I am looking for advice on circular statistics. In particular, I'd like to know if any one had any advice/ references that deal with regression models for circular variables and whether it is possible to include random effects as well.
At the moment I can fit very simple models in WinBUGS using wrapped cauchy distributions, but I don't know how to go on to the next step and add either fixed or random effects. Below is the WinBUGS code I have been using so far. I have tested it with simulated data and so far it has performed well, but trying to add in fixed/ random effects has, so far, not worked.
model{
for (t in 1:N) {
# likelihood for angles. We use the “ones” trick to sample from the
# Wrapped Cauchy distribution (see WinBUGS manual)
ones[t]<- 1
ones[t] ~ dbern(wc[t])
wc[t] <- (1/(2*Pi)*(1-rho[t]*rho[t])/(1+rho[t]*rho[t]-2*rho[t]*cos(theta[t]-
mu.t[t])))/ 300 # Density function for Wrapped Cauchy distribution
rho[t] <- lambda.t # mean cosine for the circular distribution
mu.t[t]<- nu.t# mean direction for turns
}
###### priors for mean direction of angles
nu.t ~ dunif(-3.14159265359, 3.14159265359)
lambda.t ~ dunif(0,1) # prior for mean cosine of circular distribution
Pi <- 3.14159265359 # define Pi
}
## Simulated Data ##
list(theta=c(1.57086666107637,0.624281203067249,4.83586153543422,5.52517105399153,0.250167755691792,5.24413183188724,0.175711907822086,0.503670499719972,0.00587906094477884,0.290131613934322,0.759047889069672,0.57973291007534,3.03128168541491,0.497790655905849,6.24730873150114,2.61159637947433,6.19811892339656,2.21476872674273,0.163464826891718,5.79300356573004,5.65352466175931,-0.0100726021401003,0.00574503925995024,0.260777171784755,5.8545805891331,6.09628602098184,6.07018161953988,5.90921466125829,0.0387070377090986,5.96019978900552,0.270388591408335,0.539775794451919,6.16303548945592,5.54317029065067,1.09867887761604,0.546155012914554,5.73154203573232,6.04837644493341,.242217723020124,0.201937287826239,6.19111529531002,0.602897213838987,5.53590129760264,0.304328180646957,6.12364810518025,0.0781317192586082,2.12148311222615,5.41742779164167,0.109722984863423,0.546244633029087,1.72483899231817,5.81142848191977,5.77431670621736,5.94852063016486,1.21880980868771,0.761391412364464,6.13385885651117,2.3278212791841,-0.00886837423371834,0.0509442654103693,0.919346146608449,0.22243489212092,0.0605109486858312,6.26215798187548,3.35930515203348,4.49262316826849,0.393662386151002,0.408276217352091,5.48604197934124,1.2319358669625,0.290890698266516,0.0356807866706245,5.01603150661483,2.13110569190685,5.58637984768018,0.705401496640296,0.474940761772081,5.58728776070886,6.12311166642116,0.00848809261322299,3.35074107197193,5.82089972193407,0.0531213061461832,5.97904289602246,4.31610462188531,5.61206825679503,0.184081838885041,0.288450927211418,0.594322121025956,1.07062485671203,0.400068367390392,5.08834932305335,4.35542895067301,6.08614182924595,6.14530696852739,5.25070254271081,5.91716602109256,1.78589020077607,6.23955405139402,6.09356179129423), N =100)
