Results from a loop with quarterly and weekly data are different in relation to the sort of data: What is happening here?

Lisa Wilson

Join Date: Aug 2016
Posts: 158

#16

01 Mar 2021, 18:32

Thanks. I have done that now:

Code:

. sort  quarter_date myWEEK // this sort is important 

. 
. 
. 
. gen SUBsample=.
(1,846 missing values generated)

. replace SUBsample=1 if quarter_date<tq(1999q4)  // a sample to fit the model
(850 real changes made)

. replace SUBsample=2  if SUBsample==.   // a sample to evaluate the model (out of sample)
(996 real changes made)

. 
. 
. gen prediction=.
(1,846 missing values generated)

. 
. set seed 12345 // this is done for the results to be reproducible 

. 
. levelsof myWEEK, local(levels)
1 2 3 4 5 6 7 8 9 10 11 12

. 
. foreach x of local levels {
  2.   
. lasso linear quarterly_macro var1-var30 if SUBsample == 1 & myWEEK==`x'
  3. estimates store LASSOrev 
  4. predict temp if SUBsample==2 & myWEEK==`x', postselection
  5. replace prediction=temp  if myWEEK==`x'
  6. drop temp
  7. }
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because of collinearity with another variable
note: var25 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1299048   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .5129244
Grid value 2:     lambda = .1183644   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .5233544
Grid value 3:     lambda = .1078492   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .5364788
Grid value 4:     lambda = .0982682   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .5501552
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         70
                                            No. of covariates =         26
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1299048         0       0.0899     .5129244
       2 |    lambda after    .1183644         1      -0.1121     .5233544
       4 |     last lambda    .0982682         1      -0.1690     .5501552
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var25 dropped because it is constant
note: var28 dropped because it is constant
note: var3 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1273055   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4883653
Grid value 2:     lambda =  .115996   no. of nonzero coef. =       2
Folds: 1...5....10   CVF = .491965
Grid value 3:     lambda = .1056912   no. of nonzero coef. =       2
Folds: 1...5....10   CVF = .4956619
Grid value 4:     lambda = .0963019   no. of nonzero coef. =       2
Folds: 1...5....10   CVF = .5002015
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         23
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1273055         0       0.0488     .4883653
       2 |    lambda after     .115996         2      -0.0566      .491965
       4 |     last lambda    .0963019         2      -0.0743     .5002015
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
note: var25 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1469631   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4840107
Grid value 2:     lambda = .1339073   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4870012
Grid value 3:     lambda = .1220114   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4900909
Grid value 4:     lambda = .1111722   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .492393
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         23
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1469631         0       0.0395     .4840107
       2 |    lambda after    .1339073         1      -0.0459     .4870012
       4 |     last lambda    .1111722         1      -0.0575      .492393
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .079373   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .5158857
Grid value 2:     lambda = .0723217   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .52118
Grid value 3:     lambda = .0658968   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .5218032
Grid value 4:     lambda = .0600427   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .5206043
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda     .079373         0       0.1079     .5158857
       2 |    lambda after    .0723217         4      -0.1193       .52118
       4 |     last lambda    .0600427         5      -0.1181     .5206043
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1115648   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4831735
Grid value 2:     lambda = .1016537   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4852746
Grid value 3:     lambda = .0926231   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4889328
Grid value 4:     lambda = .0843947   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4938684
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1115648         0       0.0377     .4831735
       2 |    lambda after    .1016537         1      -0.0422     .4852746
       4 |     last lambda    .0843947         1      -0.0607     .4938684
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .116832   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4950638
Grid value 2:     lambda =  .106453   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4987938
Grid value 3:     lambda =  .096996   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .5031363
Grid value 4:     lambda = .0883792   no. of nonzero coef. =       2
Folds: 1...5....10   CVF = .5082863
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda     .116832         0       0.0632     .4950638
       2 |    lambda after     .106453         1      -0.0712     .4987938
       4 |     last lambda    .0883792         2      -0.0916     .5082863
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .0922869   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .5015781
Grid value 2:     lambda = .0840883   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .5078456
Grid value 3:     lambda = .0766182   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .5120959
Grid value 4:     lambda = .0698116   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .514441
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .0922869         0       0.0772     .5015781
       2 |    lambda after    .0840883         3      -0.0907     .5078456
       4 |     last lambda    .0698116         4      -0.1048      .514441
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .0978168   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4869643
Grid value 2:     lambda = .0891271   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4915056
Grid value 3:     lambda = .0812093   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4971674
Grid value 4:     lambda = .0739949   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .5038661
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .0978168         0       0.0458     .4869643
       2 |    lambda after    .0891271         1      -0.0556     .4915056
       4 |     last lambda    .0739949         3      -0.0821     .5038661
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1263635   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4842843
Grid value 2:     lambda = .1151377   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4873655
Grid value 3:     lambda = .1049092   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4943139
Grid value 4:     lambda = .0955894   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .5027705
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         70
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1263635         0       0.0260     .4842843
       2 |    lambda after    .1151377         1      -0.0325     .4873655
       4 |     last lambda    .0955894         1      -0.0651     .5027705
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1331209   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4934726
Grid value 2:     lambda = .1212948   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4949057
Grid value 3:     lambda = .1105193   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .496512
Grid value 4:     lambda = .1007011   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4985962
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         24
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1331209         0       0.0598     .4934726
       2 |    lambda after    .1212948         1      -0.0629     .4949057
       4 |     last lambda    .1007011         1      -0.0708     .4985962
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var25 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1335231   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4854478
Grid value 2:     lambda = .1216613   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4852986
Grid value 3:     lambda = .1108532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4870591
Grid value 4:     lambda = .1010053   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4895512
Grid value 5:     lambda = .0920323   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4929817
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         23
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda    .1335231         0       0.0426     .4854478
     * 2 | selected lambda    .1216613         1      -0.0422     .4852986
       3 |    lambda after    .1108532         1      -0.0460     .4870591
       5 |     last lambda    .0920323         1      -0.0587     .4929817
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)
note: var3 dropped because it is constant
note: var9 dropped because it is constant
note: var11 dropped because it is constant
note: var21 dropped because it is constant
note: var22 dropped because it is constant
note: var25 dropped because it is constant
note: var28 dropped because it is constant
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda = .1335061   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4863952
Grid value 2:     lambda = .1216458   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4886327
Grid value 3:     lambda = .1108391   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .49106
Grid value 4:     lambda = .1009925   no. of nonzero coef. =       2
Folds: 1...5....10   CVF = .4948401
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =         71
                                            No. of covariates =         23
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
     * 1 | selected lambda    .1335061         0       0.0446     .4863952
       2 |    lambda after    .1216458         1      -0.0494     .4886327
       4 |     last lambda    .1009925         2      -0.0627     .4948401
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with postselection coefficients)
(83 real changes made)

.
end of do-file

. sort quarter_date myWEEK

. br quarter_date myWEEK prediction

. dataex quarter_date myWEEK prediction if prediction!=.

----------------------- copy starting from the next line -----------------------

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(quarter_date myWEEK prediction)
159  1  .1105143
159  2 .10566197
159  3 .10566197
159  4 .10566197
159  5 .10566197
159  6 .10566197
159  7 .10566197
159  8 .10566197
159  9 .10755715
159 10 .10566197
159 11 .05600106
159 12 .10566197
160  1  .1105143
160  2 .10566197
160  3 .10566197
160  4 .10566197
160  5 .10566197
160  6 .10566197
160  7 .10566197
160  8 .10566197
160  9 .10755715
160 10 .10566197
160 11 .05600106
160 12 .10566197
161  1  .1105143
161  2 .10566197
161  3 .10566197
161  4 .10566197
161  5 .10566197
161  6 .10566197
161  7 .10566197
161  8 .10566197
161  9 .10755715
161 10 .10566197
161 11 .05600106
161 12 .10566197
162  1  .1105143
162  2 .10566197
162  3 .10566197
162  4 .10566197
162  5 .10566197
162  6 .10566197
162  7 .10566197
162  8 .10566197
162  9 .10755715
162 10 .10566197
162 11 .05600106
162 12 .10566197
163  1  .1105143
163  2 .10566197
163  3 .10566197
163  4 .10566197
163  5 .10566197
163  6 .10566197
163  7 .10566197
163  8 .10566197
163  9 .10755715
163 10 .10566197
163 11 .05600106
163 12 .10566197
164  1  .1105143
164  2 .10566197
164  3 .10566197
164  4 .10566197
164  5 .10566197
164  6 .10566197
164  7 .10566197
164  8 .10566197
164  9 .10755715
164 10 .10566197
164 11 .05600106
164 12 .10566197
165  1  .1105143
165  2 .10566197
165  3 .10566197
165  4 .10566197
165  5 .10566197
165  6 .10566197
165  7 .10566197
165  8 .10566197
165  9 .10755715
165 10 .10566197
165 11 .05600106
165 12 .10566197
166  1  .1105143
166  2 .10566197
166  3 .10566197
166  4 .10566197
166  5 .10566197
166  6 .10566197
166  7 .10566197
166  8 .10566197
166  9 .10755715
166 10 .10566197
166 11 .05600106
166 12 .10566197
167  1  .1105143
167  2 .10566197
167  3 .10566197
167  4 .10566197
end
format %tq quarter_date

I hope this helps to identify what is wrong with the -lasso- use in the loop.

I look forward to hearing your response. Thank you so much.

Comment

Clyde Schechter

Join Date: Apr 2014

Posts: 30150
#17

01 Mar 2021, 22:45

I see a problem. If you look at the -lasso- output, focusing on the tables with the lambdas, you will see that in nearly all of the iterations, the selected result is the one with 0 variables selected. In other words, for all but a couple of the weeks the model selected is just the constant term--hence the lack of variation in the results. I think the ultimate problem is that your data are just not suitable for this approach. -lasso- works best when there are many predictors, most of which are destined to be left out of the model, but the few that enter the model are fairly strong. In your case, what you have are a bunch of variables that are all of essentially no predictive value. Even where there is a selected variable, the out-of-sample R squared is close to zero, actually negative. I notice that in many of the weeks, several of the variables are dropped because they are constant. And I wonder if the variables that remain are close to constant--that would explain their inability to explain outcome variance.

Anyway, I don't have a deep understanding of -lasso- and what I have written above is the extent of my insight. But I do believe the essence of it is that you are just asking the data to do more than it is capable of. You need a data set where the variables have more predictive capacity in order to apply this method.

If somebody following along has a better or different understanding of the situation, I hope they will chime in. I'd like to learn more about this, too.
Comment

Lisa Wilson

Join Date: Aug 2016
Posts: 158

#18

02 Mar 2021, 00:47

Thank you so much Clyde Schechter

I want to also share the results when I run the same code but without -myWEEK=`x' in the same line when we run the lasso. In this case, I get sensible results, and the lasso selects several variables. Note that the R2 may not be high but the macro variable is in fact measured as errors or revisions which are very difficult to be predicted.
Please have a look:

Code:

. sort  quarter_date myWEEK // this sort is important 

. 
. 
. 
. gen SUBsample=.
(1,846 missing values generated)

. replace SUBsample=1 if quarter_date<tq(1999q4)  // a sample to fit the model
(850 real changes made)

. replace SUBsample=2  if SUBsample==.   // a sample to evaluate the model (out of sample)
(996 real changes made)

. 
. 
. gen prediction=.
(1,846 missing values generated)

. 
. set seed 12345 // this is done for the results to be reproducible 

. 
. levelsof myWEEK, local(levels)
1 2 3 4 5 6 7 8 9 10 11 12

. 
. foreach x of local levels {
  2.   
. lasso linear quarterly_macro var1-var30 if SUBsample == 1 
  3. estimates store LASSOrev 
  4. predict temp if SUBsample==2 & myWEEK==`x', penalized
  5. replace prediction=temp  if myWEEK==`x'
  6. drop temp
  7. }
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4679962
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4680501
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4681945
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4682741
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4678852
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4670921
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .46651
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4660178
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4653309
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4642204
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4628241
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .461378
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4601129
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .45925
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4586102
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4581069
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4577602
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .457408
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4571716
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .4569787
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4568816
Grid value 22:    lambda = .0107269   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4572275
Grid value 23:    lambda = .0097739   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4578764
Grid value 24:    lambda = .0089056   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .458571
Grid value 25:    lambda = .0081145   no. of nonzero coef. =      18
Folds: 1...5....10   CVF = .4592524
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0031     .4679962
      20 |   lambda before    .0129206        15       0.0205     .4569787
    * 21 | selected lambda    .0117727        17       0.0208     .4568816
      22 |    lambda after    .0107269        17       0.0200     .4572275
      25 |     last lambda    .0081145        18       0.0157     .4592524
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4675557
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4673491
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4674566
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4674734
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4671639
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .466731
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4662746
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4659209
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4652793
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4641166
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .462926
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4616517
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4606399
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4600805
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4599324
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4600541
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4601551
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4603565
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4605374
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .460739
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4613779
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0021     .4675557
      14 |   lambda before    .0225791        11       0.0139     .4600805
    * 15 | selected lambda    .0205732        11       0.0142     .4599324
      16 |    lambda after    .0187455        12       0.0140     .4600541
      21 |     last lambda    .0117727        17       0.0111     .4613779
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
note: var28 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4671626
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4671274
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4668262
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4662748
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4655569
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4642978
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .462946
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .461657
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .460368
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4589583
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4573456
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4560136
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4550349
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4543975
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4541725
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4538495
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4537191
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4537747
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4538085
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .4537054
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4539599
Grid value 22:    lambda = .0107269   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .454397
Grid value 23:    lambda = .0097739   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4549359
Grid value 24:    lambda = .0089056   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4555179
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         26
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0013     .4671626
      19 |   lambda before    .0141803        14       0.0273     .4538085
    * 20 | selected lambda    .0129206        15       0.0276     .4537054
      21 |    lambda after    .0117727        17       0.0270     .4539599
      24 |     last lambda    .0089056        17       0.0237     .4555179
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4678678
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4672716
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4667401
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4663807
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4657634
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4648776
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .464134
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4631294
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4618727
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4603564
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4588729
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4575057
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4564676
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4555316
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4550338
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4547335
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4544967
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4543318
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4542397
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .454405
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .454844
Grid value 22:    lambda = .0107269   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4556178
Grid value 23:    lambda = .0097739   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4568668
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0028     .4678678
      18 |   lambda before    .0155629        13       0.0262     .4543318
    * 19 | selected lambda    .0141803        14       0.0264     .4542397
      20 |    lambda after    .0129206        15       0.0261      .454405
      23 |     last lambda    .0097739        17       0.0208     .4568668
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4681504
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4678956
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4674176
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4670662
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4662588
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4653953
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4645442
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4636811
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4624568
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4612471
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4598757
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4588472
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4581462
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4578649
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .457848
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .457929
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4581118
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4586234
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4590759
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .4593571
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0034     .4681504
      14 |   lambda before    .0225791        11       0.0186     .4578649
    * 15 | selected lambda    .0205732        11       0.0187      .457848
      16 |    lambda after    .0187455        12       0.0185      .457929
      20 |     last lambda    .0129206        15       0.0154     .4593571
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4687719
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4686223
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .468399
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4682402
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4677396
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4668274
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4657136
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4647239
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4635661
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4616842
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4601508
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4590093
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4581979
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4573072
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4567259
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4560611
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4556289
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4553643
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4552192
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .4550419
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4549346
Grid value 22:    lambda = .0107269   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4549962
Grid value 23:    lambda = .0097739   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4554479
Grid value 24:    lambda = .0089056   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4562525
Grid value 25:    lambda = .0081145   no. of nonzero coef. =      18
Folds: 1...5....10   CVF = .4571315
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0047     .4687719
      20 |   lambda before    .0129206        15       0.0247     .4550419
    * 21 | selected lambda    .0117727        17       0.0249     .4549346
      22 |    lambda after    .0107269        17       0.0248     .4549962
      25 |     last lambda    .0081145        18       0.0202     .4571315
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...
Grid value 1:     lambda =  .075676   no. of nonzero coef. =       0
Folds: 1...5....10   CVF = .4683256
Grid value 2:     lambda = .0689532   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4684147
Grid value 3:     lambda = .0628276   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .468563
Grid value 4:     lambda = .0572461   no. of nonzero coef. =       1
Folds: 1...5....10   CVF = .4687462
Grid value 5:     lambda = .0521606   no. of nonzero coef. =       3
Folds: 1...5....10   CVF = .4687869
Grid value 6:     lambda = .0475268   no. of nonzero coef. =       4
Folds: 1...5....10   CVF = .4688084
Grid value 7:     lambda = .0433046   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .468757
Grid value 8:     lambda = .0394576   no. of nonzero coef. =       5
Folds: 1...5....10   CVF = .4686406
Grid value 9:     lambda = .0359523   no. of nonzero coef. =       7
Folds: 1...5....10   CVF = .4681354
Grid value 10:    lambda = .0327584   no. of nonzero coef. =       8
Folds: 1...5....10   CVF = .4674565
Grid value 11:    lambda = .0298482   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4664486
Grid value 12:    lambda = .0271966   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4655293
Grid value 13:    lambda = .0247805   no. of nonzero coef. =       9
Folds: 1...5....10   CVF = .4646018
Grid value 14:    lambda = .0225791   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4642576
Grid value 15:    lambda = .0205732   no. of nonzero coef. =      11
Folds: 1...5....10   CVF = .4643387
Grid value 16:    lambda = .0187455   no. of nonzero coef. =      12
Folds: 1...5....10   CVF = .4644699
Grid value 17:    lambda = .0170802   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4642504
Grid value 18:    lambda = .0155629   no. of nonzero coef. =      13
Folds: 1...5....10   CVF = .4640877
Grid value 19:    lambda = .0141803   no. of nonzero coef. =      14
Folds: 1...5....10   CVF = .4640245
Grid value 20:    lambda = .0129206   no. of nonzero coef. =      15
Folds: 1...5....10   CVF = .4642232
Grid value 21:    lambda = .0117727   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4649463
Grid value 22:    lambda = .0107269   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4660712
Grid value 23:    lambda = .0097739   no. of nonzero coef. =      17
Folds: 1...5....10   CVF = .4673186
... cross-validation complete ... minimum found

Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         27
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0038     .4683256
      18 |   lambda before    .0155629        13       0.0053     .4640877
    * 19 | selected lambda    .0141803        14       0.0054     .4640245
      20 |    lambda after    .0129206        15       0.0050     .4642232
      23 |     last lambda    .0097739        17      -0.0016     .4673186
--------------------------------------------------------------------------
* lambda selected by cross-validation.
(option xb assumed; linear prediction with penalized coefficients)
(83 real changes made)
note: var11 dropped because it is constant
note: var22 dropped because it is constant
note: var21 dropped because it is constant in C.V. subsamples
note: var28 dropped because it is constant in C.V. subsamples
10-fold cross-validation with 100 lambdas ...


Lasso linear model                          No. of obs        =        850
                                            No. of covariates =         26
Selection: Cross-validation                 No. of CV folds   =         10

--------------------------------------------------------------------------
         |                                No. of      Out-of-      CV mean
         |                               nonzero       sample   prediction
      ID |     Description      lambda     coef.    R-squared        error
---------+----------------------------------------------------------------
       1 |    first lambda     .075676         0       0.0025     .4677543
      20 |   lambda before    .0129206        15       0.0252     .4548254
    * 21 | selected lambda    .0117727        17       0.0258     .4545095
      22 |    lambda after    .0107269        17       0.0258      .454531
      25 |     last lambda    .0081145        18       0.0218     .4563726
--------------------------------------------------------------------------



. 
end of do-file

.

As you see here from the output, it seems that the -lasso- is being estimated for each week although we have not added this myWEEK=`x` condition in the lasso code line. If Stata estimates the model for the entire SUBsample=1 and not as per each week in SUBsample=1, shouldn't the output be for only one regression?

NOTE: I had to remove the last few tables in the results only because the forum does not allow me to send all output (Maximum is 30000).

Comment

Clyde Schechter

Join Date: Apr 2014

Posts: 30150
#19

02 Mar 2021, 10:32

As you see here from the output, it seems that the -lasso- is being estimated for each week although we have not added this myWEEK=`x` condition in the lasso code line.

No, that is not what is happening. You can see that because if you look closely at the "Lasso linear model" output tables, you will see that the sample size is 850 in each case. (By contrast, when you ran it with -if myWEEK==`x'-, the sample size was variable but always in the low 70's.) The reason the results vary by week, even though -lasso- is working with the same sample (i.e. all of SUBsample 1) in every week, is that -lasso- is inherently non-deterministic. If you were to re-do this, setting the random number seed at the top of the loop, rather than outside the loop, then you would see identical results for all weeks.

The reason the results are more sensible when you don't restrict the sample to a single week is that you are giving -lasso- more data to work with. With more data, there is more information, both in terms of variation in the predictor variables, and more evidence about how those variables relate to the outcome. Consequently the lasso is able to identify more predictors, and those predictors are actually numerous (note that the selected models have somewhere between 10 and 20 variables now).
Comment
Lisa Wilson

Join Date: Aug 2016

Posts: 158
#20

02 Mar 2021, 18:26

Thanks.

If you were to re-do this, setting the random number seed at the top of the loop, rather than outside the loop, then you would see identical results for all weeks.

I assume that you mean the following:

Code:

gen prediction=. levelsof myWEEK, local(levels) foreach x of local levels { set seed 12345 lasso linear quarterly_macro var1-var30 if SUBsample == 1 estimates store LASSOrev predict temp if SUBsample==2 & myWEEK==`x', penalized replace prediction=temp if myWEEK==`x' drop temp }

If so, I have tried it and I think the output is identical as you expected. I think this adjustment to the seed number is more sensible?!

The reason the results are more sensible when you don't restrict the sample to a single week is that you are giving -lasso- more data to work with.

If I do not restrict the model to be run on a weekly basis, this means that I run a lasso regression using all week data. Note that each quarterly_macro observation will then have 12 observations for each variable in each quarter.
Is there any statistical reason to invalidate the results in this case?
Comment
Clyde Schechter

Join Date: Apr 2014

Posts: 30150
#21

03 Mar 2021, 10:27

Well, if you want to use the same lasso results throughout, rather than re-setting the random number seed and re-running lasso, just take the -lasso- outside the loop. Do it once only. Then loop just the -predictions-. (The reason I suggested putting the -set seed- command at the top of the loop in #19 was just to demonstrate my point about what is happening, it was not intended as something to use for production code, though I did not make that clear.)

If I do not restrict the model to be run on a weekly basis, this means that I run a lasso regression using all week data. Note that each quarterly_macro observation will then have 12 observations for each variable in each quarter.
Is there any statistical reason to invalidate the results in this case?

Yes, that is a correct description of what would happen if you take that approach. There is nothing that would "invalidate" the results from a general statistical perspective. The issue is whether those results are an appropriate answer to your research question, or whether they are an answer to the wrong question. So you have to think about it in those terms. What is it you are trying to accomplish? Can it be done in this way or not? Based on the names of your variables, I am guessing that you are working in the general domain of finance or economics. If that's true, even if you were to explain your research question here, I probably would not be able to figure this out for you, as I have no expertise in those domains. If you need help figuring out this issue, you might be best off consulting a colleague in your domain.
Comment

Announcement

Comment

Comment

Comment

Comment

Comment

Comment