## regression analysis, (multiple) moderating effects

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Marina@SPSS
Posts: 4
Joined: Sun Feb 12, 2012 3:37 pm

### regression analysis, (multiple) moderating effects

Hello everyone,

For my Master's thesis, I have to establish a model and test it with (moderated) regression analysis. My supervisor told me that regression analysis can help me resolve my research question but I can't figure out how.

I notices there 5 more or less recent posts on moderation in regression but somehow I receive the messege "The requested topic does not exist" when I click on any one of them. Also, I think my question might go a bit beyond.

In my initial model, I have two independent variables - goals and pay - and one dependent variable - performance. Hypothesis 1 (goals are positively related to performance) and hypotheses 2 (rewards are positively related to performance) are supported.

In the second step, I introduce a set of possible moderators. Because I am going to test for each of them separately, I will now just look at one, uncertainty. I suggest that uncertainty moderates both main effects. The effect of goals (and rewards, respectively) on performance is greater if uncertainty is low than if uncertainty is high. I intend to test it with SPSS with two hierarchical regression analyses. In the first level, I introduce goals (and rewards, respectively) and uncertainty as independent variables, in the second level I add the interaction term, with the interaction term goals x uncertainty in the first regression, and the interaction term rewards x uncertainty in the second regression. As far as I understand, moderation would be supported by a significant change in the variance explained (R squared) after adding the interaction term.

(performance = a + b*goals + c*uncertainty + d*goals x uncertainty + e; performance = a + b*rewards + c*uncertainty + d*rewards x uncertainty + e)

Problem: Now, my supervisor wants me to find out when goals are enough to get performance and when rewards are (additionally) necessary. I can't find a way to put it more clearly and also cannot make a hypotheses out of it. I have no idea how I can test for this effect. Maybe you could understand the question by looking at the conclusion it should give. A possible conclusion could be: When uncertainty is low, goals lead to performance (even in the absence of rewards or independent of rewards); however, if uncertainty is high, goals only lead to performance if combined with rewards.

I am sorry that my explanation turned out a bit long. I tried to make it as clear as possible.

I'd be really happy if someone could help me solve my problem. Any suggestions are welcome. Please let me know if you need any addional info or clarification.
GerineL
Moderator
Posts: 1477
Joined: Tue Jun 10, 2008 4:50 pm

### Re: regression analysis, (multiple) moderating effects

Marina@SPSS wrote: Because I am going to test for each of them separately, I will now just look at one, uncertainty.
why not test all at once?

Problem: Now, my supervisor wants me to find out when goals are enough to get performance and when rewards are (additionally) necessary. I can't find a way to put it more clearly and also cannot make a hypotheses out of it. I have no idea how I can test for this effect. Maybe you could understand the question by looking at the conclusion it should give. A possible conclusion could be: When uncertainty is low, goals lead to performance (even in the absence of rewards or independent of rewards); however, if uncertainty is high, goals only lead to performance if combined with rewards.
step 1: goals
step 2: goalsXuncertainty
step 3: rewards
step 3: rewardsXuncertaitny

don't just look at the difference in Rsquare, look at the significance of the individual predictors as well.
E.g., is there a significant interaction effect in step 2?
Marina@SPSS
Posts: 4
Joined: Sun Feb 12, 2012 3:37 pm

### Re: regression analysis, (multiple) moderating effects

Thanks for your quick response, Gutnre

why not test all at once?

I wanted to test for them separately just to have less variables. I have no experience with SPSS, so maybe it would be easier to interpret for me then. But I can also test for them at once.

step 1: goals
step 2: goalsXuncertainty
step 3: rewards
step 4: rewardsXuncertaitny

Regarding step 1: should I add 'uncertainty' as a UV as well?

Regarding step 4: Now I have three UV in the model (goals, rewards, uncertainty). Is it then necessary to look at goalsXrewards or even goalsXrewardsXuncertainty ?
GerineL
Moderator
Posts: 1477
Joined: Tue Jun 10, 2008 4:50 pm

### Re: regression analysis, (multiple) moderating effects

1.
you're right on both accounts (that is: you dont need to look at the 3-way interaction, but it makes sense to do so).
I oversimplified here just to make it clear that you add the main effect for rewards after you looked at the interaction.
basically, adding a step means: I want to look whether [variable X2] adds something to the equation on top of all variables [x1] I already entered in the equation.

step 1: goals; uncertainty
step 2: add goalsXuncertainty
step 3: add rewards
step 4: add rewardsXuncertaitny
step 5: add rewardsxuncertaintyxgoals

don't forget to center your variabels first!

2.
about entering them all at once vs. entering one at the time:
look into mutliple regression.

Oversimplified, but to give you an idea:

Basically, if you have several variables that share something, you have to test them all at once rather than one by one, because otherwise you might overestimate effects (or in some cases: underestimate them).

suppose for instance you'd want to know whether social anxiety is predicted by depression and loneliness.
If you'd test them both separately, you 'd probably find that both depression and loneliness predict social anxiety.

However, depression and loneliness have some things in common. They share some variance (e.g., both depression and loneliness have a negative affect component to them, this is the same negative affect that is part of both depression and loneliness).
If you would test them separately, you'd take that shared component into accountt wice (you count "negative affect" both for depression and for loneliness). Therefore, you would overestimate the unique effect that depression and loneliness have on social anxiety.
In fact, it may very well be that if you take loneliness into account, the unique part of depression that has no overlap with loneliness, does not predict social anxiety at all.
If you would test both at the same time, you thus get a better idea of the actual relationships.

Not testing them all at once thus does not only influence how easy it is to interpet, the results aslo become different.
Marina@SPSS
Posts: 4
Joined: Sun Feb 12, 2012 3:37 pm

### Re: regression analysis, (multiple) moderating effects

Many thanks for the detailed answer

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