While testing moderating effect of a variable on the relationship between two variables using hierarchical regression analysis, the direct relationship between predictor and dependent variable is non-significant but the interaction term is significant. How should this result be interpreted? Is it logical to argue that even in the absence of direct influence of predictor variable on dependent variable, the interaction of two variables can influence the dependent variable?
Right, it is a contingency effect. DV is explained in presence of the interaction on the level of moderator and independent variable. That is why Aiken and West (1991) suggested that a post-hoc 2x2 simple slope curves shall help explain the interaction effect shown in the steepness of the curve, steeper slope explain stronger effect.
First, you do not know that there is no direct relationship - interaction terms eat up explanatory power of the primary components.
Second, the interaction term is telling you that the impact of your predictor differs significantly by the other interaction component. That is, to my mind, more interesting than a simple direct effect.
You can model the relationships using your full model coefficients or you can split your sample on the other interaction component and run two separate models to see what the impact of your predictor is for each group. Grimm & Yarnold is a good source, but I always return to Cohen & Cohen for this modeling problem. That would be Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences by Jacob Cohen and Patricia Cohen (Mar 1, 1984), although there is a more recent version from 2002.
You can work on nested hireachical models and see the chi-square differences by eliminating the insignificant paths. Then you will come up with final model. You can explain the model with indirect effects.even it does not have direct effects.
Right, it is a contingency effect. DV is explained in presence of the interaction on the level of moderator and independent variable. That is why Aiken and West (1991) suggested that a post-hoc 2x2 simple slope curves shall help explain the interaction effect shown in the steepness of the curve, steeper slope explain stronger effect.
Agree with above statements. Often you ignore the main effects in a model that includes a interaction as they're not really main effects, they're (conditional) effects at specific levels of the other predictor(s). Using a bottom-up model building approach, one would calculate the additive model only and then include the interaction in a separate model and use the AIC or -2*loglikelihood to test model fit. The presence of a significant interaction makes the main effects moot (to a degree).
However, keep in mind the answer provided by Jochen Wilhelm on a similar discussion regarding interaction effects:
"Following Fisher's philosophy [of] significance tests, the p-value gives you a (continuous) measure of the statistical significance. This can help you to make a decision if it would be worth to continue to work on the hypothesis or if you should better change your plans. It is about what you consider significant. The p-value alone is meaningless. You must consider the theory behind the hypothesis, the amount of data you have, the quality of data, the effect size, the implications and much more. And do never confuse statistical significance with (theoretical or practical) relevance! There is no statistical tool to measure, derive, or judge relevance."
Link to RG Question here: https://www.researchgate.net/post/How_can_I_interpret_regression_when_an_insignificant_interaction_term_makes_significant_predictors_insignificant)
Also,
http://stats.stackexchange.com/questions/5450/what-if-interaction-wipes-out-my-direct-effects-in-regression
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