cake {lme4} | R Documentation

## Breakage Angle of Chocolate Cakes

### Description

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.

### Format

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

`replicate`

  a factor with levels `1` to `15`

`recipe`

  a factor with levels `A`, `B` and `C`

`temperature`

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

`angle`

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

`temp`

  numeric value of the baking temperature (degrees F).

### Details

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

### Source

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

### References

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.

### Examples

    str(cake)
    ## '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 1.1-12 Index]