An Application of Dynamic Factor Analysis: An Examination of Smoking Habit Strength Measures

Abstract

Across smoking cessation studies, a variety of self-report and physiological measures have been used as outcome measures attempting to operationalize the degree of "habit strength " people experience. However, the performance of these different measures has not been adequately assessed longitudinally (Velicer, Rossi, Prochaska, & DiClemente, 1996). Employing time-series data to understand underlying physiological and/or psychological processes is a useful way to study constructs which may fluctuate daily. Although it has been applied in an extremely limited number of settings, dynamic factor analysis is one statistical method which may help to evaluate habit strength measures over time. This study has four main goals: 1) to examine three measures of smoking habit strength longitudinally in order to assess the comparative reliability and stability of the measures; 2) to test the hypothesis that across time, smoking habit strength can best be described as a multiple regulation model as was shown with this same data set using traditional time-series analyses (Velicer, Redding, Richmond, Greeley, and Swift, 1992); 3) to employ an innovative statistical procedure, dynamic factor analysis, and critically evaluate the difficulty in employing the procedure; and 4) to compare the results of two alternative dynamic factor solutions, one provided by LISREL and one provided by SAS macros (Wood & Brown, 1994). The three primary habit strength measures investigated are two biochemical measures, salivary cotinine and carbon monoxide level, and one self-report measure, number of cigarettes smoked. Two additional measures were included to provide divergent validity. Dyanamic factor analysis was not deemed especially difficult to employ, especially with the aid of the Wood & Brown SAS macros. Both LISREL and the SAS macros had advantages which the other did not possess. The relationships between the variables across time were such that dynamic factor analysis solutions were extremely inconsistent across subjects and lags. Interpreting the solutions which did converge upon proper solutions was extremely difficult. Only five of the ten subjects had consistent factor structures when additional lags were added to the models. Dynamic factor analysis was not able to show the presence of a multiple regulation model of smoking habit strength. Reasons for the difficulties leading to the inconsistent solutions are discussed.