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Re: st: Skewness estimates with svyset data


From   Steven Samuels <sjhsamuels@earthlink.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Skewness estimates with svyset data
Date   Tue, 4 Nov 2008 09:29:30 -0500

--

Richard, in the past, I found that -nlcom- gave inaccurate estimates for standard errors of differences of moments, a problem related to round-off in subtraction and to the delta method applied to square roots. Two fixes worked: 1) Standardize variables by subtracting off a constant close to the mean; 2) Request standard errors based on the jackknife. To solve your problem of bias (and probably of incorrect SE's) I'd try either fix or both.

-Steve

On Nov 4, 2008, at 8:00 AM, Richard Palmer-Jones wrote:

Thanks for all your contributions.

I worked out the missing "^3" last night (and the x^3 = (_b[ht])^3 -
good old Yule and Kendal)  i.e.:

nlcom ((_b[ht])^3 - 3*_b[ht2] * _b[ht] + 2*(_b[ht])^3)/(_b[ht2] -
_b[ht] *  _b[ht])^3/2

but I am not convinced it gives sensible results - but then how to judge?

In this dataset (NHANES3) using summarize with weights shows heights
are not greatly skewed at any age; but weights are clearly negatively
skewed up to the age of 5, and positively skewed thereafter (ditto for
BMI). The nlcom calculation is quite close to the estimated skewness
for height but for weight, although Pearson r  = .5, the absolute
sizes are not that close (skewness = 0.51 * nlcom - 0.079, r2 = .29,
N=49, both coefs p< .000). The nlcom estimate seriously underestimates
skewness after age 5 compared to the summarize estimate (with
weights).

?

I actually want to compare adult heights, weights, and BMIs in a
situation where nutritional status has apparently been improving quite
rapidly. Heights, weights & BMIs for 25 year olds are greater than
those of 45 year olds (assuming no differntial mortalities, which I
doubt). Most programs which compute anthopometry z-scores (zanthro, or
WHO's Anthro macros) are for children or adolescents, so I wanted
something like a zanthro for adults. One might set the standards using
USA or UK heatlh surveys which give heights and weights of adults, but
then one might want to compute skewness both to test for normality
(they are not) and to use the LMS method (Cole et al. 2008) to develop
the standards. Height at each age group for both sexes may not be
normal, but as noted above weights are generally not (different tests
give different results, but omninorm suggests weight is seriously not
normal, and height slightly (p between 0.05 & 0.01) not).

I suspect that pro temp I am better off using summarize, and smoothing
the skewness estimates (and median and cv, but any further advice
welcomed.

Thanks again

Richard

On Mon, Nov 3, 2008 at 10:11 PM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
--- Richard Palmer-Jones <richard.palmerjones@gmail.com> wrote:
Thanks - I did check using summarize with weights, and other tests
(sktest), and qnorm/pnrom, and generally skewness is no problem, but
for some subsamples it may be. I am jconcerned that  stratification
is lost by these views.

It looks like you are worried about normality assumptions. This worries
me for two reasons: First, these assumptions typically refer to the
residuals, and not the dependent variable (or in other words the
dependent variable is normally distributed conditional on the
explanatory variables). Your reference to subsamples suggests that you
are not looking at the residuals. Second, when you are doing survey
methods, you are automatically using robust/Huber/White/sandwich
estimators, so you are effectively bypassing many if not all the
normality assumptions.

Hope this helps,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------



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