# Logistic regression equation for calculating participant risk scores

#### WilliamB

##### New Member
I was hoping you could help me in how I can generate a participant risk score from the logistic regression equation to calculate a ROC curve? Thanks!

#### fed2

##### Active Member
usually it is the estimated probability for the logistic model itself, for example take 'inverse logit' of the sum product of Betas and covariates.

#### WilliamB

##### New Member
Thanks, fed2. So, for example, would this be correct:
Predicted logit (risk score) = intercept + (Beta x variable) + (Beta x variable) + (Beta x variable)
Then would you do
predicted risk score = risk score / (1 + risk score)

#### hlsmith

##### Less is more. Stay pure. Stay poor.
That seems about right. So for the ROC curve, which is usually the Sen vs 1-spec, are you gonna follow up with creating a threshold for the outcome for every predicted probability value then?

#### WilliamB

##### New Member
I'm a little bit stuck as to how I now use this predicted probability / risk score that I have created for all participants and then put them all into a ROC curve? Thanks in advance!

#### fed2

##### Active Member
predicted risk score = risk score / (1 + risk score)
I feel like there should be e^risk score right : I'm a little bit stuck as to how I now use this predicted probability
Should just be usual ROC procedure, but use the risk scores instead. Sorry I did not realize this was SPSS question, so I don't know what buttons to click. SAS does this auto-matic if you got multiple covariates.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yes, it surprises my how much information it conveys. I should stare at it to see if I can come up with another path.

#### WilliamB

##### New Member
Thanks, fed2. So, for example, would this be correct:
Predicted logit (risk score) = intercept + (Beta x variable) + (Beta x variable) + (Beta x variable)
Then would you do
predicted risk score = risk score / (1 + risk score)
Or am I confusing that with a linear regression, when I am trying to do this for a logistic regression?
Thanks

#### fed2

##### Active Member
I think as far as the 'skull' goes, the logit( risk score ) is on the viewers far right. You need to go through the mouth region to get back to risk score. If you are doing it right, you will get a number between 0 and 1. Also you may want to check that inverse logit( logit( a ) ) = a, if you have the right inverse logit function. The formula you give above looks like it is taking odds to probability, rather than log odds, which is what is estimated by the logistic regression model.