How do I compare two weighted regressions in MatLab? - matlab

Question

I've been using MatLab as a statistics tool. I like how much I can customise and code myself.
I was delighted to find that it's fairly straightforward to do a weighted linear regression in MatLab. As a slightly silly example, I can load the "carbig" data file and compare horsepower vs mileage for US cars to that of cars from other countries, but decide I only trust 8-cylinder cars.
load carbig
w=(Cylinders==8)+0.5*(Cylinders~=8)%1 if 8 cylinders, 0.5 otherwise.
for i=1:length(org)
o(i,1)=strcmp(org(i,:),org(1,:));%strcmp only works on one string.
end
x1=Horsepower(o==1)
x2=Horsepower(o==0)
y1=MPG(o==1)
y2=MPG(o==0)
w1=w(o==1)
w2=w(o==0)
lm1=fitlm(x1,y1,'Weights',w1)
lm2=fitlm(x2,y2,'Weights',w2)
This way, data from 8-cylinder cars will count as one data-point, and data frm 3,4,5,6-cylinder cars will count as half a data point.
Problem is, the obvious way to compare the two regressions is to use ANCOVA, which MatLab has a function for:
aoctool(Horsepower,MPG,o)
This function compares linear regressions on the two groups, but I haven't found an obvious way to include weights.
I suspect I can have a closer look at what the ANCOVA does and include the weights manually. Any easier solution?

Answer 1

I figured if I give the "trusted" measuremets weight 2, the "untrusted" measurements weight 1, for regression purposes that's the same thing as having an extra 1 identical measurement for each trusted one. Setting the weight to 1 and 0.5 should do the same thing. I can do this with a script.
That also increases the degrees of freedom quite a bit, so I manually set the degrees of freedom to sum(w)-rank instead on n-rank.
x=[];
y=[];
g=[];
w=(Cylinders==8)+0.5*(Cylinders~=8);
df=sum(w)
for i=1:length(w)
while w(i)>0
x=[x;Horsepower(i)];
y=[y;MPG(i)];
g=[g;o(i)];
w(i)=w(i)-0.5
end
end
I then copied the aoctool.m file (edit aoctool) and inserted the value of df somewhere in the new file. It isn't elegant, but it seems to work.
edit aoctool.m
%(insert new df somewhere. Save as aoctool2.m)
aoctool2(x,y,g)