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Re: st: REOPROB


From   Tim Waring <twaring@ucdavis.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: REOPROB
Date   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 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
n.j.cox@durham.ac.uk

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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