What is the statistical model that can best be used to analyze data from a cross-over design in which 4 sheep were randomly assigned to 2 diets in the first period and then switched diets in the second period. Parameters of interest were DM intake, Nutrient digestibility, VFA concentration and methane emissions.
You have a repeated measures design.
To keep it simple: Doubly Multivariate Repeated Measures ANOVA
This is a model that allows the specification of multiple dependent variables (DM intake, Nutrient digestibility, VFA concentration, and methana emissions), within-subject factors (period 1/2), and between-subject factors (group 1/2).
The tougher, but better model: a mixed-effect model (also called multilevel analysis). If you want to go this route, I would suggest reading up on it. The linked pdf does a great job at explaining why and how mixed-effect models should be used for repeated measures designs.
http://www.sfs.uni-tuebingen.de/~hbaayen/publications/BaayenHandbookLabPhonLMM2012.pdf
Dear David,
I suggest you this article which is in my contributions in RG. Thank you.
a) Optimal crossover designs are statistically efficient and so require fewer subjects than do non-crossover designs (even other repeated measures designs).
b) The Kruskal-Wallis test is used for comparing ordinal or non-Normal variables for more than two groups, and is a generalisation of the Mann-Whitney U test. The technique is beyond the scope of this book, but is described in more advanced books and is available in common software (Epi-Info, Minitab, SPSS).
(c) Analysis of variance is a general technique, and one version (one way analysis of variance) is used to compare Normally distributed variables for more than two groups, and is the parametric equivalent of the Kruskal-Wallis test.
Hi,
The usual model to analyse such a cross-over design is
Yijkl = µ+Si + Pj + Tk(ij)+ Indl/Si + epsijkl
where
- Yijkl is the observation obtained in the lth sheep from the sequence i at period j ; this sheep has received the treatment k(ij) with k(11) = 1 k(12) =2 k(21)=2 and k(22)=2.
- Si is the effect of the jth sequence ; the sequence denotes the order of administation of the treatments
- Pj is the effect of the jth period
- Tk(ij) is the effect of treatment k
- Indl/Si is the random effect of the lth sheep belonging to the ith sequence (this is a nested effect)
- epsijkl is the residual term.
This is a linear mixed effects model
You can have much more details by reading :
Design and analysis of cross-over trials from Byron Jones and Michael G. Kenward.
I think that google scholar gives you a free reading of the chapter devoted to the 2 by 2 cross-over design.
Cheers,
Didier
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