Dear Allstat,

 

A kind thanks to all who wrote to me.

 

Here is a quick summary of the 29 replies I have so far received:

 

25 of you agreed with the usage of "fitting a model to data" and of this
group 23 did not like the connotation in "fitting data to a model".

3 of you consider both to be correct with usage depending on purpose.

Finally 1 considers both correct with usage depending on philosophical
slant (my favorite response, and one I am tempted to choose for the
reviewer).

 

From searches on google or Rseek you find a few examples where the title
of a section of text was "fitting data to models" and then the author
went on to talk about "fitting models" and "fitted models" which just
seems to be a lack of consistency.  And also if you do a google search
you will find 1,000s of entries for "fitting models to data" and only
hundreds of entries for "fitting data to models" and many of these are
teaching regression. For example
http://documents.wolfram.com/applications/eda/FittingDataToLinearModelsB
yLeast-SquaresTechniques.html .  So both seem to be in use but "fitting
data to models" is in the minority.

 

The main point seemed to be that it is not something that any of the
respondents would comment on as reviewers.  However, some interesting
points were raised, Plato even got a mention!

 

Here is a long summary of replies received!  Points made / opinion
expressed, in no specific order:

 

I think this is a philosophical point.

If you subscribe to Platonism, ideas (and therefore models) are out
there in mental space and possibly have a superior status of "being"
..... data are (or should I write "is"?, and this is grammar I believe!)
then but an imperfect expression of some ulterior perfection as
contained within the realm of the mind (and hence finite and roughly
hewn data is fitted to models).

If you are a realist, our mental constructs (and hence models) are
savage approximations of an infinitely complex real world which provides
irrefutable evidence in the form of hard evidence (and hence model will
be fitted to data).

 

Fitting data to models has the connotation that the model is the 'truth'
and the data can be changed to fit in with the model. For example,
people might wish to delete observations which do not fit in with their
theory.

If data are not compatible with a model, the next move is to consider
possible causes for this, not to change the data to fit the model. If a
straight line is not a good model for the relation between weight and
height, you don't change the data to make it a straight line.

 

I am an applied econometrician and we always talk in terms of modelling
the data as we are seeking something that will predict the data series
outside the sample. But pure economists begin with an economic model
derived from theory and then see if the data fits the theory. This is
less onerous on full predictability of each data point. So which is
right depends on what your objective and starting point is.

 

Surely the semantic implication of the word "data" (literally "givens"
or "that which is given") is that the data are not meant to be modified.
Models are our simplifications, explanations or summaries of observed
phenomena. Models involving parameters (e.g. linear regression) are made
to explain a particular set of data by fitting the model to the data.

Talk of `fitting data to models' suggests a black box or "drag-and-drop"
approach to data analysis. I've also heard this usage amongst physical
scientists who are fanatically averse to statistics. But in both cases
this usage is in the minority, even in the speaker's own community.

In any case, speaking of 'fitting data to models' would make it clumsy
to express concepts like `the fitted model' and comparisons between
fitted models, etc.

I do think we have to be very careful about what we say, as it is easily
misunderstood. I usually distinguish between a model selection stage, in
which we choose the appropriate form of model, followed by a model
calibration stage, in which we obtain estimates of the values (and
uncertainty) of the parameters of the model, by using the evidence from
datasets. And this is a model fitting stage, so we fit the model using
the data.

Part of the semantic problem comes from the fact that the noun 'model'
is used in lots of different ways both within and between disciplines.
It always has the same general meaning (as some sort of approximate
representation of something else), but the detailed implications can be
quite different. When it is used as a verb it tends to carry all of
these special implications - certainly when an IT person talks about
modelling they mean something completely different from what a
statistician would mean. The same problem applies to the word 'fit',
again available as both noun and verb. We fit the model to the data, but
part of the result is the fit of the data to the model.

The answer to your question is..it depends ... i.e. whether it was 

a) about using the data to investigate which is the 'best' model from a
range of possible models, indicating what hypothesis/hypotheses you were
testing; or

b) collecting & using data to provide best parameter estimates for a
model whose structure you already know (where the 'fitting' involves for
example investigation of outliers or potential systematic causes of bias
in the data, in order to ensure you have the best possible parameter
estimates)

 

I would agree with your interpretation and logic .... Slightly contrary
to your statement, I would always consider the fitting as a *mutual*
process, with the possibility of reconsidering both the model and
specific data points.  It's a forensic process of looking for patterns
and exceptions.

 

I was told off, in the nicest possible way, for using the phrase fitting
the model to the data in the context of Rasch models where the idiom
fitting the data to the model is usual. My understanding of this is that
if you take a strong line about the Rasch model and its measurement
properties then if the model does not fit the data you get more data,
the model is paramount. Implicit in this observation is the fact that in
other areas we fit the model to the data and if it does not fit we get
another model.

 

I think this indicates the ambiguity of the word 'model(s)' that is in
use in statistics.  <removed text basically saying that nested models
should be considered as one model> Non-nested models are one of the
reasons why we observe disagreement between economists and between
econometricians and I suspect practitioners in other disciplines. A
single author might also present results for non-nested models. However,
methodologically, if an author suggests a second non- nested model they
are implicitly stating that the first is not valid and hence any
statistical procedures that might have been applied to it are also
invalid.  Logically therefore the first should not be mentioned.

Of course one solution that statistics offers is the (sometimes rather
artificial) attempts to combine two or more seemingly non-nested models
into some form for which each may be considered nested. This allows
statistical tests to select between them.