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Re: st: REOPROB
Tim Waring <email@example.com>
Re: st: REOPROB
Thu, 5 Nov 2009 08:33:37 -0800
Thank you all.
To clear up this thread on STATA-list about REOPROB - Yes, REOPROB
does include fixed effects, and the syntax for fixed effects is as
The Annals of Statistics
2005, Vol. 33, No. 1, 1–53
Excerpt from Page 20:
"6. fixed and random effects.
Before discussing the technical issues, we brieﬂy review what is
meant by fixed
and random effects. It turns out that different—in fact,
are used in different contexts. [See also Kreft and de Leeuw (1998),
for a discussion of the multiplicity of definitions of fixed and
random effects and
coefficients, and Robinson (1998) for a historical overview.] Here
we outline five
definitions that we have seen:
1. fixed effects are constant across individuals, and random effects
example, in a growth study, a model with random intercepts αi and
slope β corresponds to parallel lines for different individuals i ,
or the model
yi t = αi + β t . Kreft and de Leeuw [(1998), page 12] thus
fixed and random coefficients.
2. Effects are fixed if they are interesting in themselves or random
if there is
interest in the underlying population. Searle, Casella and McCulloch
Section 1.4] explore this distinction in depth.
3. “When a sample exhausts the population, the corresponding
variable is fixed;
when the sample is a small (i.e., negligible) part of the population
corresponding variable is random” [Green and Tukey (1960)].
4. “If an effect is assumed to be a realized value of a random
variable, it is called
a random effect” [LaMotte (1983)].
5. fixed effects are estimated using least squares (or, more
likelihood) and random effects are estimated with shrinkage
prediction” in the terminology of Robinson (1991)]. This definition
in the multilevel modeling literature [see, e.g., Snijders and
Section 4.2] and in econometrics.
Of these definitions, the first clearly stands apart, but the other
differ also. Under the second definition, an effect can change from
random with a change in the goals of inference, even if the data and
design are unchanged. The third definition differs from the others
in defining a finite
population (while leaving open the question of what to do with a
large but not
exhaustive sample), while the fourth definition makes no reference
to an actual
(rather than mathematical) population at all. The second definition
effects to come from a distribution, as long as that distribution is
not of interest,
whereas the fourth and fifth do not use any distribution for
inference about fixed
effects. The fifth definition has the virtue of mathematical
precision but leaves
unclear when a given set of effects should be considered fixed or
summary, it is easily possible for a factor to be “fixed”
according to some of the
definitions above and “random” for others. Because of these
it is no surprise that “clear answers to the question ‘fixed or
random?’ are not
necessarily the norm” [Searle, Casella and McCulloch (1992), page
y_ij = α_j + β x_ij (of units i in groups j )
has a constant slope and varying intercepts, and
y_ij = α_j + βj x_ij
has varying slopes and intercepts. In this terminology (which we
would apply at any level of the hierarchy in a multilevel model),
varying effects occur in batches, whether or not the effects are
interesting in themselves (definition 2), and whether or not they
are a sample from a larger set (definition 3). Definitions 4 and 5
do not arise for us since we estimate all batches of effects
hierarchically, with the variance components σ_m estimated from
On Nov 5, 2009, at 4:00 AM, Nick Cox wrote:
It is kind of Maarten to presume that, but my comments were on the
level of "I see no mention of fixed effects here".
--- Maarten buis wrote:
In this type of literature the term fixed effects has
two very different meanings: 1) the non-random effects
of explanatory variables in a random effects model,
2) a model that only uses information from changes
within an level.
--- On Wed, 4/11/09, Tim Waring wrote:
I actually only need to do number 1 (non-random effects of
explanatory variables), not number 2 (model that only uses
information from changes within an level).
Nick, do you think even this is not possible?
If you look at the STB article introducing this program you
will see that it can estimate fixed effects of type 1. I am
guessing that Nick and Scott are referring to fixed effects
of type 2.
The STB's are now freely available, so you can download that
(the article is on pages 23 till 27)
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