Dummy and continuous interaction - TWO VIEWS

[Paul Leeds]

Dear All,

My research involve testing the interaction between a dummy variables (change=take the value 1 if manager is changed, 0 otherwise) and continuous variable (tenure=being the log of the number of years 1-10). the dependent variable is "Read" being the readership of disclosure which ranges 1-100.

Now the results came as follows:

Dependent Variable: Read	Model (1)	Model (2)
Independent Variables
Change	0.545	-4.308**
	(0.608)	(1.324)
tenure	-0.345**	-0.350**
	(0.120)	(0.121)
change*Tenure		1.1891*** (.2459)
Constant	41.26***	41.39***
	(2.156)	(2.111)
R2	0.0941	0.0966

As can be seen, in model 1 the results of the relationship between Read and Change is insignificant, whereas in model 2 the interaction is significant.

Does the interpretation of this relationship that the relationship is negative and that those who change their manager have less readership and that the increase in Tenure make positive or is it the reverse since the interaction term is positive?

Kind Regards

Paul

[Carole J. Wilson]

In model 1, increasing tenure leads to a decline in readership, and a change in manager increases readership
In model 2, when there is no manager change (change=0): increasing tenure leads to a decline in readership (-0.35)
In model 2, when there is a manager change (change=1): average readership is lower (change = -4.3) and increasing tenure increases readership (1.1891+ -0.35= 0.84)


See Clyde's comments in the other post about the appropriateness of comparing these models.

[Richard Williams]

I would say that the answer depends on the value of tenure. Suppose you plot read vs tenure, and have separate lines for changed vs not changed. Because the slopes are different for the two groups, at some point the lines will cross. Before they cross, those who did not change will have higher scores. After the cross, those who changed will have the higher scores. If I am doing the math right in my head, that will occur at around tenure = 5.25. But that is outside the observed range of values, right? e.g. log of 10 is as high as tenure goes, which is well below 5.25.

Here is an example, where I use the user-written mcp command (available from SSC) but you could accomplish the same thing using margins and marginsplot:

webuse nhanes2f, clear
reg weight height i.female i.female#c.height
mcp height female, var1(20)

The model (which isn't very good) says that at small values of height, women weigh more than men. Indeed, if a man and woman were both 0 centimeters tall, the woman would weight 50 kilograms more. Of course, nobody is that short!

What you are probably most interested in is what happens within the observed range of your data. In your case it sounds like change is bad, but less bad the longer the tenure is.

Incidentally, that -4.308 may not mean much. It is just the predicted difference between changed and non-changed places when tenure = 0. In this case it sounds like tenure can equal 0 but sometimes 0 isn't even a possible value. You have to careful about looking at main effects when interactions are added to the model.

[Paul Leeds]

Many Thanks Clarole and Richard

The value of tenure is the natural log of the values 1-10 years.

My understanding of the replies here and the other thread that, in model 2, as tenure increase the relationship between change and Read becomes positive, meaning longer tenure is preferred!

Is that accurate interpretation?

Regards

[Clyde Schechter]

No. That might be true if the values of tenure went up high enough. But in the other thread you state that the largest value is 9 and that you used natural logarithms. So at the highest value of tenure, 9, the effect of change on read is -4.308 + 1.891*log(9) which evaluates to approximately -1.7, which is still negative. It is substantially less negative than when tenure = 1, where the effect of change on read is -4.308 + 1.891*log(1) = -4.308. But you never reach positive territory for the effect of change.

What does go from negative to positive is the effect of a unit increase in (log) tenure on Read. When change = 0, that effect is -0.35, but when change = 1, that effect is -0.35 + 1.891, which is approximately 1.54. So in the change = 0 condition, increased tenure is actually associated with reduced values of Read, but when change = 1, increased tenure is actually associated with increased values of Read. Do run the code involving -mcp-, as Richard suggested in #3: it will give you a visual grasp of this that words can at best convey with difficulty.

As for what is preferred, that depends, first on what the meanings of these variables are, and second on a value judgment about what outcomes are better.

[Paul Leeds]

Thanks Clyde,

Theoretically, tenure cannot get high enough to level -4. and so Read becomes positive.

So, we can say that the effect of change on read is negative and that as tenure increases the effect of change on read is mitigated?

[Clyde Schechter]

So, we can say that the effect of change on read is negative and that as tenure increases the effect of change on read is mitigated?

Well, again I think "mitigated" is a word that implies a value judgment, and not knowing what Read actually represents, I'm hesitant to endorse it. But, value-neutrally, we can definitely say that as tenure increases, the effect of change on read is attenuated. You can say whether that's a good thing or a bad thing.

[Richard Williams]

Theoretically, tenure cannot get high enough to level -4. and so Read becomes positive.

I am not sure what you mean by that. But the intercept is 41 and Read ranges from 1-100 so yes, Read is always positive. But according to the model a place that doesn't change managers should do better than an otherwise identical place that does.

But I would wonder about the adequacy of your model. Granted I know nothing about the theory here and not a whole lot more about the variables. But I wonder if places change managers because they are doing poorly on Read (whatever that is). So yes, the change places do worse, but they might have done worse still if they had not changed managers. Put another way, if we could construct an alternate universe in which nobody changed managers, we might find that "places that would have changed but we magically prevented them from doing so" would have fared even worse than they did by making the change.

This sort of issue comes up with remedial programs. So, for example, children in a remedial reading program probably won't score as high as children not in the remedial program. But (if the program is good) their scores would be even lower if they had not been in the program. (I am assuming here that selection in the program is not random, i.e. those who get into the program do so because they have more reading problems than those who do not.)

In short, I would probably want some additional controls that it was really the change in managers that was important, as opposed to the fact that those who changed managers were in worse shape to begin with.

[Steve Samuels]

This is an interesting thread. Like Richard, I have doubts about this model. You speak of the effect of an 'increase in tenure". "Tenure" means a length of time ("a period for which an office is held" in my Apple Dictionary). Using "tenure" to describe a logged variable is therefore misleading. Simply use the term "log years" or "log years of tenure".

The log transformation complicates interpretation. It implies that equal relative differences in years are associated with same difference in mean readership. Thus a difference between 1 and 2 years and a difference between 4 and; 8 years have the same effect. I'd find this surprising. Is this what you observe in the raw data? The only evidence for the log that I would find convincing is linearity in plots of readership against years (log scale), stratified by change.

[Paul Leeds]

Thanks Clyde, Richard and Steve,

Read here being a scale of 1-100. Lower score denotes lower readability which is unfavorable.
Manager who perform good should have higher score of Read. However, the hypothesis is whether managers who have longer tenure (log of years 1-9) may mitigate the negative relationship between Change and Read.

So, as the coefficient of Tenure indicate, longer tenure is associated with lower Read scores. This is expected to have an effect on Change/Read relationship.
As I got it now, in the second model, the effect of Change on Read is negative. However, longer tenure (to unknown threshold) may have inverse effect.
Nevertheless, as the model tells us, the effect of change on read is still negative even if tenure is at the maximum (log of 9 years).

Is that accurate?