# transform multinomial variable to continous for testing

Following Glenn comments im editing my question and posting an example:

I want to know if my procedure here is valid.

We tested the relationship between ecomorph and escape behavior across ten species using Phylogenetic Generalized Least Squares. To assess if environmental context (sand versus leaf litter) affected escape strategy within each species, we used a phylogenetic t-test (package phytools) that compares the response among contexts and across species. Both analyses assume escape strategy is a continous variable in which burrowing is coded as 3,hiding as 2 and running as 1. Despite this maneuver allows accounting for phylogenetic non independence, is not the best description for the response variable, which conforms with a typical multinomial ordered variable. Thus we also fitted a categorical ordered model with both morphotype and environment simultaneously predicting escape strategy using the “polr” function. The high t-values and z-tests agree with phylogenetic analyses suggesting significant effects of both, morphotype and environment (see tables and figure)

Results of multinomial ordered model assessing effects of morphology and environmental context on the odds of using different escape strategies

                  Estimate  Std. Error   z value        Pr(>|z|)
morph snake-like    3.38739 0.24791      13.6637        < 2.2e-16
treatment sand     -1.42388 0.20554     -6.9275         4.28E-12


Results of PGLS test of the effects of morphotype on escape response.

PGLS: n=10, lambda= -0.1878671, coeff= 1.103697, t-value= 10.01984, p <0.001).

Results of Phylogenetic t-test of the effect otf the context over escape strategy Pt-test: n=10, lambda=1, t= 2.430056, p=0.04541684)

• You can't. Imagine 40% of the values are "bury". Whatever transformation you apply to the value "bury" -- whatever it maps to -- will have 40% of the values there. Oct 10 '14 at 15:07
• Thanks Glen, could you explain this a bit more please, or refer any information source? Oct 10 '14 at 18:19
• Consider two categories with the labels 0 and 1. You have four $0$'s and six $1$'s. Whatever function you use to transform your data, all four $0$'s will become whatever you make $0$ become when you transform it. So if you say "$0$ becomes $5$ and $1$ become $17$", you've specified a transformation. How does that help? Your discrete data is still discrete. Oct 10 '14 at 22:40
• If that doesn't convince you, you'll need to show an example of a transformation in your question that doesn't behave that way (feel free to do it on the 0/1 example in my previous comment). The only thing I can conceive is not so much transformation as it is "making up data". Oct 10 '14 at 22:45