Two-Way Interaction

[pthane]

Hi @jvcasillas ,

Here is the output of the code you sent me. I'm not entirely sure what these lines imply :)… Also, this isn't exactly a "dummy variables" situation, is it? Or is that exactly what it is…? Again, not connecting the dots with my own data.

Saludos, Patrick

[jvcasillas]

No, not dummies. You are using the linear equation to make predictions. It makes it easier to understand the interaction. It might be more intuitive in this case if you switch the order of the variables in the function call to plot_model. Try that and then we'll take a stab at interpreting it.

[pthane]

OK. So, question. You mentioned the mood omnibus for HS (which is not properly named, I now realize). However, the negative interaction is with L2ers in comprehension. That's what I sent you above. Did you mean to refer to the negative interaction? If so, the above plot relates to that. I'm pasting the plot with the "switched" variables below:

[jvcasillas]

Well, it applies to any interaction. The original code I sent you was for HB in the omnibus model (the real one), I think.

[pthane]

Yes, I know, but the negative interaction that you commented on was not the HS Omnibus model. It was the L2 comprehension. I changed the code from what you sent to match the appropriate model, assuming that you were referring to the negative interaction that I described with L2ers in comprehension. The interaction in the HS Omnibus model was positive.

I guess what I am trying to discern is: Did you mean L2 comprehension, where the negative effect was? or Am I misunderstanding and you did indeed mean the omnibus model with HS where there was a positive interaction? That way I can actually give you the right graphs :)…

[jvcasillas]

I meant all the interactions that were reported as significant in your results section. I just commented one so to avoid repeating the same thing. So wherever there is a significant interaction, it doesn't matter which model, you need to interpret it and you can use the same strategy (plotting predictions) for all of them. There is no sense in referring to them as positive or negative. That doesn't mean anything.

[pthane]

OK, makes sense. Thanks. Silvia asked me to mention the directionality of my effects, so I just sort of assumed. However, I'm not sure upon looking at those figures whether my interpretation is correct or not.

[jvcasillas]

She's right. You absolutely should always interpret the directionality of your effects (as we've done all semester). Normally you just check the parameter estimate and you're done. Unfortunately that doesn't work the same way with an interaction. This is also why we said in class that main effects are unreliable when you have an interaction.... because one of the effects depends on another variable. There is no easy way to do this by looking at the sign of the coefficient, so in order to interpret your interactions you need to plot them.

So look at the last plot you posted. Pick one line, say the green one, and interpret it like you normally would (for high FofA the effect of token_whatever is associated with an increase/decrease in subj)... then do it for the other two lines.

[pthane]

She's right. You absolutely should always interpret the directionality of your effects (as we've done all semester). Normally you just check the parameter estimate and you're done. Unfortunately that doesn't work the same way with an interaction. This is also why we said in class that main effects are unreliable when you have an interaction.... because one of the effects depends on another variable. There is no easy way to do this by looking at the sign of the coefficient, so in order to interpret your interactions you need to plot them.

Yes; I understand that directionality of the coefficients for the main effect signifies positive/negative correlation. I understand that reporting this is important.

So look at the last plot you posted. Pick one line, say the green one, and interpret it like you normally would (for high FofA the effect of token_whatever is associated with an increase/decrease in subj)... then do it for the other two lines.

Granted, I posted the wrong plot. I was looking at the subordinate verb but for L2ers the interaction is with the matrix verb. So, let me share the correct plot with you and see if I am interpreting it correctly:

1. The blue line where frequency of use is at its "average" level implies that subjunctive use is relatively constant across token frequencies.
2. The red line indicates that the directionality of the effect is as I would anticipate. That is, lower levels of use increase the sensitivity to token frequency.
3. Does the green line implies that higher levels of use result in less use of the subjunctive with more frequent matrix verbs? That makes no sense…. Then again maybe there is nobody in the dataset but unsure…

[jvcasillas]

That is spot on. Check the range for FofA and find out what the individuals with the highest level are doing in the raw data. Judging by the error band there is probably limited data at that extreme.

[pthane]

That is spot on. Check the range for FofA and find out what the individuals with the highest level are doing in the raw data. Judging by the error band there is probably limited data at that extreme.

There are two participants over a standard score of 2. I don't want to discard this but it makes no sense that they would do the complete OPPOSITE of the low-activation users?