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Re: st: Nonparametric Methods for Longitudinal Data


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Nonparametric Methods for Longitudinal Data
Date   Mon, 11 Feb 2013 13:55:54 +0000

This is contentious territory. I give preference to my own views, but
I think they are widely shared.

There is still widespread reference to "non-parametric statistics",
but its complement "parametric statistics" is not a term I think now
used by many statistically-minded people who are reasonably
well-informed and up-to-date, not least because there is little in
common to the rest of statistics, except that of not being
"non-parametric". It is my strong impression that  "parametric
statistics" is a kind of back-formation of terminology from some
social scientist textbook writers in the 1950s or 1960s who wanted a
name to contrast with the methods they were advocating. It predates
most of the methods for categorical data now usually disussed under
that heading.

Quibbles aside, I just would not agree that using such methods to
ordinal data is "simply wrong". That's absolute and definite when
there are many, many exceptions. For example, I am very happy to apply
Pearson correlation to ranked data when it seems appropriate: that's
Spearman correlation in another guise. I am even happy to average
grades that are assigned on an ordinal scale; indeed some fraction of
my day job is based on that practice.

See also references given in
http://www.stata.com/statalist/archive/2012-08/msg01401.html

You have a bigger problem yet, in that it's my impression that
non-parametric methods for longitudinal data is a largely empty
category. The framework of non-parametric methods does not really
extend without breaking to multiple predictors and panel structure,
let alone any time dependence too. It would be good if Roger Newson's
programs solved your problem, but I fear they won't.

If this were my problem, I think I would be looking at -xt- commands,
just treading especially carefully.

Nick

On Mon, Feb 11, 2013 at 1:32 PM, Thomas Herold <thomasherold@gmx.net> wrote:
> Dear Nick,
>
> Thank you very much for your answer.
>
>> Questions like this raise more questions in their wake.
>>
>> It is a bit puzzling that you have apparently only just discovered how
>> your response variable is defined. However, many medical and psychiatric
>> analyses make use of scores usually devised according to the answers to
>> multiple questions. They often work at least
>> approximately like measured variables; many researchers would argue that
>> treating them as ordinal is too pessimistic and indeed there are
>> usually too many distinct values for many standard models for ordinal
>> responses to work well.
>>
>> IQ is an example familar to many.
>
> I have not been involved in the design of the study. I was just asked to
> evaluate it. You certainly have a point when you say that my approach might
> be too pessimistic. However, it seems to be common belief that the scale I
> am talking about (Hospital Anxiety and Depression Scale - HADS) only
> generates ordinal data. And if we take this seriously we have to admit that
> one basic assumption of parametric analysis is not fulfilled. Would you
> agree with that?
>
>
>>
>> Statistically, it's a myth on several levels that "parametric analysis"
>> requires a response variable to be normally distributed. At
>> most, it's a secondary assumption of some regression-like methods that
>> error disturbances be normally distributed. There are also many
>> methods that are not non-parametric for other distributions (exponential,
>> gamma, etc., etc.).  Also, what about transformations or
>> similar link functions.
>> So, manifestly I can't see your data but I'd suggest that your impression
>> that you need quite different methods is jumping to conclusions prematurely.
>>
> Again, I could not agree more. However, that does not really answer my
> question. You have to know that my statistical background knowledge is
> limited. For example, I would have thought that using parametric methods for
> ordinal data is not only "optimistic" but simply wrong.
> Therefore, I would highly appreciate it if you (or someone else) could tell
> me a regression type that is supported by Stata (sorry for the spelling
> error in my first post) and might be worth having a look at in this context.
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