Sawa's bayesian information criterion

Sawa's bayesian information criterion for model selection.

Usage

ols_sbic(model, full_model)

Arguments

model

An object of class lm.

full_model

An object of class lm.

Value

Sawa's Bayesian Information Criterion

Details

Sawa (1978) developed a model selection criterion that was derived from a Bayesian modification of the AIC criterion. Sawa's Bayesian Information Criterion (BIC) is a function of the number of observations n, the SSE, the pure error variance fitting the full model, and the number of independent variables including the intercept.

$$SBIC = n * ln(SSE / n) + 2(p + 2)q - 2(q^2)$$

where \(q = n(\sigma^2)/SSE\), n is the sample size, p is the number of model parameters including intercept SSE is the residual sum of squares.

References

Sawa, T. (1978). “Information Criteria for Discriminating among Alternative Regression Models.” Econometrica 46:1273–1282.

Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.

See also

Other model selection criteria: ols_aic(), ols_apc(), ols_fpe(), ols_hsp(), ols_mallows_cp(), ols_msep(), ols_sbc()

Examples

full_model <- lm(mpg ~ ., data = mtcars)
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_sbic(model, full_model)
#> [1] 70.27599