Elaborating, it’s not relevant how badly the chosen function would predict y in the region where it’s impossible for x to lie… It’s like asking how well physiological models predict the caloric needs of 7 story fire breathing dragons

]]>I remember David Cox warning us not to do that in one of the Phd seminars – unless you know you have the true model (e.g. output from a simulation.)

He used a simple one variable regression model where physics would guarantee the y value had to be 0 when x was zero.

Now do not set the intercept to zero because the relationship will not be strictly linear, there will be lack of fit and the lower order terms (here the intercept) do a better job of allowing for lack of fit. So you get the true intercept value but a worse overall fit.

Daniel seems to making the same argument – “If y really is in reality a*x1 + b*x2 + error for some certain a,b”

As this is just another distraction for me – does any know of reference for this or counter arguments?

]]>I was wondering if there are some rigorous bounds that one could put on the errors. Suppose we consider a more textbook-ish example of a spherical constraint, x1^2 + x2^2 = 1. Then nature of the predictors are fundamentally different different in that the underlying space of variation is a circle. Can we still make go through and fit y = b1*x1 + b2*x2 + error and expect reasonable answers?

]]>“Democrats go up by 1% and peace and freedom party go down by 1%”

Well in the US the Peace and Freedom party is an irrelevantly small group of people. They receive far less than 1% of the vote for example, but even if they did, a *swing* of 1% from Democrats to PFP is totally unlikely. This “direction” just doesn’t make sense as telling you much of anything.

Principal component analysis would at least give you reasonable “directions”, that’s what it does, rotate the coordinate systems until they align with the maximal variation directions.

]]>What it will do is give you a reasonably fast way to get starting values / initialization points for HMC that don’t take as long a time to converge to the stable equilibrium position.

]]>another option is a linear model of logistic-transformed vote shares

Maybe I don’t understand whats being asked but cant you basically use any method to generate the logits and then softmax?

https://en.wikipedia.org/wiki/Softmax_function