lme4 (version 0.999375-37)

Pastes: Paste strength by batch and cask

Description

Paste str

Usage

data(Pastes)

source

O.L. Davies and P.L. Goldsmith (eds), Statistical Methods in Research and Production, 4th ed., Oliver and Boyd, (1972), section 6.5

Details

The data are described in Davies and Goldsmith (1972) as coming from deliveries of a chemical paste product contained in casks where, in addition to sampling and testing errors, there are variations in quality between deliveries ...As a routine, three casks selected at random from each delivery were sampled and the samples were kept for reference. ...Ten of the delivery batches were sampled at random and two analytical tests carried out on each of the 30 samples.

Examples

str(Pastes)
dotplot(cask ~ strength | reorder(batch, strength), Pastes,
        strip = FALSE, strip.left = TRUE, layout = c(1, 10),
        ylab = "Cask within batch",
        xlab = "Paste strength", jitter.y = TRUE)
## Modifying the factors to enhance the plot
Pastes <- within(Pastes, batch <- reorder(batch, strength))
Pastes <- within(Pastes, sample <- reorder(reorder(sample, strength),
          as.numeric(batch)))
dotplot(sample ~ strength | batch, Pastes,
        strip = FALSE, strip.left = TRUE, layout = c(1, 10),
        scales = list(y = list(relation = "free")),
        ylab = "Sample within batch",
        xlab = "Paste strength", jitter.y = TRUE)
## Four equivalent models differing only in specification
(fm1 <- lmer(strength ~ (1|batch) + (1|sample), Pastes))
(fm2 <- lmer(strength ~ (1|batch/cask), Pastes))
(fm3 <- lmer(strength ~ (1|batch) + (1|batch:cask), Pastes))
(fm4 <- lmer(strength ~ (1|batch/sample), Pastes))
## fm4 results in redundant labels on the sample:batch interaction
head(ranef(fm4)[[1]])
## compare to fm1
head(ranef(fm1)[[1]])
## This model is different and NOT appropriate for these data
(fm5 <- lmer(strength ~ (1|batch) + (1|cask), Pastes))
image(fm1@L, sub = "Structure of random effects interaction in pastes model")