View source: R/family.binomial.R

betageometric | R Documentation |

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 |

`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}.
See |

A random variable `Y`

has a 2-parameter beta-geometric distribution
if `P(Y=y) = p (1-p)^y`

for `y=0,1,2,\ldots`

where
`p`

are generated from a standard beta distribution with
shape parameters `shape1`

and `shape2`

.
The parameterization here is to focus on the parameters
`p`

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-p) / (p-\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.

`geometric`

,
`betaff`

,
`rbetageom`

.

```
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, bdata, weight = wts, trace = TRUE)
fitg <- vglm(y ~ 1, geometric, 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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