[R-sig-ME] R-sig-mixed-models Digest, Vol 32, Issue 24

[David Duffy]

On Sun, 23 Aug 2009, David Evans wrote:

>
> David, would it be possible to help me with some references on using 
> Gaussian errors for binary data which you mention below.  I've read the 
> Paper by Cheung, A modified least-squares regression approach to the 
> estimation of risk difference, AJE 2007, 166:1337-1344 but was hoping to 
> find some more on this.  In particular, any references which say 
> Gaussian errors are acceptable in mixed models would be most appreciated 
> (I have an outcome prevalence in the 0.2's).
>

A couple of reviews defending the general idea ;):

Harvey WR (1982). Least-squares analysis of discrete data. J Anim Sci 
54:1067-1071

http://jas.fass.org/cgi/reprint/54/5/1067

And also

Ch 17 in Gianola and Hammond Advances in Statistical Methods for
Genetic Improvement of Livestock.

The latter suggests:

V. Guiard, G. Herrend Örfer, A. Tuchscherer (1985).  Variance Component
Estimation for Dichotomous Characters and Its Use for Estimating
Heritability. Biometric J 27: 653-658.

The heritability is the proportion of variance due to genetic random
effects.

A couple of genetics example I am aware of, where simulation finds that
the linear model gives similar answers to a GLMM or similar:

Visscher PM, Haley CS, Knott SA (1996). Mapping QTLs for binary traits
in backcross and F2 populations. Genetical Research 68(1):55-63.

http://genepi.qimr.edu.au/contents/p/staff/CVPV020.pdf

Zeegers MP, Rice JP, Rijsdijk FV, Abecasis GR and Sham PC (2003).
Regression-based sib pair linkage analysis for binary traits.
Hum Hered 55:125-31


There are many other applications of the approach in the animal 
breeding literature for heritability estimation.

But I'm afraid these merely support the approach in general - they
haven't usually applied a standard program like lme()/lmer(), but I
think one can argue that the same analysis of variance machinery is
being used.  The literature on binary intraclass/interclass correlations
in cluster sampling etc (Landis and Koch onwards) is also relevant.

Maybe also:

Lunney GH (2005).  Using analysis of variance with a dichotomous
dependent variable: an empirical study. J Educ Meas 7:263-269.

Cheers, David Duffy.

-- 
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v