## SAS test for a rank regression

Occasional Contributor
Posts: 5

# SAS test for a rank regression

Is there a SAS procedure to do a regression with a rank as the outcome variable?

Thanks!

Posts: 2,116

## SAS test for a rank regression

If your sample size is reasonably large, you can just do regular regression using the ranks.  The ranks are asymptotically normal, so the inferences are valid.

Occasional Contributor
Posts: 5

## SAS test for a rank regression

Thanks for your response. Are you saying to use a linear regression and invoke the central limit theorem? My sample size is only around 100 so I don't think that it would qualify. If I don't use the central limit theorem the outcome should be normally distributed and if it the outcome is a ranking then a graph of the outcome would be a horizontal line and completely nonnormal. I'm not sure what you mean by the ranks are asymptotically normal. Thanks.

Occasional Contributor
Posts: 5

## SAS test for a rank regression

Any other thoughts? I think the suggestion was to due a linear regression and use the central limit theorem but my sample size is not that large, or would 100 be considered okay? There is no SAS procedure to run a regression with ranks as the outcome?

Posts: 2,116

## SAS test for a rank regression

In something like a t-test, 20 in a group is sufficiently large for the CLT to be used.  How large you might need depends on how many predictor variables you are considering.  Another option might be "robust regression", see

Occasional Contributor
Posts: 5

## SAS test for a rank regression

My understanding is that the CLT is not related to the number of predictors but to the degree of non-normality of the data. So for a dataset that is very nonnormal, a very large sample size may be needed, and if there is a mild departure from normality not that much of a sample size. There is no specific cutoff number for linear regression.

While if there are many predictors, a bigger dataset would be needed, this is due to overfitting, not to CLT.

Super User
Posts: 10,205

## SAS test for a rank regression

As my opinion. It is very hard to use linear regression.

Linear Regression is firstly assuming the residual conform a known distribution Such as Normal....

But your data is Rank, It is to say you should use some non-parameter methods to do.

Ksharp

Occasional Contributor
Posts: 5

## SAS test for a rank regression

HI Ksharp, yes I was asking for what method could be used instead of linear regression, whether there is a particular regression that is aimed at ranks. However I should still be able to use the CLT based on sample size and run it as a linear regression.

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