Bootstrap multi linear model

2021 10 4
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Hi. I'm trying to bootstrap a multilinear model using bootstrp. I can get it to work with regress, but not with fitlm. Unfortunatly, the help doesn't provide an example for this. Here's some model code:
x = (1:1000)';
y1 = 2*x+1 + random('normal',0,2,1000,1);
y2 = 0.5*x - 2 + random('normal',0,2,1000,1);
z = 3 * y1 + 2 * y2 + 1 + random('normal',0,2,1000,1);
b1 = bootstrp(1000, @regress, z, [y1 y2 ones(1000,1)] ); % <-- This works
b2 = bootstrp(1000, @fitlm, [y1 y2], z); % < -- This doesn't work
Could someone please explain how to use fitlm withn bootstrp?
Thanks a lot,
Fabrice

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Jeff Miller
Jeff Miller 2021-10-4

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The problem is that fitlm produces a complicated output structure and bootstrp doesn't know what to do with it.
x = (1:1000)';
y1 = 2*x+1 + random('normal',0,2,1000,1);
y2 = 0.5*x - 2 + random('normal',0,2,1000,1);
z = 3 * y1 + 2 * y2 + 1 + random('normal',0,2,1000,1);
% look at the very different outputs of regress vs fitlm:
b11 = regress(z,[y1 y2 ones(1000,1)])
b21 = fitlm([y1 y2],z)
% One way around the problem is to define & bootstrap your own version
% of the function fitlm that returns only a vector of values
b2 = bootstrp(1000, @myfitlm, [y1 y2], z); % < -- This works
function myout = myfitlm(preds,tobepred)
% select out the coefficients that are to be bootstrapped.
b21 = fitlm(preds,tobepred);
myout = b21.Coefficients.Estimate;
end

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Fabrice Lambert
Fabrice Lambert 2021-10-5
Hi. Yes, that will work, but it is essentially the same as regress as you're left with only the coefficients.
I think my confusion stems from the phrasing in the bootstrp help:
"This example uses regress, which is useful when you simply need the coefficient estimates or residuals of a regression model and you need to repeat fitting a model multiple times, as in the case of bootstrapping. If you need to investigate a fitted regression model further, create a linear regression model object by using fitlm."
That second sentence confused me and I thought it is possible to use bootstrp with fitlm. But I think you're right, these two are essentially incompatible for the moment. Thanks
Jeff Miller
Jeff Miller 2021-10-5
In the myfitlm function, you could select out different or additional information from the b21 structure if you wanted to bootstrap something other than the coefficients. I think you can select whatever / as much as / you want from that structure as long as you assemble all of it into a numerical vector myout.
Fabrice Lambert
Fabrice Lambert 2021-10-5
yes, good point. That makes it more flexible than using regress. Thanks for the help!

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