[SciPy-User] ODR fitting several equations to the same parameters
Thu Nov 12 09:46:43 CST 2009
Bruce Southey ha scritto:
> On 11/12/2009 05:35 AM, ms wrote:
>>> Although b is known without error you still have potentially effects due
>>> to each data set.
>>> What I would do is fit:
>>> y= mu + dataset + a*x + dataset*a*x
>>> Where mu is some overall mean,
>> Mean of what? The b's?
> Depending on what your terms are, y=a*x +b can be viewed is a simple
> linear regression then b is an intercept and a is a slope. Under a
> different view (typically general linear modeling), b can be a factor or
> class variable where 'b' can have multiple levels. As in the model
> above, this is analysis of covariance. You can get your estimate of 'b'
> for each data set as mu plus the appropriate solution of dataset. (While
> you can parameterize the model as y= dataset + ..., it is not as easy to
> interpret as the one using mu.)
> The reason for using this type of model is that you can quantify the
> variation between the data sets.
This sounds interesting, but my problem is much more mundane: what are
the "mu" or "dataset" quantities?
>>> dataset is the effect of the ith dataset - allows different intercepts
>>> for each data set
>>> dataset*a is the interaction between a and the dataset - allows
>>> different slopes for each dataset.
>> I don't really understand what quantities you mean by "effect" and
>> "interaction", and why should I want to allow different slopes for each
>> dataset -the aim to fit one and only one slope from all datasets.
> The reason is that you can test that the slopes are the same and see if
> any data sets appear unusual. If the slopes are the same then you are
> back to what you wanted to know. Otherwise, you need to address why one
> or more data sets are different from the others.
Agree. My point is however that the data sets fitting to the same slope
is an *assumption* that I have to make. Of course checking it is a good
idea, but again, I don't know what are the mathematical definitions of
the quantities you are talking about.
> Again it depends on the function because some of these do have
> linearized forms or can be well approximated by a linear model.
A linear model cannot do it for sure, and I don't think it can be
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