# Re: st: nested design and logistic regression

 From Joseph Coveney To Statalist Subject Re: st: nested design and logistic regression Date Thu, 06 Jul 2006 17:44:32 +0900

```Denis Haine wrote:

I have a 2 factors nested design model, where treatment received by siblings
(low dose vs. high dose)  is nested in same treatment received by their
maternal parents (received or not). I could fit an anova for nested design
for a continuous dependent variable, e.g. anova y trt_mat / trt_sib|trt_mat
/, but how to fit a logistic regression taking into account this nesting of
the 2 treatments if I have a binary dependent variable?

--------------------------------------------------------------------------------

Wouldn't it be something like that below?

It's helpful to start out in familiar territory in order to get your
bearings, and progress in stages to terra incognita, with checkpoints along
the way.

So, the trail starts with -anova-,

and then passes through -xtmixed , reml- (comparing the variance components)

to -xtmixed , ml-

to -gllamm , family(gaussian) link(identity)-

before arriving at -glamm , family(binomial) link(logit)-.

The ANOVA setup for nested factors (a.k.a. hierarchal design) can be found
in B. J. Winer, D. R. Brown & K. M. Michels, _Statistical Principles in
Experimental Design_ Third Edition. (New York: McGraw-Hill, 1991),
pp. 358--62.  www.stata.com/bookstore/sped.html

I used -xtmixed- as the bridge, an illustrative analogy, to -gllamm-.

Joseph Coveney

clear
set more off
set memory 100M
set matsize 11000
set seed `=date("2006-07-06", "ymd")'
set obs 200
generate int mother = _n
generate float sigma_mother = 3 * invnorm(uniform())
generate treatment = mod(_n, 2)
forvalues dose = 0/1 {
generate float sigma_motherdose`dose' = 2 * ///
invnorm(uniform())
}
reshape long sigma_motherdose, i(mother) j(dose)
forvalues child = 1/2 {
generate float sigma_child`child' = ///
invnorm(uniform()) * _pi / sqrt(3)
}
reshape long sigma_child, i(mother dose) j(child)
generate float response = treatment + sigma_mother + ///
dose + sigma_motherdose + sigma_child
*
* Begin here
*
anova response treatment / mother|treatment ///
dose treatment*dose / mother|treatment*dose /
local n = e(N) / (e(df_m) + 1)
local sigma2_e = e(rss) / e(df_r)
local MSmotherdose = e(ssdenom_4) / e(dfdenom_4)
local sigma2_motherdose = (`MSmotherdose' - `sigma2_e' ) / `n'
local sigma2_mother = (e(ssdenom_1)/ e(dfdenom_1) - ///
`MSmotherdose') / `n' / (e(df_4) + 1)
display `sigma2_mother'
display `sigma2_motherdose'
display `sigma2_e'
*
* Bridge
*
quietly xi3 e.treatment*e.dose
quietly compress
egen int motherdose = group(mother dose)
xtmixed response _I* || mother: || motherdose:, reml ///
nolrtest variance nolog
xtmixed response _I* || mother: || motherdose:, mle ///
nolrtest variance nolog
gllamm response _I*, i(motherdose mother) nrf(1,1) ///
*
* Analogous logistic regression
*
summarize response, meanonly
generate byte binary_response = response > r(mean)
quietly gllamm binary_response _I*, i(motherdose mother) nrf(1,1) ///
matrix A = e(b)
gllamm binary_response _I*, i(motherdose mother) nrf(1,1) ///