Bayesian Information Criterion

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

BICvlm(object, ..., k = log(nobs(object)))

Arguments

object, ...

Same as AICvlm.

k

Numeric, the penalty per parameter to be used; the default is log(n) where n is the number of observations).

Details

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.

Value

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

Author

T. W. Yee.

Note

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.

Warning

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!!

See also

AICvlm, VGLMs are described in vglm-class; VGAMs are described in vgam-class; RR-VGLMs are described in rrvglm-class; BIC, AIC.

Examples

pneumo <- transform(pneumo, let = log(exposure.time))
(fit1 <- vglm(cbind(normal, mild, severe) ~ let,
              cumulative(parallel = TRUE, reverse = TRUE), data = pneumo))
#> 
#> 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 
coef(fit1, matrix = TRUE)
#>             logitlink(P[Y>=2]) logitlink(P[Y>=3])
#> (Intercept)          -9.676093         -10.581725
#> let                   2.596807           2.596807
BIC(fit1)
#> [1] 56.41885
(fit2 <- vglm(cbind(normal, mild, severe) ~ let,
              cumulative(parallel = FALSE, reverse = TRUE), data = pneumo))
#> 
#> 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 
coef(fit2, matrix = TRUE)
#>             logitlink(P[Y>=2]) logitlink(P[Y>=3])
#> (Intercept)          -9.593308          -11.10479
#> let                   2.571300            2.74355
BIC(fit2)
#> [1] 58.35587