Faculty Bibliography

A common problem in statistical modelling is to distinguish between finite mixture distribution and a homogeneous non-mixture distribution. Finite mixture models are widely used in practice and often mixtures of normal densities are indistinguishable from homogenous non-normal densities. This paper illustrates what happens when the EM algorithm for normal mixtures is applied to a distribution that is a homogeneous non-mixture distribution. In particular, a population-based EM algorithm for finite mixtures is introduced and applied directly to density functions instead of sample data. The population-based EM algorithm is used to find finite mixture approximations to common homogeneous distributions. An example regarding the nature of a placebo response in drug treated depressed subjects is used to illustrate ideas

The k points that optimally represent a distribution (usually in terms of a squared error loss) are called the k principal points. This paper presents a computationally intensive method that automatically determines the principal points of a parametric distribution. Cluster means from the k-means algorithm are nonparametric estimators of principal points. A parametric k-means approach is introduced for estimating principal points by running the k-means algorithm on a very large simulated data set from a distribution whose parameters are estimated using maximum likelihood. Theoretical and simulation results are presented comparing the parametric k-means algorithm to the usual k-means algorithm and an example on determining sizes of gas masks is used to illustrate the parametric k-means algorithm.

Functional data can be clustered by plugging estimated regression coefficients from individual curves into the k-means algorithm. Clustering results can differ depending on how the curves are fit to the data. Estimating curves using different sets of basis functions corresponds to different linear transformations of the data. k-means clustering is not invariant to linear transformations of the data. The optimal linear transformation for clustering will stretch the distribution so that the primary direction of variability aligns with actual differences in the clusters. It is shown that clustering the raw data will often give results similar to clustering regression coefficients obtained using an orthogonal design matrix. Clustering functional data using an L(2) metric on function space can be achieved by clustering a suitable linear transformation of the regression coefficients. An example where depressed individuals are treated with an antidepressant is used for illustration.

In many regression applications, some of the model parameters are estimated from separate data sources. Typically, these estimates are plugged into the regression model and the remainder of the parameters is estimated from the primary data source. This situation arises frequently in compartment modeling when there is an external input function to the system. This paper provides asymptotic and bootstrap-based approaches for accounting for all sources of variability when computing standard errors for estimated regression model parameters. Examples and simulations are provided to motivate and illustrate the ideas.

This study extends a previous study of the factor structure of the neurologic examination in unmedicated schizophrenia, utilizing cluster analysis and adding a medicated condition. We administered a modified version of the Neurologic Evaluation Scale (NES) on two occasions to 80 patients with schizophrenia or schizoaffective disorder, once while on antipsychotic medications and once while off medication. Data were distilled by combining right- and left-side scores, and by excluding rarely abnormal and unreliable items from the analysis. Principal components analysis yielded an intuitive four-factor solution in the unmedicated condition, but an inscrutable five-factor solution during medication. Cluster analysis revealed three groups: normal, cognitively impaired, and diffusely impaired. These results were also less interpretable with data from the medicated condition. Neurologic performance was better in the medicated than in the unmedicated condition. As is the case with other domains of symptoms and performance in schizophrenia, relationships among neurologic exam variables are altered by the presence of antipsychotic medication.

Factor structure of the Neurological Evaluation Scale (NES) was evaluated in 95 unmedicated patients with schizophrenia using confirmatory factor analysis (CFA). CFA was used to test four competing models that were based on prior empirical work examining the factor structure of the NES, as well as on theoretical considerations. A three-factor solution composed of "repetitive motor," "cognitive-perceptual," and "balance-tandem" factors best accounted for the data. These findings are consistent with prior exploratory studies that have suggested the NES is a multidimensional procedure that assesses diverse neurological domains. The current results contribute to the development of empirical subscales for neurological assessment procedures to be used in psychiatric conditions.