On Mon, 27 Nov 2006, Michael Kubovy wrote:
> In the course of exploring response prediction, I stumbled upon a
> small discrepancy between the CIs produced by predict.lm() and
> all.effects()
>
> require(mlmRev)
> require(effects)
> hsb.lm <- lm(mAch ~ minrty * sector, Hsb82)
> hsb.new <- data.frame(
> minrty = rep(c('No', 'Yes'), 2),
> sector = rep(c('Public', 'Catholic'), each = 2))
> hsb.eff <- all.effects(hsb.lm)
> cbind(
> hsb.new,
> predict(hsb.lm, hsb.new, interval = 'confidence', type =
> 'response')
> )
> # the following lower and upper bounds differ starting with the
> fourth decimal place
> data.frame(
> hsb.new,
> fit = hsb.eff[[1]]$fit,
> lwr = hsb.eff[[1]]$lower,
> upr = hsb.eff[[1]]$upper
> )
>
> Is this due to rounding or algorithm?
Neither: a statistical methodology difference.
predict.lm uses a t reference distribution. effect.lm uses a Normal
reference distribution. (My guess is because it is designed to work also
with GLM fits, but perhaps John Fox can elaborate and consider using a t
distribution for lm and gaussian glm models.) Of course in this example
there is no practical difference, but there could be in others.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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