Moderation-analysis with a hierarchical multiple regression analysis For my thesis I perform a moderation analysis via a hierarchical multiple regression analysis. More specifically, I want to investigate whether closeness in the parent-child relationship is a moderator in the association between conflict in the teacher-student relationship and the working memory performance of primary school children. In the analysis I work with two models (model 1 without interaction and model 2 with interaction as in this file: https://www.sheffield.ac.uk/polopoly_fs/1.885172!/file/90_Moderation_Meditation.pdf)
I would like a good example of another thesis or paper that works with the same analysis as me, but I haven't found one yet.
In addition, with the second model I do not arrive at a statistically significant R2 change after adding the interaction. Can I continue with a moderation analysis or should I stop? According to my promoter, there are articles that use less strict criteria and that do continue with moderation analysis, but I haven't found them yet.
Thank you in advance!
Regards,
Elise

In brief, if the change in the coefficient of determination $R^2$ from the parsimonious model (without interaction) to the more complex model (with interaction) is not statistically significantly different, then you are not justified in using the more complex model.  The "rule of parsimony" applies here: if the simpler approach is just as good as the complicate approach...then stick with the simpler approach.
However, this does not mean you do not have valuable information that should be reported.  There still may be a difference in the relationship with regard to the intercepts of the models (the main effects) even if the slopes of the models can be constrained to be equal.
Additionally, you may be able to report on the effect size of the interaction effect, even if you do not actually use the more complicated model for further/follow-up analyses.
