the distributional properties of the tests, and that in the case that the data contains outlying observations the new procedure had a significantly higher power than the rest of the tests.     

Employment status, psychiatric disability and quality of life: comparison of men and women with schizophrenia in Malaysia

This study explores the association between employment opportunities, psychiatric disability and quality of life of male and female patients with schizophrenia. The data were collected from 100 male and 100 female patients and their primary caregivers through personal interviews. The Disability Assessment Schedule and the Quality of Life Interview were used to collect the data. The results of the present study indicate that a large number of both the men and women were unemployed, although they suffered from only mild psychotic symptoms and had no or only minimum psychiatric disability. However, in almost all areas and levels of psychiatric disability, a significantly higher number of men than women were employed. However, the subjective Quality of Life of the employed men was significantly lower than that of the unemployed. Keeping in mind these two results, the present study argues that there is minimal community recognition in Malaysia for the employment potential of people with schizophrenia. The study also argues that policy makers must legislate to create more appropriate workplaces for the mentally ill. People with schizophrenia are entitled to just and fair treatment, and workplaces should be made attractive to them.     

A simple least squares method for estimating a change in mean

A simple least squares method for estimating a change in mean of a sequence of independent random variables is studied. The method first tests for a change in mean based on the regression principle of constrained and unconstrained sums of squares. Conditionally on a decision by this test that a change has occurred, least squares estimates are used to estimate the change point, the initial mean level (prior to the change point) and the change itself. The estimates of the initial level and change are functions of the change point estimate. All estimates are shown to be consistent, and those for the initial level and change are shown to be asymptotically jointly normal. The method performs well for moderately large shifts (one standard deviation or more), but the estimates of the initial level and change are biased in a predictable way for small shifts. The large sample theory is helpful in understanding this problem. The asymptotic distribution of the change point estimator is obtained for local shifts in mean, but the case of non-local shifts appears analytically intractable.     

Long-term low-dose dehydroepiandrosterone replacement therapy in aging males with partial androgen deficiency

Dehydroepiandrosterone (DHEA) and dehydroepiandrosterone sulfate (DHEAS) age-related withdrawal is very likely to be involved in the aging process and the onset of age-related diseases, giving rise to the question of whether preventing or compensating the decline of these steroids may have endocrine and clinical benefits. The aim of the present trial was to evaluate the endocrine, neuroendocrine and clinical consequences of a long-term (1 year), low-dose (25?mg/day) replacement therapy in a group of aging men who presented the clinical characteristics of partial androgen deficiency (PADAM). Circulating DHEA, DHEAS, androstenedione, total testosterone and free testosterone, dihydrotestosterone (DHT), progesterone, 17-hydroxyprogesterone, allopregnanolone, estrone, estradiol, sex hormone binding globulin (SHBG), cortisol, follicle stimulating hormone (FSH), luteinizing hormone (LH), growth hormone (GH) and insulin-like growth factor 1 (IGF-1) levels were evaluated monthly to assess the endocrine effects of the therapy, while β-endorphin values were used as a marker of the neuroendocrine effects. A Kupperman questionnaire was performed to evaluate the subjective symptoms before and after treatment.

The results showed a great modification of the endocrine profile; with the exception of cortisol levels, which remained unchanged, DHEA, DHEAS, androstenedione, total and free testosterone, DHT, progesterone, 17-hydroxyprogesterone, estrone, estradiol, GH, IGF-1 and β-endorphin levels increased significantly with respect to baseline values, while FSH, LH and SHBG levels showed a significant decrease. The Kupperman score indicated a progressive improvement in mood, fatigue and joint pain.

In conclusion, the present study demonstrates that 25?mg/day of DHEA is able to cause significant changes in the hormonal profile and clinical symptoms and can counteract the age-related decline of endocrine and neuroendocrine functions. Restoring DHEA levels to young adult values seems to benefit the age-related decline in physiological functions but, however promising, placebo-controlled trials are required to confirm these preliminary results.