[R] Bootstrap 95% confidence intervals for splines

[mitchell wachtel]

Dr Hesterberg:

"Independent" and "dependent" were used for convenience. A person selling
hot dogs would render "HD"  the Y variable. The real cause of both WL and HD
is likely hormonal derangement associated with diabetes. 

One other question. A log negative binomial regression 

m.ln<-glm.nb( Count ~ ns( X1, df=4 ) * ns( X2, df=4 ) + ns( X3, df=4 ) + X4
+ offset( log( Total ), data=M)

could not be made to predict values on new data, even though GLM assumptions
were not violated. Why does 

predict( m.ln, newdata ) 

not work? This is vital if one is to draw a graph showing the relationship
of X1 and X2 to Y.

Thank you so much for your wisdom.

Mitchell Wachtel




  
Tim Hesterberg-2 wrote:
> 
> You're mixing up two concepts here,
>   - splines
>   - bootstrap confidence intervals
> Separating them may help cut the confusion.
> 
> First, to do a bootstrap confidence interval for a difference in
> predictions
> in the linear regression case, do:
> 
> repeat 10^4 times
>   draw a bootstrap sample of the observations (subjects, keeping x & y
> together)
>   fit the linear regression to the bootstrap sample
>   record the difference in predictions at the two x values
> end loop
> The bootstrap confidence interval is the range of the middle 95% of
> the recorded differences.
> 
> For a spline, the procedure is the same except for fitting a spline
> regression:
> 
> repeat 10^4 times
>   draw a bootstrap sample of the observations (subjects, keeping x & y
> together)
>   fit the SPLINE regression to the bootstrap sample
>   record the difference in predictions at the two x values
> end loop
> The bootstrap confidence interval is the range of the middle 95% of
> the recorded differences.
> 
> Tim Hesterberg
> 
> P.S. I think you're mixing up the response and explanatory variables.
> I'd think of eating hot dogs as the cause (explanatory variable),
> and waistline as the effect (response, or outcome).
> 
> P.P.S.  I don't like the terms "independent" and
> "dependent" variables,
> as that conflicts with the concept of independence in probability.
> "Independent" variables are generally not independent, and the
> "dependent"
> variable may be independent of the others.
> 
> >There appear to be reports in the literature that transform continuous
> >independent variablea by the use of splines, e.g.,  assume the
> dependent
> >variable is hot dogs eaten per week (HD) and the independent variable
> is
> >waistline (WL), a normal linear regression model would be:
> >
> >nonconfusing_regression  <- lm(HD ~ WL)
> >
> >One might use a spline,
> >
> >confusion_inducing_regression_with_spline <- lm(HD ~ ns(WL, df = 4)
> )
> >
> >Now is where the problem starts.
> >
> >>From nonconfusing_regression , I get, say 2 added hot dogs per
> week for each
> >centimeter of waistline along with a s.e. of 0.5 hot dogs per week,
> which I
> >multiply by 1.96 to garner each side of the 95% c.i.
> >If I want to show what the difference between the 75th percentile (say
> 100
> >cm) and 25th percentile (say 80 cm) waistlines are, I multiply 2 by
> >100-80=20 and get 40 hot dogs per week as the point estimate with a
> similar
> >bumping of the s.e. to 10 hot dogs per week.
> >
> >What do I do to get the point estimate and 95% confidence interval for
> the
> >difference between 100 cm persons and 80 cm persons with
> >confusion_inducing_regression_with_spline ?
> >
> >Best regards.
> >
> >Mitchell S. Wachtel, MD
> 
> ______________________________________________
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
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> 


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