Overview of Computer Measures of the Referential Process

Abstract

The Referential Process (RP) has three functions or processes, called Arousal, Symbolizing, and Reflecting/Reorganizing. Taken together, these provide a framework within which to address the question: how do people connect nonverbal experience and verbal forms. The purpose of this paper is to describe the Discourse Attributes Analysis Program (DAAP), which uses certain dictionaries or word lists to produce measures that model the referential process functions. These dictionaries are also described. The referential process may occur in any type of discourse context and the DAAP computer system may be applied to any type of verbal data. The focus in this paper is on transcripts of psychotherapy sessions. DAAP provides numeric and graphic data at several levels of discourse including word-by-word data concerning dictionary matches; average data for each turn of speech; average data for each speaker for each session; numeric data and graphic images for each session; and overall session data for each treatment. Graphic images of the ebb and flow of these computer generated functions of the referential process over the course of a therapy session are presented and interpreted. There are also discussions of new relational measures, as well as the referential process data base, which currently contains numerical data for 22 treatments, and presentations of several applications.

Appendix

The DAAP smoothing operator is basically a mathematical process. This appendix contains a broad description of that process in non-mathematical terms; a precise mathematical description can be found in the forthcoming DAAP Technical Manual (www.thereferentialprocess.org). The process has two steps: A fold-ever procedure and a moving weighted averaging procedure. The basic idea of the moving weighted average is that we replace the dictionary value at each word with a weighted average of the dictionary values at nearby words, where the weighting is greatest at the word itself, called the central word, and decreases steadily with distance from this central word until it reaches zero 100 words away. The weighting function we use here is an exponential function related to the normal curve; the graph of this function is shown in Fig. 

Fig. 5

The weighting function

5. The weighting function W is positive exactly for the indices, − 100 < i < 100; W(i) is increasing from i = − 100 to i = 0, has a unique maximum at i = 0, and decreases from i = 0 to 100.

There is a difficulty with this operation in that for a central word near the beginning of a turn, we do not have 100 previous words for computing this moving weighted average; likewise, for a central word near the end of a turn, we do not have 100 following words. This difficulty is overcome by using a fold-over procedure in which we extend the definition of the dictionary function to values at indices before the beginning and after the end of a turn. Label the dictionary values at the N words of a turn in order as U(1), …, U(N). Now extend this function U to have values at the indices N + 1, N + 2, etc. by folding over; that is, by setting U(N + 1) = U(N), U(N + 2) = U(N − 1), …, U(2N) = U(0). If 2N < 100, more values of U are needed beyond 2N; these additional values are obtained by folding over again; U(2N + 1) = U(2N) = U(0), U(2N + 2) = U(2N − 1) = U(2), etc. Likewise the definition of the function U can be extended to 0 and negative indices by folding over in the opposite direction; that is, U0) = U(1), U(− 1) = U(2), U(− 2) = U(3), etc.

Having extended the definition of the function U as far as necessary, the moving weighted average at each of the N words of the turn can be defined by the sum:

S(n) = Σ U(t + m) W(m), where the sum is taken over all m in the range − 100 < m < 100.

This smoothing operator has two mathematical features that are of some interest. One is that the mean of the smoothed dictionary values for a turn of speech is equal to the mean of the original dictionary values. The other is that if the original dictionary values are all equal to some constant, the smoothed dictionary values are all equal to this same constant.

We are usually concerned primarily with turns of more than 25 words. For shorter turns, S(n) is close to being constantly equal to the mean of the unsmoothed dictionary values. In general, for longer turns, the graph of the smooth dictionary function shows variations that indicate the changes in the speakers’ style of speech. The particular weighting function, W was chosen so that the value of the smooth dictionary function at a word depends strongly on the unsmoothed dictionary values of nearby words. For example, the dictionary value of the word itself together with the dictionary values of the 25 closest words in both directions account for over 70% of the value of the smooth dictionary function. This also holds for words close to the beginning or end of a turn. For example, if there are fewer than 25 preceding words and more than 25 following words, then the dictionary values of all the preceding words, together with the dictionary values of the 25 following words account for over 70% of the value of the smooth dictionary function.