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Re: st: Nonparametric Methods for Longitudinal Data


From   "Roger B. Newson" <r.newson@imperial.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Nonparametric Methods for Longitudinal Data
Date   Mon, 11 Feb 2013 14:06:26 +0000

I would argue that there are no such things as "non-parametric statistics". There are rank methods and spline methods, and both are frequently called "non-parametric", but both are actually based on parameters, which can be estimated with confidence limits (not just P-values).

My usual mnemonic (for teaching first-year medical students) is that measurements on indiViduals are called Variables, measurements on Populations are called Parameters, and measurements on Samples are called Statistics. So, we use Variables measured on indiViduals to calculate Statistics on Samples, which we use to estimate Parameters in the corresponding Population. And these parameters may be rank or spline parameters.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 11/02/2013 13:55, Nick Cox wrote:
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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