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# Logistic regression for continuous predictor

Standard logistic regression works for predict binary 0 & 1. Now I have a data set with predict value between 0 and 1, such as 0.2, 0.5, .... How can use logistic regression build a model out of it? thanks.

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Contributor
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## Re: Logistic regression for continuous predictor

For example, I have a sample, which contains 100 pool information. there are some independent variables which are pool average characteristics, such as loan size, loan coupon. I have a predictor variable, which is a pool average of 0 and 1, so they 0.115, 0.234, .... I want to build a logistic regression model to predict (0.115, 0.234, ...) from pool average characteristics, such as pool average loan size etc. If the predictor are 90, 0, 1, 0, 1, 1, ..). Then it's easy to do. But for continuous variable, I can not use proc logistic to do it. Is there a way out? Thanks.

Jian

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## Re: Logistic regression for continuous predictor

As your dependent variable is continuous so try proc reg instead of logistic regression.

Contributor
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## Re: Logistic regression for continuous predictor

proc reg is sum of each component, I want to do multiplying of each component. Thanks.

SAS Employee
Posts: 340

## Re: Logistic regression for continuous predictor

1. You can take the logarithm of variables, and create a model using those new variables.

2. If you want to model a proportion, maybe you could use PROC GENMOD with DIST=GAMMA

Do I understand correctly: individual data is not available, only aggregated?

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## Re: Logistic regression for continuous predictor

1. logarithm is not a linear transformation, so optimal fit for logarithm of variables are not optimal fit for the variables themselves. I have proved this.

2. Can you explain more how to use DIST=GAMMA? Normally I use d=b.

Thanks.

SAS Employee
Posts: 340

## Re: Logistic regression for continuous predictor

1. You are right. But it also depends how you define "optimal", what are your model assumtions, and how you transform "back" your predicted variable (if you transformed the target variable)

2. Sorry, it is not GAMMA it is BETA. But beta distribution is not available in GENMOD.

proc glimmix data=input;

model target=x1 / d=beta;

run;

With GLIMMIX you might find the appropriate model you need (with, or without variable transformations).

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Posts: 30

## Re: Logistic regression for continuous predictor

For 1, what do you mean how your transform "back" your predicted variable? Is there more than 1 way to transform back? I just exp() it back.

Thanks.

Jian

SAS Employee
Posts: 340

## Re: Logistic regression for continuous predictor

When you transform predictions using exp(log_target) you will get the unbiased prediction of the median on the original scale.

To get an unbiased  prediction of the mean on the original scale use: exp(log_target+0.5*std**2)

std is the prediction standard deviation.

This is true if your log transformed variable is (conditionally) normally disributed (the original variable is lognormal).

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Hi Gergely,

Thanks,

Naeem

SAS Employee
Posts: 340

## Re: Logistic regression for continuous predictor

Unbiased estimation of the median.

On the log scale the prediction of the mean is the prediction of the median at the same time. (Remember, we have a normally distributed variable (on the log scale), which is a symetric distribution.)

Now, if you apply a monotonic function (like exp()) to the prediction... the median still sits in the middle of the distribution

I don't know what happens to the geometric mean.

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## Re: Logistic regression for continuous predictor

Thanks - Just trying to understand this because when we exponent like exp(log_target) we end up with geometric mean.

SAS Employee
Posts: 340

## Re: Logistic regression for continuous predictor

stat@sas: I thought about it and you are right. In case of exp mean becomes the geometric mean (and also remains the median). Thx.

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