Outliers and Multicollinearity for Regression

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Super Contributor
Posts: 482

Outliers and Multicollinearity for Regression

I would like to detect a outliers and multicollinearity for my regression (both linear and logistic) analysis. Appreciate if someone guide me through options/procs for that.

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Solution
‎07-24-2016 02:09 AM
Super User
Posts: 10,200

Re: Outliers and Multicollinearity for Regression

```For proc reg :
Outliers  - Check Cook Distance
Multicollinearity  - Check VIF   ( model y=x / vif )

For proc logistic:
Outliers  - Check INFLUENCE option and see Chi-square :

proc logistic data=sashelp.class;
model sex=age height/ influence;
run;

Regression Diagnostics
Case
Number	Covariates	Pearson Residual	Deviance Residual	Hat Matrix Diagonal	Intercept DfBeta	Age DfBeta	Height DfBeta	Confidence Interval Displacement C	Confidence Interval Displacement CBar	Delta Deviance	Delta Chi-Square
Age	Height
1	14.0000	69.0000	-0.3158	-0.4361	0.1443	0.1096	0.0994	-0.1265	0.0197	0.0168	0.2070	0.1166
2	13.0000	56.5000	0.3559	0.4883	0.1644	0.1391	0.1271	-0.1562	0.0298	0.0249	0.2634	0.1515
3	13.0000	65.3000	2.4687	1.9796	0.1484	-0.6318	-0.9210	0.9706	1.2470	1.0620	4.9807	7.1566
4	14.0000	62.8000	0.8089	1.0034	0.0999	0.0598	0.1630	-0.1330	0.0807	0.0726	1.0794	0.7270

Multicollinearity  - There is not check in proc logistic, but sas will remove one variable automatically if it is colinearity with other
variables due to proc logistic is using MLE .

```

All Replies
Super User
Posts: 20,714

Re: Outliers and Multicollinearity for Regression

What's your definition of an outlier?

Super Contributor
Posts: 482

Re: Outliers and Multicollinearity for Regression

I don't have any definition for outlier. Just I want to see the
observations which is far away from normal distribution.

attachments. -##
Super User
Posts: 20,714

Re: Outliers and Multicollinearity for Regression

If your trying to learn statistical theory and SAS have you taken the first statistic e-course from SAS? It's free.

There's also a ton of videos on topics related to specific statistical procedures.

http://support.sas.com/training/tutorial/

Posts: 5,043

Re: Outliers and Multicollinearity for Regression

Suggestions:

• Make that two separate topics (questions)
• Formulate each question as a problem such as "I have the following dataset and would like to know if obs 12 is an outlier relative to this regression model, how can I do that?"
PG
SAS Super FREQ
Posts: 3,834

Re: Outliers and Multicollinearity for Regression

For linear regression you can use the ROBUSTREG procedure. The procedure has algorithms that automatically flag outliers.  The documentation contains several Getting Started examples. I suggest you start with the examples and then move on to the "Details" section if you want to understand the details about how an observation is classified as an outlier.

There is not an analogous "robust" procedure for logistic regression. However, there are still techniques for detecting potential outliers in almost every SAS procedure. The technique is to use regression diagonostic plots.

For example, in PROC REG you can use the INFLUENCE option on the MODEL statement and look at the ODS graphics to assess observations that are highly influential in the model. See the section of the doc titled "Influence Statstics".

You can do something similar for logistic regression. The LOGISTIC procedure contains many diagnostic plots.  As Reeze says, a full explanation is lengthy, but start with the doc example "Logistic Regression diagnostics", which shows how to use the INFLUENCE option and the diagnostic plots.

Solution
‎07-24-2016 02:09 AM
Super User
Posts: 10,200

Re: Outliers and Multicollinearity for Regression

```For proc reg :
Outliers  - Check Cook Distance
Multicollinearity  - Check VIF   ( model y=x / vif )

For proc logistic:
Outliers  - Check INFLUENCE option and see Chi-square :

proc logistic data=sashelp.class;
model sex=age height/ influence;
run;

Regression Diagnostics
Case
Number	Covariates	Pearson Residual	Deviance Residual	Hat Matrix Diagonal	Intercept DfBeta	Age DfBeta	Height DfBeta	Confidence Interval Displacement C	Confidence Interval Displacement CBar	Delta Deviance	Delta Chi-Square
Age	Height
1	14.0000	69.0000	-0.3158	-0.4361	0.1443	0.1096	0.0994	-0.1265	0.0197	0.0168	0.2070	0.1166
2	13.0000	56.5000	0.3559	0.4883	0.1644	0.1391	0.1271	-0.1562	0.0298	0.0249	0.2634	0.1515
3	13.0000	65.3000	2.4687	1.9796	0.1484	-0.6318	-0.9210	0.9706	1.2470	1.0620	4.9807	7.1566
4	14.0000	62.8000	0.8089	1.0034	0.0999	0.0598	0.1630	-0.1330	0.0807	0.0726	1.0794	0.7270

Multicollinearity  - There is not check in proc logistic, but sas will remove one variable automatically if it is colinearity with other
variables due to proc logistic is using MLE .

```
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