Eldad Davidov, Holger Steinmetz, Peter Schmidt University of Gießen / Germany

1. With or without constraints? An empirical comparison of two approaches to estimate interaction effects in the theory of planned behavior Eldad Davidov, Holger Steinmetz, Peter Schmidt University of Gießen / Germany Fan Yang-Wallentin University of Uppsala / Sweden

2. Outline • Introduction • Goals • Data and measurements • Results • Summary and conclusions

3. Introduction 1 • Many social psychological models postulate interaction effects • The most often applied one is the Theory of Reasoned Action (TRA; Ajzen & Fishbein, 1980) or in its newer form the Theory of Planned Behavior (TPB; Ajzen 1991) • The theory implies interaction effects • Van der Putte & Hoogstraten (1997): First test of the TRA in an SEM framework – but without interaction effects

4. The Theory of Planned Behavior-TPB (Ajzen) Strength of beliefs about consequences x Evaluations of the Outcome Attitude towards the behavior Strength of beliefs about expectations x Motivation to comply Intention Behavior Subjective Norm Strength of beliefs about control factors x Evaluation of these control factors Perceived Behavioral Control (PBC)

5. The Theory of Planned Behavior-TPB (Ajzen) Strength of beliefs about consequences x Evaluations of the Outcome Attitude towards The behavior Strength of beliefs about expectations x Motivation to comply Intention Behavior Subjective Norm Strength of beliefs about control factors x Evaluation of these control factors Perceived Behavioral Control (PBC)

6. The Theory of Planned Behavior-TPB (Ajzen) Strength of beliefs about consequences x Evaluations of the Outcome Attitude towards The behavior Strength of beliefs about expectations x Motivation to comply Intention Behavior Subjective Norm Strength of beliefs about control factors x Evaluation of these control factors Perceived Behavioral Control (PBC)

7. Introduction 2 • Generally, very few tests of interaction effects of TPB variables with real data. • For these few applications, there are no systematic accounts except for the meta-analyses in Yang-Wallentin, Schmidt, Davidov and Bamberg 2003. There was inconclusive evidence. • Behavioral research seldom use the sophisticated methods to test interaction effects with latent variables. • There are several methods to test an interaction between latent variables in SEM  Which method should one use?

8. Goals • We compare two methods to test interaction effects: • The “constrained approach” (Jöreskog &Yang, 1996) and • the “unconstrained approach” (Marsh, Wen, & Hau, 2004) There are other methods but we focus on these two. • The constrained method is the first developed approach but complicated to use • The unconstrained is new and easy to use: it simply drops the constraints except for the following: • The means of the additive latent predictors are fixed to zero • The mean of the product term equals the covariance between the additive latent predictors • The unconstrained has only been evaluated with simulation studies – not with real data yet.

9. Data Study • Real data from a theory-driven field study • Explanation of travel mode choice • Sample (N = 913) representative for the population in Frankfurt / Germany

10. Measures Intention: “My intention to use public transport rather than the car for everyday purposes here in Frankfurt in the next weeks is … • … small – large” (rating 1 to 5) • … improbable – probable” (rating 1 to 5) • “I intend to use public transport rather than the car for everyday purposes here in Frankfurt in the next weeks (improbable-probable ) (1 to 5) Perceived behavioral control (PBC): • “It would be impossible-possible for me to use public transportation in Frankfurt… (ranging from 1 (not possible) to 5 (possible)) • “I am sure that I can use public transport rather than the car for everyday purposes here in Frankfurt in the next weeks …(ranging from 1 (not sure) to 5 (sure)) Behavior:Percentage of public transport use from the total use (car and public transport)

11. Procedure Data • Centering predictor items • Creating product indicators • Calculating covariance matrix, asymptotic covariance matrix and mean vector • Robustified maximum likelihood (RML) Model A (Constrained approach, Jöreskog & Yang, 1996) • Various non-linear constraints involving item intercepts, error variances, factor loadings and latent variances Model B (Unconstrained approach; Marsh, Wen, & Hau, 2004) • The means of latent intention and PBC are 0 (k1 / k2 = 0) • The mean of the latent product term equals the covariance between both latent predictors (k3 = f12)

12. PBC1 PBC 1.0 PBC2 Int1 1.0 Intention Behavior 1.0 % use Int2 Int3 PBC1Int1 1.0 IntPBC PBC1Int2 PBC1Int3 Model specification CO - - - - only unconstrained approach

13. Results Note. SBc2 = Satorra-Bentler corrected c2

14. Summary • In both approaches, we found a similar and significant interaction effect. • The additive effects differed. • This result may depend on the concrete data we used (pbc2 lacked discriminant validity). Therefore, we will replicate the model with two different real data sets. • Since the unconstrained approach is much more easy to use for the applied researcher, one can use it - but caution is still needed. • Since the simulation results are restricted to the specific setting, applications with real data can give additional information. In our case, 2 conditions have not been studied: - correlations higher than .40 between predictors - error covariances Future simulation studies should take this into account. 6) A full test of TPB with all of the interaction effects specified seems to be more feasible with the unconstrained approach

15. Thank you very much for your attention!!!!