BIC {ICglm}

Bayesian Information Criterion

Description

Calculates Bayesian Information Criterion (BIC) and its variants (BICadj, BICQ) for "lm" and "glm" objects.

Usage

BIC(model)

BICadj(model)

BICQ(model, q = 0.25)

Arguments

model

a "lm" or "glm" object

q

adjustment parameter for BICQ. Default is 0.25.

Details

BIC (Schwarz, 1978) is calculated as

-2LL(theta) + klog(n)

Adjusted BIC (Dziak et al., 2020) as

-2LL(theta) + klog(n/2pi)

and BICQ (Xu, 2010) as

-2LL(theta) + klog(n) - 2klog(q/(1-q))

.

Value

BIC, BICadj or BICQ measurement of the model

References

Dziak, J. J., Coffman, D. L., Lanza, S. T., Li, R., & Jermiin, L. S. (2020). Sensitivity and specificity of information criteria. Briefings in bioinformatics, 21(2), 553-565.

Xu, C. (2010). Model Selection with Information Criteria.

Schwarz, G. 1978. Estimating the dimension of a model The Annals of Statistics 6 (2), 461–464. <doi:10.1214/aos/1176344136>

Examples

x1 <- rnorm(100, 3, 2)
x2 <- rnorm(100, 5, 3)
x3 <- rnorm(100, 67, 5)
err <- rnorm(100, 0, 4)

## round so we can use it for Poisson regression
y <- round(3 + 2*x1 - 5*x2 + 8*x3 + err)

m1 <- lm(y~x1 + x2 + x3)
m2 <- glm(y~x1 + x2 + x3, family = "gaussian")
m3 <- glm(y~x1 + x2 + x3, family = "poisson")

BIC(m1)
BIC(m2)
BIC(m3)
BICadj(m1)
BICadj(m2)
BICadj(m3)