R: Bayesian Information Criterion

BICvlm {VGAM} | R Documentation

## Bayesian Information Criterion

### Description

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

### Usage

    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`.

### 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!!

### 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. Preliminary testing shows absolute differences with some VGAM family functions such as `gaussianff`, however, they should agree with non-normal families.

BIC has not been defined for QRR-VGLMs yet.

### Author(s)

T. W. Yee.

### 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))
    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)

    # These do not agree in absolute terms:
    gdata <- data.frame(x2 = sort(runif(n <- 40)))
    gdata <- transform(gdata, y1 = 1 + 2*x2 + rnorm(n, sd = 0.1))
    fit.v <- vglm(y1 ~ x2, gaussianff, data = gdata)
    fit.g <-  glm(y1 ~ x2, gaussian  , data = gdata)
    fit.l <-   lm(y1 ~ x2, data = gdata)
    c(BIC(fit.l), BIC(fit.g), BIC(fit.v))
    c(AIC(fit.l), AIC(fit.g), AIC(fit.v))
    c(AIC(fit.l) - AIC(fit.v),
      AIC(fit.g) - AIC(fit.v))
    c(logLik(fit.l), logLik(fit.g), logLik(fit.v))

[Package VGAM version 1.0-3 Index]