Can Variance be used as an output variable?

#1
For example, in an experiment the output data (y axis) becomes more dispersed as some input variable (x axis) is changed. So if there seems to be a relationship between variance (or standard deviation) and the input... is variance an acceptable predictor of the input?

Thanks :wave:
 

Dason

Ambassador to the humans
#2
That doesn't really make much sense. Think about how you would use this model to get a prediction. If you're like "ok so x will be 5 and then since I used variance as a predictor if I want a prediction I need to plug in the variance... Uh... guys what's the variance of the point we're trying to predict?"
 
#3
That doesn't really make much sense. Think about how you would use this model to get a prediction. If you're like "ok so x will be 5 and then since I used variance as a predictor if I want a prediction I need to plug in the variance... Uh... guys what's the variance of the point we're trying to predict?"
Well it would be more like this: measure vibrations from a beam being bent in the wind, the higher the wind speed the greater the fluctuations in bending and so the greater the variance in the data is... therefore once wind speed vs variance is plotted, could the measurement (or recording) of variance be used to estimate the wind speed hitting the beam?

PS It doesn't sound right to me and it's not my idea! But I can't quite explain why it's not right. :confused:
 

rogojel

TS Contributor
#6
Well, I guess anything is legitimate that makes a practical sense. In this case, physically, you are interested in the amplitude of the vibrations and the variance is a poor proxy for this. I mean, theoretically, you could have a large variance even for a smaller amplitude - so if you really care about the amplitude, that is what you would need to model.

regatds
 
#7
For example, in an experiment the output data (y axis) becomes more dispersed as some input variable (x axis) is changed.
Yes, the output variable i.e. the dependent variable, can be the variance or the standard deviation.

Have a look at gamlss and these notes (look at slide 26). Read their education papers.

Also have a look at DHGLM (double hierarchical glm) with both mean and dispersion as dependent variable by Lee Nelder and Pawitan. (e.g. at this)

These methods will make a breakthrough in the future.