Comparing two approaches to testing within-level interactions using panel data.

Organizational scholars are increasingly using panel data to test within-level interaction effects. However, potential confounding in the estimation of such interaction effects may arise because commonly used strategies could reintroduce between-level variability to the estimation. The present study compares two such strategies for testing within-level interactions, namely group-mean centering the predictors (i.e., remove-then-multiply or RTM approach) and employing a fixed-effect estimator after the interaction term is formed (i.e., the multiply-then-remove or MTR approach). Examining the estimation equations of these approaches, we show that whereas the RTM estimates of within-level interactions match with researchers’ within-level theorization (hence are unbiased), the MTR approach can produce biased estimates because this approach creates a “forced average” among the within-level interaction effect and two cross-level interaction effects. Our Monte Carlo simulation study provides empirical evidence that the MTR approach can inflate or deflate the estimate of the true within-level interaction effect. We propose a revised MTR approach that overcomes the potential bias and discuss how our findings help researchers more effectively plan new studies and retrospectively examine prior data to avoid erroneous conclusions."