vselect without intercept

[Marco Mello]

Hi all,

I have a problem which is driving me crazy. I want to perform a Best Subsets Selection in order to detect the subset of independent variables in my dataset which have the highest explanatory power for my dependent variable. I am using both gvselect and vselect, but I cannot find a way to exclude the intercept from their procedures. Does it exist a way to do so and therefore to perform the best selection procedure by only considering your regressors without a constant?

Thank you for taking your time to help me,
Marco

[Mike Lacy]

From a quick experiment I made, it appears that the -allpossible- command available from ssc, which is another all possible subsets utility, will allow and pay attention to the -noncons- option on a -regress- command. -allpossible- allows users to specify their own choice of estimation command.

[Marco Mello]

Thank you very much for your response Mike.

Unfortunately, the -allpossible- command seems to be very slow, since it was originally meant for a maximum number of 6 predictors if I understood correctly. Does anybody have any other suggestion? I need to perform a best selection procedure among a large number of predictors and vselect was working fast enough. However, I would like to check what happens to the algorithm's results if I remove the intercept.

[Steve Samuels]

Selecting the best subset is just a souped up version of stepwise regression and has the same defects. All the criticisms listed in this Stata FAQ apply. Do it only if you plan to cross-validate the R-square and stability of the "best" model.

I'm curious : what is the empirical or theoretical rationale for omitting the intercept?

[Marco Mello]

Thank you for your reply Steve.

I know the drawbacks of the stepwise regression and therefore of the BSS procedure. However, I have a bunch of predictors and I want to understand which are, among them, the regressors with the highest predictive power for my dependent variable. I do not want to establish any causal relationship between my dependent variable and the regressors, but I just want to detect which seems to be the best predictors at explaining my dependent variable. I am following a similar approach to the one used by Becker to try to explain the Brexit vote in this paper : http://cep.lse.ac.uk/pubs/download/dp1480.pdf

Do you have any better suggestion?

Thanks, Marco

[Steve Samuels]

Ah, the goal is frankly exploratory. I agree with the approach. The authors are not fooling themselves.

However the authors did not omit intercepts from their models, just from their tables. From page 4:

, ...we have less to say about the overall level of support for Vote Leave. Put differently, our paper focuses on slope coefficients, not intercepts.

Page 7 Equation 2 has an intercept

Page 10

The positive relationship is striking. A simple regression line has an intercept of around 25 percent and a slope close to unity, yielding an R2 of 75 percent.

Page 27

Therefore, while the intercept of support for Vote Leave is clearly lower in Scotland,...

[Steve Samuels]

I'm a little disappointed that the authors did not qualify the statements about significance and p-values. However to their credit, they report they report many models besides the "best subset"-a good example to follow.

[Marco Mello]

Thank you very much Steve, your comments are helping me a lot.

I am glad that you agree with the approach, I woud like to try even different approaches based on Lasso, Ridge and Stepwise to check whether there is a sort of consistency among their outputs. I finally understood that the authors are not omitting the intercept, which is definitely what I am going to do as well. Thus, I guess I can also include dummy variables among my independent variables. So far I was a bit skeptical about this because I was convinced that they omitted the intercept, instead they are just removing it from the tables.

Thank you again,
Marco

[Steve Samuels]

Crossed with your post.
Added: I have to withdraw my statement that the authors' analysis was "exploratory".

Many of the analyses in the paper were based on substantive understanding and were not exploratory . Many or most reported results appear to be from models that were not "best". You have stated that your goal is to find the one best subset. If so, your strategy differs from that in the paper and I think that the criticisms of stepwise will still apply.

Added: The shrinkage techniques you mention will help, but I still think that you should find some of validation scheme.

[Marco Mello]

My goal is to detect which independet variables in my dataset have the highest predictive power to explain my dependent variable, which is an election result like the Brexit vote for them. I am planning to perform the BSS procedure and to explore this by observing the results of the algorithm for any possible combination of regressors. Do you think this is not the right approach?

[Steve Samuels]

Becker, Fetzer and Novy (BFN) authors of the Brexit paper, had two approaches besides subset selection: an elaborate "Full Model" and "Within-City" analysis. About best-subset selection they say:

The result is a sequence of models M1, ..., Ms, .., Mp, where the overall optimal model Ms∗ is chosen by using either cross validation or some degree-of-freedom- adjusted measure of goodness of fit such as the Akaike information criterion (AIC). Throughout, we use the AIC to decide upon the overall optimal model Ms∗ robustly explaining the variation in the dependent variable.

Before proceeding, I'd suggest that you look at Chapters 4 and 5 of these class notes

[Marco Mello]

Thank you very much Steve, I will look at these chapters before proceeding!

[Jessica Thacker]

Hi, I wanted to ask if vselect works with independent dummy variable? Eg, if sex1=1 if female, sex2=0 if male. Then do we include both of them in vselect or only one of them?