MULTIVARIATE ANALYSIS WITH STATIONARY ERROR: AN APPLICATION TO AUDITORY EVOKED POTENTIALS
Authors: Arbuckle James L. 
Published: August 2014

Evoked potential measurements are influenced by several factors that are present even in the absence of the stimulus under study. Such “noise” is generated mainly by recording equipment, by stray electromagnetic fields and by any ongoing electrical activity that is unrelated to stimulus presentation.

The most widely used method of dealing with noise consists of presenting a stimulus a large number of times and averaging the set of responses obtained. This technique rests on the assumption that each measured response is the sum of a noise signal, which is uncorrelated from trial to trial, and a “true” evoked response, which remains constant from trial to trial. The assumption that successive presentations of identical stimuli lead to identical responses is thought to be invalid in many cases. The methods presented in this thesis are intended to provide a test of this assumption as well as a technique for dealing with those cases in which it does not hold.

We make the weaker assumption that each evoked response can be expressed as a weighted average of some small number of waveforms, called “reference potentials.” Two methods for estimating the reference potentials and the weights are proposed. The first, the method of principal components, has been used previously in evoked potential studies by John, Ruchkin and Villegas (1964) and by Donchin (1966). In these studies, however, the component analyses were based upon response averages, where each average was calculated from responses obtained under a fixed experimental condition at a fixed recording site in a given subject. Component analysis was thus used to detect changes in response waveform due to differences in subjects, recording sites and experimental conditions. The task of noise elimination had presumably been completed before component analysis was applied. The present study undertakes the simultaneous description of individual differences and elimination of noise. It is demonstrated that the method of principal components provides estimates of the reference potentials under the condition that the noise signal is of the type known as “white noise,” that is, that the noise amplitudes obtaining at any two sample points are uncorrelated.

Spectral studies of the EEG have shown, however, that ongoing activity cannot be described as white noise. An alternative method is developed for the case where the white noise requirement is not met. We assume that the noise signal is a sample from a second order stationary process. This assumption leads to a procedure that we have called “Multivariate Analysis with Stationary Error” (MASE).

Several sets of artificial data are constructed. The methods of component analysis and MASE are applied to this artificial data. When white noise has been inserted in the artificial data, both methods perform adequately. When second order stationary nonwhite noise is present, only the MASE technique provides acceptable estimates of the reference potentials.

These methods were also applied to data obtained from four adult cats, each of which was used in two separate recording sessions of 24 minutes each. Thus eight sets of data were available for analysis. Square wave clicks were presented at intervals of 800 milliseconds. Recordings were made from monopolar electrodes chronically implanted in left auditory cortex.

Component analyses indicated the existence of at least one reference potential in each case. In some cases there was evidence for more than one reference potential. Careful examination of these other reference potentials suggested that they might reflect the effects of nonwhite noise. Application of the MASE technique clearly confirmed the existence of one reference potential in each set of data. Therefore, the method of averaging would have been appropriate for the present data.