Description Usage Arguments Details Value Warning Note Author(s) See Also Examples

Calculates the Bayesian information criterion (BIC) for a fitted model object for which a log-likelihood value has been obtained.

1 |

`object, ...` |
Same as |

`k` |
Numeric, the penalty per parameter to be used;
the default is |

The so-called BIC or SBC (Schwarz's Bayesian criterion)
can be computed by calling `AICvlm`

with a
different `k`

argument.
See `AICvlm`

for information and caveats.

Returns a numeric value with the corresponding BIC, or ...,
depending on `k`

.

Like `AICvlm`

, this code has not been double-checked.
The general applicability of `BIC`

for the VGLM/VGAM classes
has not been developed fully.
In particular, `BIC`

should not be run on some VGAM family
functions because of violation of certain regularity conditions, etc.

Many VGAM family functions such as
`cumulative`

can have the number of
observations absorbed into the prior weights argument
(e.g., `weights`

in `vglm`

), either
before or after fitting. Almost all VGAM family
functions can have the number of observations defined by
the `weights`

argument, e.g., as an observed frequency.
`BIC`

simply uses the number of rows of the model matrix, say,
as defining `n`

, hence the user must be very careful
of this possible error.
Use at your own risk!!

BIC, AIC and other ICs can have have many additive constants added to them. The important thing are the differences since the minimum value corresponds to the best model.

BIC has not been defined for QRR-VGLMs yet.

T. W. Yee.

`AICvlm`

,
VGLMs are described in `vglm-class`

;
VGAMs are described in `vgam-class`

;
RR-VGLMs are described in `rrvglm-class`

;
`BIC`

,
`AIC`

.

1 2 3 4 5 6 7 8 9 | ```
pneumo <- transform(pneumo, let = log(exposure.time))
(fit1 <- vglm(cbind(normal, mild, severe) ~ let,
cumulative(parallel = TRUE, reverse = TRUE), data = pneumo))
coef(fit1, matrix = TRUE)
BIC(fit1)
(fit2 <- vglm(cbind(normal, mild, severe) ~ let,
cumulative(parallel = FALSE, reverse = TRUE), data = pneumo))
coef(fit2, matrix = TRUE)
BIC(fit2)
``` |

```
Loading required package: stats4
Loading required package: splines
Call:
vglm(formula = cbind(normal, mild, severe) ~ let, family = cumulative(parallel = TRUE,
reverse = TRUE), data = pneumo)
Coefficients:
(Intercept):1 (Intercept):2 let
-9.676093 -10.581725 2.596807
Degrees of Freedom: 16 Total; 13 Residual
Residual deviance: 5.026826
Log-likelihood: -25.09026
logitlink(P[Y>=2]) logitlink(P[Y>=3])
(Intercept) -9.676093 -10.581725
let 2.596807 2.596807
[1] 56.41885
Call:
vglm(formula = cbind(normal, mild, severe) ~ let, family = cumulative(parallel = FALSE,
reverse = TRUE), data = pneumo)
Coefficients:
(Intercept):1 (Intercept):2 let:1 let:2
-9.593308 -11.104791 2.571300 2.743550
Degrees of Freedom: 16 Total; 12 Residual
Residual deviance: 4.884404
Log-likelihood: -25.01905
logitlink(P[Y>=2]) logitlink(P[Y>=3])
(Intercept) -9.593308 -11.10479
let 2.571300 2.74355
[1] 58.35587
```

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