[R] Use predict() after lmer() (library lme4)

[Thierry Onkelinx]

Dear Marc,

This question is more suited for R-Sig-mixed models to which I'm forwarding
it.

Your manual predictions for out3 are wrong. Here are the correct manual
predictions.

fixed <- model.matrix(~effect, data = dataF) %*% fixef(out3)
random <- rowSums(model.matrix(~Sector, data = dataF) *
ranef(out3)$Beach[dataF$Beach, ])
range(fixed + random - predict(out3))

Best regards,


ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2016-02-03 8:08 GMT+01:00 Marc Girondot <marc_grt op yahoo.fr>:

> Bonjour, (don't worry, after I will write in English [at least I will try
> ;) ])
>
> I try to understand better mixed models and then I have generated data and
> I try to understand how the fixed and the random effects are used in
> predict(). I understand when the random effect is of the form (1 | rf] but
> I don't understand for the form (rf1 | rf2]. Let do an example. The last
> formula does not give the same than predict().
>
> Thanks if someone could explain what formula use to reproduce the
> predict() results.
>
> Marc
>
> # 1/ Generate data in a data.frame, 1 response (number), one effect
> (effect) and two factors (sector and beach) that I want use as random
> effect. These two factors are hierarchical beach within sector
>
> Sector <- c(rep("I", 100), rep("II", 100))
> Beach <- c(
>   sample(c("A", "B", "C", "D", "E"), 100, replace=TRUE),
>   sample(c("F", "G"), 100, replace=TRUE)
>   )
>
> number <- rnorm(200, 10, 1)
>
> # Sector effect
> number[1:100] <- number[1:100] +0.1
> number[101:200] <- number[101:200] +0.5
>
> # beach effect
> beach.value <- 1:7
> names(beach.value) <- LETTERS[1:7]
> number <- number + unname(beach.value[Beach])
>
>
> dataF <- data.frame(number=number, effect= number/10+runif(200, 0, 2),
>                     Sector=Sector, Beach=Beach)
>
> plot(dataF$number, dataF$effect)
>
> ##############
> library("lme4")
> ##############
>
> ##############
> # 2/ Random effect is (1 | Beach). I can reproduce the predict()
> ##############
>
> out1 <- lmer(formula = number ~ effect + (1 | Sector) , data=dataF)
> head(predict(out1))
> ef <- fixef(out1)
> er <- ranef(out1)
>
> head(ef["(Intercept)"]+dataF$effect*ef["effect"]+
>   er$Sector[dataF$Sector, "(Intercept)"]
>   )
>
> ##############
> # 3/ Random effect is (1 | Beach) + (1 | Sector). I can reproduce the
> predict()
> ##############
>
> out2 <- lmer(formula = number ~ effect + (1 | Sector)  + (1 | Beach),
> data=dataF)
>
> head(predict(out2))
> ef <- fixef(out2)
> er <- ranef(out2)
>
> head(ef["(Intercept)"]+dataF$effect*ef["effect"]+
>        er$Sector[dataF$Sector, "(Intercept)"] +
>        er$Beach[dataF$Beach, "(Intercept)"]
>      )
>
> ##############
> # 4/ Random effect if (Sector | Beach). I don't understand how to
> reproduce the predict()
> ##############
>
> out3 <- lmer(formula = number ~ effect + (Sector | Beach), data=dataF)
>
> head(predict(out3))
> ef <- fixef(out3)
> er <- ranef(out3)
>
> head(ef["(Intercept)"]+dataF$effect*ef["effect"]+
>        er$Beach[dataF$Beach, "(Intercept)"]+
>        er$Beach[dataF$Beach, "SectorII"]
> )
>
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