inv.tt {GMCM} | R Documentation |
Reparametrization of GMCM parameters
Description
These functions map the four GMCM parameters in the model of Li et. al.
(2011) and Tewari et. al. (2011) onto the real line and back. The mixture
proportion is logit transformed. The mean and standard deviation are log
transformed. The correlation is translated and scaled to the interval (0,1)
and logit transformed by rho.transform
.
Usage
inv.tt(par, d, positive.rho)
tt(tpar, d, positive.rho)
Arguments
par |
A vector of length 4 where |
d |
The dimension of the space. |
positive.rho |
is logical. If |
tpar |
A vector of length 4 of the transformed parameter values where
|
Details
The functions are used only in the wrapper to optim
when the GMCM
log-likelihood is optimized.
par[1]
should be between 0 and 1. par[2]
and par[3]
should be non-negative. If positive.rho
is FALSE
,
par[4]
should be between -1/(d-1)
and 1. Otherwise,
positive.rho
should be between 0 and 1.
Value
inv.tt
returns tpar
as described above.
A numeric
vector of the transformed or inversely transformed
values of length 4.
tt
returns par
as described above.
Author(s)
Anders Ellern Bilgrau <anders.ellern.bilgrau@gmail.com>
References
Li, Q., Brown, J. B. J. B., Huang, H., & Bickel, P. J. (2011). Measuring reproducibility of high-throughput experiments. The Annals of Applied Statistics, 5(3), 1752-1779. doi:10.1214/11-AOAS466
Tewari, A., Giering, M. J., & Raghunathan, A. (2011). Parametric Characterization of Multimodal Distributions with Non-gaussian Modes. 2011 IEEE 11th International Conference on Data Mining Workshops, 286-292. doi:10.1109/ICDMW.2011.135
Examples
par <- c(pie1 = 0.3, mu = 2, sigma = 0.5, rho = 0.8)
tpar <- GMCM:::inv.tt(par, d = 3, positive.rho = FALSE)
GMCM:::tt(tpar, d = 3, positive.rho = FALSE)