Maximum Likelihood Estimation of TPPXG Regression Coefficients {TPXG} | R Documentation |
Estimation of the TPPXG regression coefficients.
Description
This function estimates the Two Parameter Poisson Xgamma regression coefficients as well as the
\alpha
parameter of the Two Parameter Poisson Xgamma distribution using the maximum likelihood method.
Usage
tppxg.reg(y, x)
Arguments
y |
A numeric vector containg non-negative integer values. |
x |
A matrix or a data.frame with the predictor variables. |
Details
The \theta
parameter has been transformed as a function of the expected value of the response variable Y
in the following manner:
\theta=\frac{1-\alpha \mu +\sqrt{(\alpha \mu -1)^2+12\alpha \mu}}{2\mu}
Given that the response variable satisfies Y_i \sim \text{TPPXG}(\alpha, \mu_i)
, then the
i^{\text{th}}
mean of Y is related to the predictor variables using the log link function:
\mu_i=e^{x_i^T \beta} \quad i=1,2,3,\dots n
For more details, see the paper referenced below.
Value
A named list containing \alpha
parameter, a vector containing the \beta
coefficients and the maximum likelihood value.
Author(s)
Nikolaos Kontemeniotis.
R implementation and documentation: Nikolaos Kontemeniotis kontemeniotisn@gmail.com and Michail Tsagris mtsagris@uoc.gr.
References
"Wani, M. A., Ahmad, P. B., Para, B. A. and Elah, N. (2023). A new regression model for count data with applications to health care data. International Journal of Data Science and Analytics."
See Also
Examples
x <- matrix( rnorm(100 * 2), ncol = 2 )
y <- rtppxg(100)
tppxg.reg(y, x)