cake {lme4}R Documentation

Breakage Angle of Chocolate Cakes


Data on the breakage angle of chocolate cakes made with three different recipes and baked at six different temperatures. This is a split-plot design with the recipes being whole-units and the different temperatures being applied to sub-units (within replicates). The experimental notes suggest that the replicate numbering represents temporal ordering.


A data frame with 270 observations on the following 5 variables.


a factor with levels 1 to 15


a factor with levels A, B and C


an ordered factor with levels 175 < 185 < 195 < 205 < 215 < 225


a numeric vector giving the angle at which the cake broke.


numeric value of the baking temperature (degrees F).


The replicate factor is nested within the recipe factor, and temperature is nested within replicate.


Original data were presented in Cook (1938), and reported in Cochran and Cox (1957, p. 300). Also cited in Lee, Nelder and Pawitan (2006).


Cook, F. E. (1938) Chocolate cake, I. Optimum baking temperature. Master's Thesis, Iowa State College.

Cochran, W. G., and Cox, G. M. (1957) Experimental designs, 2nd Ed. New York, John Wiley & Sons.

Lee, Y., Nelder, J. A., and Pawitan, Y. (2006) Generalized linear models with random effects. Unified analysis via H-likelihood. Boca Raton, Chapman and Hall/CRC.


## 'temp' is continuous, 'temperature' an ordered factor with 6 levels

(fm1 <- lmer(angle ~ recipe * temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm2 <- lmer(angle ~ recipe + temperature + (1|recipe:replicate), cake, REML= FALSE))
(fm3 <- lmer(angle ~ recipe + temp        + (1|recipe:replicate), cake, REML= FALSE))

## and now "choose" :
anova(fm3, fm2, fm1)

[Package lme4 version 1.1-35.5 Index]