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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.

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 ismeant by fixedand random effects. It turns out that different—in fact,incompatible—definitionsare 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 andrandom effects andcoefficients, and Robinson (1998) for a historical overview.] Herewe outline fivedefinitions that we have seen:1. fixed effects are constant across individuals, and random effectsvary. Forexample, in a growth study, a model with random intercepts αi andfixedslope β corresponds to parallel lines for different individuals i ,or the modelyi t = αi + β t . Kreft and de Leeuw [(1998), page 12] thusdistinguish betweenfixed and random coefficients.2. Effects are fixed if they are interesting in themselves or randomif there isinterest 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 correspondingvariable is fixed;when the sample is a small (i.e., negligible) part of the populationthecorresponding variable is random” [Green and Tukey (1960)].4. “If an effect is assumed to be a realized value of a randomvariable, it is calleda random effect” [LaMotte (1983)].5. fixed effects are estimated using least squares (or, moregenerally, maximumlikelihood) and random effects are estimated with shrinkage[“linear unbiasedprediction” in the terminology of Robinson (1991)]. This definitionis standardin the multilevel modeling literature [see, e.g., Snijders andBosker (1999),Section 4.2] and in econometrics.Of these definitions, the first clearly stands apart, but the otherfour definitionsdiffer also. Under the second definition, an effect can change fromfixed torandom with a change in the goals of inference, even if the data anddesign are unchanged. The third definition differs from the othersin defining a finitepopulation (while leaving open the question of what to do with alarge but notexhaustive sample), while the fourth definition makes no referenceto an actual(rather than mathematical) population at all. The second definitionallows fixedeffects to come from a distribution, as long as that distribution isnot of interest,whereas the fourth and fifth do not use any distribution forinference about fixedeffects. The fifth definition has the virtue of mathematicalprecision but leavesunclear when a given set of effects should be considered fixed orrandom. Insummary, it is easily possible for a factor to be “fixed”according to some of thedefinitions above and “random” for others. Because of theseconﬂicting definitions,it is no surprise that “clear answers to the question ‘fixed orrandom?’ are notnecessarily the norm” [Searle, Casella and McCulloch (1992), page15].We prefer to sidestep the overloaded terms “fixed” and“random” with a cleanerdistinction by simply renaming the terms in definition 1 above. Wedefine effects(or coefficients) in a multilevel model as constant if they areidentical for all groups in a population and varying if they areallowed to differ from group to group. For example, the modely_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_ijhas varying slopes and intercepts. In this terminology (which wewould apply at any level of the hierarchy in a multilevel model),varying effects occur in batches, whether or not the effects areinteresting in themselves (definition 2), and whether or not theyare a sample from a larger set (definition 3). Definitions 4 and 5do not arise for us since we estimate all batches of effectshierarchically, with the variance components σ_m estimated fromdata. "

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 thelevel 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) * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: REOPROB***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**References**:**Re: st: REOPROB***From:*Tim Waring <twaring@ucdavis.edu>

**Re: st: REOPROB***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**RE: st: REOPROB***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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