Statistically comparing the standerdized coefficent of two models.

[Erik Mikael Johnson]

Hi, statlister!

I have a dataset that represents number of crimes by day(DV), where the observations represent days.

My two dichotomous IVs represents: (1) an intervention (area and period) with a baseline condition. (2) Coding corresponds to that of the first IV but the area is the greater city of the intervention area, excluding the area for the intervention. ex. a part of a city vs. the whole city

A consequence of this is that I can't use those variables in the same model (they cancel each other out), and that the number of observations are slightly larger for the second IV and that it has a lot larger mean of crime per day (i.e., represents a much larger area).

What I'm after is this, I want to able to compare a potential effect of the intervention ( first IV) to the effect of the second IV, in an attempt to control that the effect in the intervention area cannot be explained by a general trend.
As such, if I'm understanding it correctly, I need a test of the standardized coefficients between two models to see if they are significantly different.

If anyone knows how to do this or knows some reading pointers I would be very appreciative.

Here is an example of my data-set if anyone would need it.
It is a collapsed version of the original.
----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. For more info, type help dataex
clear
input int date float(IV_1 IV_2) double crime_by_date
22147 0 .  7
22130 0 .  3
22089 0 .  1
22194 0 .  7
22268 0 .  2
22190 0 . 10
22131 0 .  3
22197 0 .  5
22283 0 .  1
21995 0 .  3
21997 0 .  3
22110 0 .  2
22216 0 .  2
22237 0 .  2
22101 0 .  3
22209 0 .  1
22249 0 . 12
22202 0 .  1
22288 0 .  2
22128 0 .  5
end
format %td date
label values IV_1 järn
label def järn 0 "Baseline", modify

[George Ford]

suest?

[Erik Mikael Johnson]

Thanks for the fast response George.

I used the suest with the lincom option. The problem is that suest "reports" the unstandardized coefficients - .19 and 17.26 which are not comparable in the sense that it does not provide any meaningful information.

But maybe I did it wrong?

[George Ford]

How are you estimating the model?

[George Ford]

Could you standardize the variables prior to estimation?

[George Ford]

egen sY = std(Y)
egen sX = std(X)
egen sZ = std(Z)

eststo e1: reg sY sX
eststo e2: reg sY sZ
suest e1 e2

[Erik Mikael Johnson]

Perfect! Thanks once again, George.

So just to make sure, using lincom sZ-sX, a significant coefficient would mean that there is a difference then?

I might be out on a bit of a limb here, but is it also possible from the same premise to investigate if model 2 affects the relationship in model 1, similar to if one added the variables in the same model?
Ex. e1= -.001 insignificant (suprise) and e2 = -.091 significant, the difference is -.09 or .09 and significant.
Is it theoretically possible to see if this significant difference might indicate something on the relationship in the first model, in a sense controlling for the effect in the second model?

[George Ford]

It would mean there's a difference, yes.

I suppose this could also be implemented using Seemingly Unrelated Regression.

sureg (sY sX) (sY sZ)

Can part of a city get the treatment if the whole city does not (it appears from your statement that the two are perfectly correlated)? If not, then why bother with part of the city, and why are the coefficients different? If the whole city gets a 1 if any part gets a 1, then look at the parts, since if some parts don't get it, then the whole city=1 is mis-spsecified.

That is to say, I don't get the problem and the dataex is unhelpful in that regard.

[Erik Mikael Johnson]

Okay, thanks.

Well in my case the treatment (IV) was implemented only on a small delineated public space and period (1) (e.g a few blocks) and the preceding period for the same area got a (0)
The addresses corresponding to that space was then excluded from the second IV (City), which got a 1 on all addresses in the city which did not correspond with the treatment area, and a 0 for the same addresses but for the period preceding.
As you said, they are perfectly correlated, as "corr" display error message "no observations)

The unstandardized coefficients are different because of the large difference in crime by day. The second IV representing a much larger area have naturally more crime by day. This is why I'm after the effect relative to its standard deviations, which you help me with so eloquently.

What I need to do then is to see or test if the effect as observed in the treatment area is significantly different from the "natural" effect in the surrounding city, and if possible, to get results indicating how this general "effect" or trend affects the focal relationship in the treatment area

Eg. The lincom difference in #7 is -.09 but that does not mean that the "real" effect for sY sX was .09 i.e., crime by day has significantly risen in the treatment area when considering the general "trend", right?
Similar to if a control variable in a regression is related to the IV it will affect the coefficient in the focal relationship.

I'm not very handy with dataex and I'm not sure how to provide examples describing this particular problem.