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Re: st: REOPROB
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
follows:
reoprob dependant_var fixedeffect_var1 fixedeffect_var2,
i(randomeffect_var)
My original worry was that the location of fixedeffect_var1 was being
treated as a random effect, rather than a fixed effect. This is not
the case, random effects are specifies within the i() term.
One final point on the meaning of fixed effects - there seems to be
some confusing differences in how people use the term. The safest
meaning is that used by statisticians, but there are many other uses.
It is probably good that everyone know what those uses are, and Andrew
Gelman provides a nice summary of the different meanings that people
use for "fixed effects":
Andrew Gelman
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,
incompatible—definitions
are used in different contexts. [See also Kreft and de Leeuw (1998),
Section 1.3.3,
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
vary. For
example, in a growth study, a model with random intercepts αi and
fixed
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
distinguish between
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
[(1992),
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
the
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
generally, maximum
likelihood) and random effects are estimated with shrinkage
[“linear unbiased
prediction” in the terminology of Robinson (1991)]. This definition
is standard
in the multilevel modeling literature [see, e.g., Snijders and
Bosker (1999),
Section 4.2] and in econometrics.
Of these definitions, the first clearly stands apart, but the other
four definitions
differ also. Under the second definition, an effect can change from
fixed to
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
allows fixed
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
random. In
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
conflicting definitions,
it is no surprise that “clear answers to the question ‘fixed or
random?’ are not
necessarily the norm” [Searle, Casella and McCulloch (1992), page
15].
We prefer to sidestep the overloaded terms “fixed” and
“random” with a cleaner
distinction by simply renaming the terms in definition 1 above. We
define effects
(or coefficients) in a multilevel model as constant if they are
identical for all groups in a population and varying if they are
allowed to differ from group to group. For example, the model
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
data. "
Best,
Tim
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".
Nick
[email protected]
Maarten buis
--- 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
article from:
http://www.stata.com/products/stb/journals/stb59.pdf
(the article is on pages 23 till 27)
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