## Regularized regression

Occasional Contributor
Posts: 9

# Regularized regression

I am running a regularized regression on several traits using the following code:

Proc glmselect data = DalReg1 plots(stepaxis=normb)=coefficients;
Model TW = Protein TGW SGD GL GW Size Shape / selection = LASSO(stop=none choose = cvex);
run;

The output is great. However, I am wondering how to obtain standard errors for each coefficient. Help suggestions on this, please?

Thanks,

Dalitso

Super User
Posts: 13,521

## Re: Regularized regression

[ Edited ]

The standard error for the coefficients appears in the parameter estimates results which should be in the output by default. Do mean to ask how to get that information into a data set?

Occasional Contributor
Posts: 9

## Re: Regularized regression

Ballardw: Here is the output. There is no SE.

SAS Output

Analysis of Variance Source DF Sum of Squares Mean Square F Value Model Error Corrected Total
 5 4523.89 904.77703 208.11 1271 5525.89 4.34767 1276 10050

Root MSE Dependent Mean R-Square Adj R-Sq AICAI CCS BC CVEX PRESS
 2.08511 58.9225 0.4501 0.448 3161.72 3161.81 1913.63 4.8573

Parameter Estimates Parameter DF Estimate Intercept Protein TGW SGD GL Shape
 1 19.1415 1 -0.221838 1 0.1929 1 15.1118 1 0.040392 1 0.195827
Posts: 5,523

## Re: Regularized regression

There are no SE provided when variable selection is performed with LASSO. There might be a good reason for that. Models resulting from variable selection methods do not account in their parameter estimates SE for model uncertainty. You can get parameter SEs for the chosen model, conditional on that choice, with other regression procedures, such as GLM, GENMOD or GLIMMIX.

PG
Occasional Contributor
Posts: 9

## Re: Regularized regression

Thanks PG. I agree. I thought there must be a good reason for not having SEs in LASSO procedure. I might have to do some more literature review on this. I chose LASSO because I have multicollinearity in my data but I am curious what SEs would be, if it is possible to generate them. Thanks again!

SAS Employee
Posts: 386

## Re: Regularized regression

You might consider doing LASSO selection via PROC NLMIXED instead as illustrated in this note

Occasional Contributor
Posts: 9

## Re: Regularized regression

Hi Dave,

I am not sure if I am familiar with NLMIXED. Is there any other way with proc GLMSELECT? If not I might just to have a go at NLMIXED and see.

Thanks Dave.

Super User
Posts: 10,770

## Re: Regularized regression

``````proc hpgenselect data=sashelp.class ;class sex;model weight = sex height age/ CL ; selection method=Lasso(choose=SBC) details=all;performance details;run;
``````

You will see :

`````` NOTE: The CL option is not available for the LASSO method.
NOTE: The HPGENSELECT procedure is executing in single-machine mode.
NOTE: * Optimal Value of Criterion
NOTE: There were 19 observations read from the data set SASHELP.CLASS.``````
Occasional Contributor
Posts: 9

## Re: Regularized regression

Ksharp,

This is what I have seen:

NOTE: The CL option is not available for the LASSO method.
NOTE: The HPGENSELECT procedure is executing in single-machine mode.
NOTE: * Optimal Value of Criterion
NOTE: There were 1496 observations read from the data set WORK.DALREG1.
NOTE: PROCEDURE HPGENSELECT used (Total process time):
real time 1.07 seconds
cpu time 0.51 seconds

I just read about Bayesian LASSO that has the ability to generate SE. However, it requires a macro, an area I am, sadly, not competent with. Any help from anybody please?

Thanks,

DNY

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