| loglinb3 {VGAM} | R Documentation |
Loglinear Model for Three Binary Responses
Description
Fits a loglinear model to three binary responses.
Usage
loglinb3(exchangeable = FALSE, zero = c("u12", "u13", "u23"))
Arguments
exchangeable |
Logical.
If |
zero |
Which linear/additive predictors are modelled as
intercept-only?
A |
Details
The model is
P(Y_1=y_1,Y_2=y_2,Y_3=y_3) =
\exp(u_0+u_1 y_1+u_2 y_2+u_3 y_3+u_{12} y_1 y_2+
u_{13} y_1 y_3+u_{23} y_2 y_3)
where y_1, y_2 and y_3 are 0
or 1, and the parameters are u_1, u_2,
u_3, u_{12}, u_{13},
u_{23}.
The normalizing parameter u_0 can be expressed as a
function of the other parameters.
Note that a third-order association parameter,
u_{123} for the product y_1 y_2 y_3,
is assumed to be zero for this family function.
The linear/additive predictors are
(\eta_1,\eta_2,\ldots,\eta_6)^T =
(u_1,u_2,u_3,u_{12},u_{13},u_{23})^T.
Value
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm,
rrvglm and vgam.
When fitted, the fitted.values slot of the object
contains the eight joint probabilities, labelled as
(Y_1,Y_2,Y_3) = (0,0,0), (0,0,1), (0,1,0),
(0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1), respectively.
Note
The response must be a 3-column matrix of ones and zeros only. Note that each of the 8 combinations of the multivariate response need to appear in the data set, therefore data sets will need to be large in order for this family function to work. After estimation, the response attached to the object is also a 3-column matrix; possibly in the future it might change into a 8-column matrix.
Author(s)
Thomas W. Yee
References
Yee, T. W. and Wild, C. J. (2001). Discussion to: “Smoothing spline ANOVA for multivariate Bernoulli observations, with application to ophthalmology data (with discussion)” by Gao, F., Wahba, G., Klein, R., Klein, B. Journal of the American Statistical Association, 96, 127–160.
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
See Also
Examples
lfit <- vglm(cbind(cyadea, beitaw, kniexc) ~ altitude, loglinb3,
data = hunua, trace = TRUE)
coef(lfit, matrix = TRUE)
head(fitted(lfit))
summary(lfit)