Predicting xb with (temporary) alterations to x

[Leah Bevis]

I realize there must be an easy option that I'm missing here... I want to predict "yhat" after a regression, with various alterations to the matrix of covariates. Of course I can do this by changing the X matrix, but if I want to do this over and over, basically predicting the outcomes under various X scenarios, it becomes a pain to change X back and forth from it's original values. I thought either "predict" or "margins" would allow me to do this, but predict doesn't allow the "at" option, and margins doesn't seem to have an option for actually predicting a variable (aka a value for each observation)? Is there an efficient way to do this that I'm missing? Thanks!

[Richard Williams]

I'm not totally sure why you want to do this, but I think you can. Margins has an undocumented generate function:

https://www.statalist.org/forums/for...ted-gen-option

Example:

webuse nhanes2f, clear
logit diabetes weight i.female i.black
margins, at(weight = (30(10)180)) gen(xweight)
sum xw*

[Mike Lacy]

Another possibility would be to make up a dataset containing observations with the combinations of x values of interest, and then appending it or otherwise putting it into your dataset, along with a variable marking these cases ("predict_only =1 vs. 0"). Then you could do -regress y x1 x2 if (predict_only == 0)-, and then do -predict yhat if (predict_only ==1), xb- The important principle is that cases used by -predict- must have all the x values, but need not have been in the estimation sample for the regression model. This approach might or might not be more useful or convenient than -margins- in your situation.

[Leah Bevis]

Hi, thanks both! Richard, I didn't know margins could do that, neat. I thought it was the perfect solution, until I realized that the "at" option under margins takes only 1 variable (multiple values, but 1 variable) at at time, where I want to change a few variables at once. I guess this just isn't what margins was set up to do.

Mike, your solution is good, and I thought about doing that too. I can also use preserve and restore around (1) variable changes, (2) a prediction, which is then (3) exported into a tempfile, to be later merged back on. At the moment I'm just saving original variable values in a second variable called var_orig, so that I can move variable values back and forth from original values, simulating predictions under various scenarios. I guess it was silly to expect a canned way to do this. Thanks again!

[Richard Williams]

Richard, I didn't know margins could do that, neat. I thought it was the perfect solution, until I realized that the "at" option under margins takes only 1 variable (multiple values, but 1 variable) at at time, where I want to change a few variables at once. I guess this just isn't what margins was set up to do.

Not true. If you can keep the parentheses straight (a non-trivial task) you can do all sorts of convoluted and complicated things.

webuse nhanes2f, clear
logit diabetes weight height i.female i.black
margins, at(weight = (30(50)180) height = (135(20)200)) gen(xweight)
sum xw*

That gives you predictions for 16 height/weight combinations.

You can even have multiple at statements:

margins, at(weight = (30(50)180)) at(height = (135(20)200)) gen(zweight)
sum zw*

That gives you 8 predicted values, 4 for different values of height and 4 for different values of weight.

I'm not sure how complicated you want to make this, but the mtable command (part of mpost13_ado) can make for much more readable output.

 webuse nhanes2f, clear
 logit diabetes i.female i.black c.age c.age#c.age, nolog
 * Nice looking output
 mtable, at (black = (0 1) age = 20 ) at (black = (0 1) age = 47 ) at (black = (0 1) age = 74 ) dec(4) statistics(all)
 * even nicer looking output
 quietly mtable, at (black = 0 age = 20 ) rown(20 year old white) dec(4) statistics(all)
 quietly mtable, at (black = 1 age = 20 ) rown(20 year old black) dec(4) statistics(all) below
 quietly mtable, at (black = 0 age = 47 ) rown(47 year old white) dec(4) statistics(all) below
 quietly mtable, at (black = 1 age = 47 ) rown(47 year old black) dec(4) statistics(all) below
 quietly mtable, at (black = 0 age = 74 ) rown(74 year old white) dec(4) statistics(all) below
 mtable, at (black = 1 age = 74 ) rown(74 year old black) dec(4) below statistics(all)

Here is the output produced by the nice and even nicer mtable commands:

Expression: Pr(diabetes), predict()

           |    black       age     Pr(y)        se         z         p        ll        ul
 ----------+-------------------------------------------------------------------------------
         1 |        0        20    0.0033    0.0010    3.4674    0.0005    0.0015    0.0052
         2 |        1        20    0.0069    0.0021    3.3149    0.0009    0.0028    0.0109
         3 |        0        47    0.0325    0.0028   11.7688    0.0000    0.0271    0.0380
         4 |        1        47    0.0647    0.0081    7.9553    0.0000    0.0487    0.0806
         5 |        0        74    0.1078    0.0101   10.6929    0.0000    0.0881    0.1276
         6 |        1        74    0.1990    0.0237    8.3827    0.0000    0.1524    0.2455

Expression: Pr(diabetes), predict()

                    |    Pr(y)        se         z         p        ll        ul
 -------------------+-----------------------------------------------------------
  20 year old white |   0.0033    0.0010    3.4674    0.0005    0.0015    0.0052
  20 year old black |   0.0069    0.0021    3.3149    0.0009    0.0028    0.0109
  47 year old white |   0.0325    0.0028   11.7688    0.0000    0.0271    0.0380
  47 year old black |   0.0647    0.0081    7.9553    0.0000    0.0487    0.0806
  74 year old white |   0.1078    0.0101   10.6929    0.0000    0.0881    0.1276
  74 year old black |   0.1990    0.0237    8.3827    0.0000    0.1524    0.2455

Specified values of covariates

           |    black       age
 ----------+-------------------
     Set 1 |        0        20
     Set 2 |        1        20
     Set 3 |        0        47
     Set 4 |        1        47
     Set 5 |        0        74
   Current |        1        74

For more, see

https://www3.nd.edu/~rwilliam/stats3/Margins04.pdf

https://www3.nd.edu/~rwilliam/stats3/Margins05.pdf

In short, pretty much anything can be done. Doing it correctly may be a challenge though. Mike's suggestion may be tedious but it may be less error-prone than trying to do everything with a single mega command.