LONG-TERM TIME-SERIES ANALYSIS FOR PSYCHOLOGICAL RESEARCHKeiko I. Powers, Ph.D.andDominique M. Hanssens, Ph.D.Anderson Graduate School of ManagementUniversity of California, Los AngelesDecember, 1998_______________________________Address Correspondence to:Dominique M. HanssensAnderson Graduate School of Management at UCLABox 951481Los Angeles, CA 90095-1481Phone: (310) 825-4497E-mail: [email protected] research was supported in part by National Institute on Drug Abuse research grantsDA06250 and DA07699. We would like to thank Douglas Anglin and Marnik Dekimpe fortheir helpful comments and suggestions on an earlier draft.2LONG-TERM TIME-SERIES ANALYSIS FOR PSYCHOLOGICAL RESEARCHKeiko I. Powers1andDominique M. Hanssens2University of California, Los AngelesDecember, 1998_______________________________1 Associate Researcher, Anderson Graduate School of Management, UCLA, Box 951481,Los Angeles, California 90095-1481 (E-mail: [email protected]; Tel(805)480-9534)2 Professor, Anderson Graduate School of Management, UCLA, Box 951481, Los Angeles,California 90095-1481 (E-mail: [email protected]; Tel(310) 825-4497)3ABSTRACTBehavioral scientists often face empirical questions on time-series processes in which itis important to make a distinction between long-term versus short-term relationships amongvariables. Lately, many time-series researchers have developed approaches that assess long-term relationships. This paper describes these new time-series techniques that allow us toexamine three research objectives related to long-term relationships: (1) to measure the degreeof persistence of each time series variable, (2) to measure the strength of a hypothesized long-term effect of an intervention on another variable, and (3) to examine the long-term equilibriumrelationship of two or more variables. The paper reviews relevant literature and provides astep-by-step description of these long-term time-series procedures with some examples of theirapplication, and demonstrates that they add new dimensions to existing time-series methodsused in psychology research.1Psychological Research on Dynamic RelationshipsFor many researchers in psychology, the analysis of data with repeated observations, ortime-series data, is an important part of their research agenda. Various statistical approachesare available to investigate time-related relationships, and these researchers typically applymethods suitable for analyzing several time points, such as repeated measures ANOVA(Analysis of Variance) or P-technique factor analysis. Less often is the case that they performtraditional time-series approaches, such as Box-Jenkins ARIMA or transfer-function modeling.One possible reason for the lack of popularity of such time-series methods in psychology is thatcollecting data with many observation points is often difficult, particularly with survey data. Forexample, Cook and Campbell (1979) state that 50 observations would be required to performa competent statistical analysis of time-series data, and Velicer and Harrop (1983) note thateven this number is not adequate for accurate model identification. As a result, appliedresearchers often collect data with only a few observation points representing critical time eventsand then apply statistical techniques appropriate for analyzing such data. Meanwhile, severalmethodological researchers have developed time-series procedures that require a smallernumber of observations (e.g., Crosbie, 1993). However, as modern information technologymakes databases with large numbers of repeated observations more accessible, various timeseries approaches become a valuable and often superior alternative tool to examine time-relatedresearch problems.In fact, many research questions asked by behavioral scientists pertain to the nature ofdynamic relationships over time. Some examples from the literature are:Example 1. What are the short-term and long-term psychological effects on people who suffertraumatic experiences, such as an airplane crash or a natural disaster? Psychological traumamay persist for a fairly long time period (Butcher & Hatcher, 1988; Williams, Solomon, &Bartone, 1988). Assessment of the length and impact of negative effects of traumaticexperiences on an individual's psychological status is essential in providing adequate therapy.2Example 2. A major issue in drug abuse research is the relationship between drug use andcriminal activity among drug abusers. Many researchers (see Greenberg & Adler, 1974 orSpeckart & Anglin, 1986 for a review) have investigated the dynamic relationship between thetwo. For example, these studies have reported a strong positive relationship between narcoticsuse and property crime involvement.Example 3. Psychologists in marketing are often asked about the effects of advertising onconsumers' purchasing behavior (Wilkie, 1990). The key question is whether advertising affectsconsumers' behavior beyond the exposure period and, if so, to what extent the lagged effectspersist.Example 4. Attention deficit disorder (ADD) with hyperactivity has been studied by manydevelopmental psychologists (Van Hasselt, Strain, & Hersen, 1988). Of particular interest isthe relationship between ADD children and their parents over time. Research has indicated theimportance of examining the parent-child interaction patterns in order to understand ADD.Example 5. Social psychological research has demonstrated that one way to influence behavioris by affecting relevant attitude. For example, anti-tobacco campaigns often provideinformation on the negative effects of smoking in order to change people's attitude towardsmoking. However, to claim a successful attitude change, the newly acquired attitude shouldpersist over time (e.g., Boninger et al., 1990). Therefore, in order to examine the long-termeffects of anti-tobacco campaigns, it is important to observe how long the attitude change lastsover time.These examples require empirical studies in which observations are repeated over time.For example, to investigate the effects of a traumatic experience (Example 1), victims arefollowed up and observed repeatedly to measure changes in their behavior over time. Examples3 and 5 also require repeated observations on the corresponding behavioral changes that reflectthe impact of an intervention or "shock" (such as advertising or anti-tobacco campaigns). As forExamples 2 and 4, both variables