CAIC {ICglm}

Consistent Akaike's Information Criterion and Consistent Akaike's Information Criterion with Fisher Information

Description

Consistent Akaike's Information Criterion (CAIC) and Consistent Akaike's Information Criterion with Fisher Information (CAICF) for "lm" and "glm" objects.

Usage

CAIC(model)

CAICF(model)

Arguments

model

a "lm" or "glm" object.

Details

CAIC (Bozdogan, 1987) is calculated as

-2LL(theta) + k(log(n) + 1)

CAICF (Bozdogan, 1987) as

-2LL(theta) + 2k + k(log(n)) + log(|F|)

F is the Fisher information matrix.

Value

CAIC or CAICF measurement of the model.

References

Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52(3), 345-370.

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")

CAIC(m1)
CAIC(m2)
CAIC(m3)
CAICF(m1)
CAICF(m2)
CAICF(m3)