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Plotting the probability curve from a logit model with 10 predictors

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Abraham Mathew

Plotting the probability curve from a logit model with 10 predictors

I have a logit model with about 10 predictors and I am trying to plot the
probability curve for the model.

Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi

If the model had only one predictor, I know to do something like below.

mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
family=binomial(link="logit"))

all.x <- expand.grid(won=unique(won), bid=unique(bid))
y.hat.new <- predict(mod1, newdata=all.x, type="response")
plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
lwd=5, col="blue", type="l")

I'm not sure how to proceed when I have 10 or so predictors in the logit
model. Do I simply expand the
expand.grid() function to include all the variables?

So my question is how do I form a plot of a logit probability curve when I
have 10 predictors?

would be nice to do this in ggplot2.

Thanks!

--
*Abraham Mathew
Statistical Analyst
www.amathew.com
720-648-0108
@abmathewks*

[[alternative HTML version deleted]]

______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Bert Gunter

Re: Plotting the probability curve from a logit model with 10 predictors

You have an about 11-D response surface, not a curve!

-- Bert

On Thu, Jul 5, 2012 at 2:39 PM, Abraham Mathew <[hidden email]> wrote:

> I have a logit model with about 10 predictors and I am trying to plot the
> probability curve for the model.
>
> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>
> If the model had only one predictor, I know to do something like below.
>
> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
> family=binomial(link="logit"))
>
> all.x <- expand.grid(won=unique(won), bid=unique(bid))
> y.hat.new <- predict(mod1, newdata=all.x, type="response")
>
> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
> lwd=5, col="blue", type="l")
>
>
> I'm not sure how to proceed when I have 10 or so predictors in the logit
> model. Do I simply expand the
> expand.grid() function to include all the variables?
>
> So my question is how do I form a plot of a logit probability curve when I
> have 10 predictors?
>
> would be nice to do this in ggplot2.
>
> Thanks!
>
>
> --
> *Abraham Mathew
> Statistical Analyst
> www.amathew.com
> 720-648-0108
> @abmathewks*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

[[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Abraham Mathew

Re: Plotting the probability curve from a logit model with 10 predictors

Ok, so let's say I have a logit equation outlined as Y= 2.5 + 3X1 + 2.3X2 +
4X3 + 3.6X4 + 2.2X5

So a one unit increase in X2 is associated with a 2.3 increase in Y,
regardless of what the other
predictor values are. So I guess instead of trying to plot of curve with
all the predictors accounted
for, I should plot each curve by itself.

I'm still not sure how to do that with so many predictors.

Any help would be appreciated.

On Thu, Jul 5, 2012 at 4:23 PM, Bert Gunter <[hidden email]> wrote:

> You have an about 11-D response surface, not a curve!
>
> -- Bert
>
> On Thu, Jul 5, 2012 at 2:39 PM, Abraham Mathew <[hidden email]>wrote:
>
>> I have a logit model with about 10 predictors and I am trying to plot the
>> probability curve for the model.
>>
>> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>>
>> If the model had only one predictor, I know to do something like below.
>>
>> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
>> family=binomial(link="logit"))
>>
>> all.x <- expand.grid(won=unique(won), bid=unique(bid))
>> y.hat.new <- predict(mod1, newdata=all.x, type="response")
>>
>> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
>> lwd=5, col="blue", type="l")
>>
>>
>> I'm not sure how to proceed when I have 10 or so predictors in the logit
>> model. Do I simply expand the
>> expand.grid() function to include all the variables?
>>
>> So my question is how do I form a plot of a logit probability curve when I
>> have 10 predictors?
>>
>> would be nice to do this in ggplot2.
>>
>> Thanks!
>>
>>
>> --
>> *Abraham Mathew
>> Statistical Analyst
>> www.amathew.com
>> 720-648-0108
>> @abmathewks*
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
> --
>
> Bert Gunter
> Genentech Nonclinical Biostatistics
>
> Internal Contact Info:
> Phone: 467-7374
> Website:
>
> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>
>
>

--
*Abraham Mathew
Statistical Analyst
www.amathew.com
720-648-0108
@abmathewks*

[[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

glsnow

Re: Plotting the probability curve from a logit model with 10 predictors

In reply to this post by Abraham Mathew

Look at the Predict.Plot and TkPredict functions in the TeachingDemos
package. These will not plot all 11 dimensions at once, but will plot
2 of the dimensions conditioned on the others. You can then change
the conditioning to see relationships.

These use base rather than ggplot graphics.

On Thu, Jul 5, 2012 at 3:39 PM, Abraham Mathew <[hidden email]> wrote:

> I have a logit model with about 10 predictors and I am trying to plot the
> probability curve for the model.
>
> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>
> If the model had only one predictor, I know to do something like below.
>
> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
> family=binomial(link="logit"))
>
> all.x <- expand.grid(won=unique(won), bid=unique(bid))
> y.hat.new <- predict(mod1, newdata=all.x, type="response")
> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
> lwd=5, col="blue", type="l")
>
>
> I'm not sure how to proceed when I have 10 or so predictors in the logit
> model. Do I simply expand the
> expand.grid() function to include all the variables?
>
> So my question is how do I form a plot of a logit probability curve when I
> have 10 predictors?
>
> would be nice to do this in ggplot2.
>
> Thanks!
>
>
> --
> *Abraham Mathew
> Statistical Analyst
> www.amathew.com
> 720-648-0108
> @abmathewks*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

David Winsemius

Re: Plotting the probability curve from a logit model with 10 predictors

In reply to this post by Abraham Mathew

On Jul 6, 2012, at 4:30 PM, Abraham Mathew wrote:

> Ok, so let's say I have a logit equation outlined as Y= 2.5 + 3X1 +
> 2.3X2 +
> 4X3 + 3.6X4 + 2.2X5
>
> So a one unit increase in X2 is associated with a 2.3 increase in Y,

Assuming, that is, you also understand what Y is. From you comments so
far, I have some nagging worries regarding your understanding of that
point.

--
David.

> regardless of what the other
> predictor values are. So I guess instead of trying to plot of curve
> with
> all the predictors accounted
> for, I should plot each curve by itself.
>
> I'm still not sure how to do that with so many predictors.
>
> Any help would be appreciated.
>
>
>
>
> On Thu, Jul 5, 2012 at 4:23 PM, Bert Gunter <[hidden email]>
> wrote:
>
>> You have an about 11-D response surface, not a curve!
>>
>> -- Bert
>>
>> On Thu, Jul 5, 2012 at 2:39 PM, Abraham Mathew
>> <[hidden email]>wrote:
>>
>>> I have a logit model with about 10 predictors and I am trying to
>>> plot the
>>> probability curve for the model.
>>>
>>> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>>>
>>> If the model had only one predictor, I know to do something like
>>> below.
>>>
>>> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
>>> family=binomial(link="logit"))
>>>
>>> all.x <- expand.grid(won=unique(won), bid=unique(bid))
>>> y.hat.new <- predict(mod1, newdata=all.x, type="response")
>>>
>>> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-
>>> c(000:250)),type="response"),
>>> lwd=5, col="blue", type="l")
>>>
>>>
>>> I'm not sure how to proceed when I have 10 or so predictors in the
>>> logit
>>> model. Do I simply expand the
>>> expand.grid() function to include all the variables?
>>>
>>> So my question is how do I form a plot of a logit probability
>>> curve when I
>>> have 10 predictors?
>>>
>>> would be nice to do this in ggplot2.
>>>
>>> Thanks!
>>>
>>>
>>> --
>>> *Abraham Mathew
>>> Statistical Analyst
>>> www.amathew.com
>>> 720-648-0108
>>> @abmathewks*
>>>

David Winsemius, MD
West Hartford, CT

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

glsnow

Re: Plotting the probability curve from a logit model with 10 predictors

In reply to this post by Abraham Mathew

Try the following:

library(TeachingDemos)
?TkPredict
fit.glm1 <- glm( Species=='virginica' ~ Sepal.Width+Sepal.Length,
data=iris, family=binomial)
TkPredict(fit.glm1)

(you may need to install the TeachingDemos package first if you don't
already have it installed)

You will now see a plot that shows the predicted probability compared
to one of the predictor variables, there are controls that you can
then change which variable is shown on the x axis and what the value
of the other variables are. Play with the controls to see the effects
of the different variables. You can now do the same thing with other
logistic regression models. This also works to show nonlinear
(polynomial, spline, etc.) fits of the variables and interactions.
There is a button that you can click that will show the command to
create the same plot in regular R graphics, and you can then use that
command (and change add=TRUE to overlay multiple ones) to create a
static plot showing the relationship.

On Fri, Jul 6, 2012 at 2:30 PM, Abraham Mathew <[hidden email]> wrote:

> Ok, so let's say I have a logit equation outlined as Y= 2.5 + 3X1 + 2.3X2 +
> 4X3 + 3.6X4 + 2.2X5
>
> So a one unit increase in X2 is associated with a 2.3 increase in Y,
> regardless of what the other
> predictor values are. So I guess instead of trying to plot of curve with
> all the predictors accounted
> for, I should plot each curve by itself.
>
> I'm still not sure how to do that with so many predictors.
>
> Any help would be appreciated.
>
>
>
>
> On Thu, Jul 5, 2012 at 4:23 PM, Bert Gunter <[hidden email]> wrote:
>
>> You have an about 11-D response surface, not a curve!
>>
>> -- Bert
>>
>> On Thu, Jul 5, 2012 at 2:39 PM, Abraham Mathew <[hidden email]>wrote:
>>
>>> I have a logit model with about 10 predictors and I am trying to plot the
>>> probability curve for the model.
>>>
>>> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>>>
>>> If the model had only one predictor, I know to do something like below.
>>>
>>> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
>>> family=binomial(link="logit"))
>>>
>>> all.x <- expand.grid(won=unique(won), bid=unique(bid))
>>> y.hat.new <- predict(mod1, newdata=all.x, type="response")
>>>
>>> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
>>> lwd=5, col="blue", type="l")
>>>
>>>
>>> I'm not sure how to proceed when I have 10 or so predictors in the logit
>>> model. Do I simply expand the
>>> expand.grid() function to include all the variables?
>>>
>>> So my question is how do I form a plot of a logit probability curve when I
>>> have 10 predictors?
>>>
>>> would be nice to do this in ggplot2.
>>>
>>> Thanks!
>>>
>>>
>>> --
>>> *Abraham Mathew
>>> Statistical Analyst
>>> www.amathew.com
>>> 720-648-0108
>>> @abmathewks*
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>>
>> --
>>
>> Bert Gunter
>> Genentech Nonclinical Biostatistics
>>
>> Internal Contact Info:
>> Phone: 467-7374
>> Website:
>>
>> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>>
>>
>>
>
>
> --
> *Abraham Mathew
> Statistical Analyst
> www.amathew.com
> 720-648-0108
> @abmathewks*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Frank Harrell

Re: Plotting the probability curve from a logit model with 10 predictors

Also: require(rms); ?plot.Predict
Frank

Greg Snow wrote

Try the following:

library(TeachingDemos)
?TkPredict
fit.glm1 <- glm( Species=='virginica' ~ Sepal.Width+Sepal.Length,
data=iris, family=binomial)
TkPredict(fit.glm1)

(you may need to install the TeachingDemos package first if you don't
already have it installed)

You will now see a plot that shows the predicted probability compared
to one of the predictor variables, there are controls that you can
then change which variable is shown on the x axis and what the value
of the other variables are. Play with the controls to see the effects
of the different variables. You can now do the same thing with other
logistic regression models. This also works to show nonlinear
(polynomial, spline, etc.) fits of the variables and interactions.
There is a button that you can click that will show the command to
create the same plot in regular R graphics, and you can then use that
command (and change add=TRUE to overlay multiple ones) to create a
static plot showing the relationship.

On Fri, Jul 6, 2012 at 2:30 PM, Abraham Mathew <[hidden email]> wrote:
> Ok, so let's say I have a logit equation outlined as Y= 2.5 + 3X1 + 2.3X2 +
> 4X3 + 3.6X4 + 2.2X5
>
> So a one unit increase in X2 is associated with a 2.3 increase in Y,
> regardless of what the other
> predictor values are. So I guess instead of trying to plot of curve with
> all the predictors accounted
> for, I should plot each curve by itself.
>
> I'm still not sure how to do that with so many predictors.
>
> Any help would be appreciated.
>
>
>
>
> On Thu, Jul 5, 2012 at 4:23 PM, Bert Gunter <[hidden email]> wrote:
>
>> You have an about 11-D response surface, not a curve!
>>
>> -- Bert
>>
>> On Thu, Jul 5, 2012 at 2:39 PM, Abraham Mathew <[hidden email]>wrote:
>>
>>> I have a logit model with about 10 predictors and I am trying to plot the
>>> probability curve for the model.
>>>
>>> Y=1 = 1 / 1+e^-z where z=B0 + B1X1 + ... + BnXi
>>>
>>> If the model had only one predictor, I know to do something like below.
>>>
>>> mod1 = glm(factor(won) ~ as.numeric(bid), data=mydat,
>>> family=binomial(link="logit"))
>>>
>>> all.x <- expand.grid(won=unique(won), bid=unique(bid))
>>> y.hat.new <- predict(mod1, newdata=all.x, type="response")
>>>
>>> plot(bid<-000:250,predict(mod1,newdata=data.frame(bid<-c(000:250)),type="response"),
>>> lwd=5, col="blue", type="l")
>>>
>>>
>>> I'm not sure how to proceed when I have 10 or so predictors in the logit
>>> model. Do I simply expand the
>>> expand.grid() function to include all the variables?
>>>
>>> So my question is how do I form a plot of a logit probability curve when I
>>> have 10 predictors?
>>>
>>> would be nice to do this in ggplot2.
>>>
>>> Thanks!
>>>
>>>
>>> --
>>> *Abraham Mathew
>>> Statistical Analyst
>>> www.amathew.com
>>> 720-648-0108
>>> @abmathewks*
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>>
>> --
>>
>> Bert Gunter
>> Genentech Nonclinical Biostatistics
>>
>> Internal Contact Info:
>> Phone: 467-7374
>> Website:
>>
>> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>>
>>
>>
>
>
> --
> *Abraham Mathew
> Statistical Analyst
> www.amathew.com
> 720-648-0108
> @abmathewks*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Gregory (Greg) L. Snow Ph.D.
[hidden email]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Frank Harrell
Department of Biostatistics, Vanderbilt University