Beta-geometric Distribution Family Function
Maximum likelihood estimation for the beta-geometric distribution.
betageometric(lprob = "logitlink", lshape = "loglink",
iprob = NULL, ishape = 0.1,
moreSummation = c(2, 100), tolerance = 1.0e-10, zero = NULL)lprob, lshape |
Parameter link functions applied to the
parameters prob and phi
(called |
iprob, ishape |
Numeric.
Initial values for the two parameters.
A |
moreSummation |
Integer, of length 2.
When computing the expected information matrix a series summation from
0 to |
tolerance |
Positive numeric. When all terms are less than this then the series is deemed to have converged. |
zero |
An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. If used, the value must be from the set {1,2}. |
A random variable Y has a 2-parameter beta-geometric distribution
if P(Y=y) = prob * (1-prob)^y
for y=0,1,2,... where
prob are generated from a standard beta distribution with
shape parameters shape1 and shape2.
The parameterization here is to focus on the parameters
prob and
phi = 1/(shape1+shape2),
where phi is shape.
The default link functions for these ensure that the appropriate range
of the parameters is maintained.
The mean of Y is
E(Y) =
shape2 / (shape1-1) = (1-prob) / (prob-phi)
if shape1 > 1, and if so, then this is returned as
the fitted values.
The geometric distribution is a special case of the beta-geometric
distribution with phi=0 (see geometric).
However, fitting data from a geometric distribution may result in
numerical problems because the estimate of log(phi)
will 'converge' to -Inf.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
The first iteration may be very slow;
if practical, it is best for the weights argument of
vglm etc. to be used rather than inputting a very
long vector as the response, i.e., vglm(y ~ 1, ..., weights = wts)
is to be preferred over vglm(rep(y, wts) ~ 1, ...).
If convergence problems occur try inputting some values of argument
ishape.
If an intercept-only model is fitted then the misc slot of the
fitted object has list components shape1 and shape2.
T. W. Yee
Paul, S. R. (2005). Testing goodness of fit of the geometric distribution: an application to human fecundability data. Journal of Modern Applied Statistical Methods, 4, 425–433.
bdata <- data.frame(y = 0:11, wts = c(227,123,72,42,21,31,11,14,6,4,7,28)) fitb <- vglm(y ~ 1, betageometric, data = bdata, weight = wts, trace = TRUE) fitg <- vglm(y ~ 1, geometric, data = bdata, weight = wts, trace = TRUE) coef(fitb, matrix = TRUE) Coef(fitb) sqrt(diag(vcov(fitb, untransform = TRUE))) fitb@misc$shape1 fitb@misc$shape2 # Very strong evidence of a beta-geometric: pchisq(2 * (logLik(fitb) - logLik(fitg)), df = 1, lower.tail = FALSE)
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