[Joshua D Merfeld]

Elizabete,

Your statement that:

CR_POM would indicate the effect for firms close to a credit rating change, excluding tech industries, whilst Int_CR_POM_Tech, would measure the difference between tech firms and other when close to a credit rating change. And lastly, the CR_POM + Int_CR_POM_Tech would indicate the effect for only tech firms?

is correct. The interaction term represents the difference between the two groups (and, as you state, the addition of CR_POM and the interaction term would give you the overall effect for tech firms only). If you include the interaction term, then there is no single coefficient that gives the effect of all firms close to a change. In fact, as Clyde noted above, the idea of an overall effect does not really exist when you include the interaction term. If you want the effect of all firms close to a credit change, you would need to drop the interaction terms from the model.

Best,

Josh

[Elizabete Lurie]

Thank you so much!

[Clyde Schechter]

Elizabete, regarding #14, if this were a single interaction model, you would be correct. But given that you have two interaction terms involving CR_POM, one with Tech and one with INV_G, any effect of CR_POM that you speak about in this model must be conditional on both the value of Tech and on INV_G. The expressions you give do not take INV_G into account, so, implicitly they act as if INV_G = 0. In other words, CR_POM is the effect of CR_POM in firms with Tech = 0 and INV_G = 0. CR_POM + Int_CR_POM_Tech is the effect of CRPOM in firms where Tech = 1 and INV_G = 0. Int_CR_POM_Tech by itself is the difference between tech and non-tech firms in the effect of CR_POM conditional on INV_G = 0.

To the extent that my statement "it's not really different from the model with a single interaction" in #13 misled you into overlooking the second interaction altogether, I apologize. I had meant that the principles of interpreting the effects are the same, not that each interaction could be interpreted as if they others didn't exist.

[Elizabete Lurie]

Thank you Clyde for clearing that up!

[wanhaiyou]

Hello Elizabeth,

As can be seen in the output, the interaction terms are insignificant. Thus, they could be eliminated from the model. Note, (a) inclusion of the interactions requires strong theory, and (b) the interaction term must be (i) significant, and (ii) the percent of explained variation attributable to the interaction term (effect size) must also be significant. When the interactions are present, the interpretation of the main effects is conditional on the mean value of the interaction term. Having removed the interactions, you would be able to interpret the main effects in a straightforward way.

Hope this helps.

On a side note: the R squared appears to be very small -- did you check the model specification (i.e., tested the assumptions of OLS)?

Hi Anton,
what does the sentence mean?- (ii) the percent of explained variation attributable to the interaction term (effect size) must also be significant.
Could you please give me an example?

Best
wanhaiyou

[Nathan E. Fosse]

Interaction terms are tricky to interpret without visualization. In psychology more than other disicplines, it's common to "probe" interactions (see link with SPSS and Excel functions). In practice, this means, especially with 3-way interaction terms, it is relevant to understand when and where the interaction is statistically significant for each term.

I'd avoid the jargon in psychology and use the helpful marginsplots commands. The UCLA Stats Consulting Group (link) has some example code to provide meaningful interpretations.

A question that has been bugging me since I've heard nothing consistent: center, standardize, or leave alone interaction terms? What's the best practice (and why)?

Here's a quote from a blog on this matter in psychology citing some classic works:

A note about standardisation of variables. Standardised variables are those that are both centred around zero and are scaled so that they have a standard deviation of 1. Personally, I prefer to use these when testing interactions because the intepretation of coefficients can be slightly simpler. Some authors, such as Aiken and West (1991), recommend that variables are centred (but not standardised). The results obtained should be identical whichever method you use. If you prefer to analyse centred (but not standardised) variables, you can use the "unstandardised" versions of the Excel worksheets, and enter the mean of the variables as zero.

Source: http://www.jeremydawson.co.uk/slopes.htm