Estoy buscando consejos sobre estadística circular. En particular, me gustaría saber si alguno tenía algún consejo/ referencias que se ocupan de los modelos de regresión para circular de las variables y si es posible incluir los efectos aleatorios así.
En el momento en que me puede encajar muy simple de modelos en WinBUGS utilizando envuelto de cauchy distribuciones, pero no sé cómo ir al siguiente paso y agregar fijos o de efectos aleatorios. A continuación es el WinBUGS código que he estado usando hasta ahora. Yo lo he probado con datos simulados y a la fecha se ha realizado bien, pero tratando de agregar en fijos y de efectos aleatorios, hasta el momento, no ha funcionado.
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)
