ICglm (version 0.1.0)

ICOMP: Informational Complexity

Description

These functions calculates Informational Complexity (ICOMP) variants for "lm" and "glm" objects.

Usage

ICOMP(model, type = "IFIM", C = "C1")
ICOMP_IFIM_CF(model)
ICOMP_IFIM_C1(model)
ICOMP_IFIM_C1F(model)
ICOMP_IFIM_C1R(model)
ICOMP_PEU_CF(model)
ICOMP_PEU_C1(model)
ICOMP_PEU_C1F(model)
ICOMP_PEU_C1R(model)
ICOMP_PEU_LN_CF(model)
ICOMP_PEU_LN_C1(model)
ICOMP_PEU_LN_C1F(model)
ICOMP_PEU_LN_C1R(model)
CICOMP_CF(model)
CICOMP_C1(model)
CICOMP_C1F(model)
CICOMP_C1R(model)

Arguments

model

a "lm" or "glm" object

type

type of ICOMP. Available types are "IFIM", "PEU", "PEU_LN" and "CICOMP". Default is "IFIM".

C

type of complexity. Available types are "CF", "C1", "C1F" and "C1R". Default is "C1".

Value

Informational Complexity measurement of the model

Details

ICOMP(IFIM) (Bozdogan, 2003) is calculated as

$$-2LL(theta) + 2C(F^{-1})$$

ICOMP(IFIM-peu) (Koc and Bozdogan, 2015) as

$$-2LL(theta) + k + 2C(F^{-1})$$

ICOMP(IFIM-peuln) (Bozdogan, 2010) as

$$-2LL(theta) + k + 2log(n)C(F^{-1})$$

and CICOMP (Pamukcu et al., 2015) as

$$-2LL(theta) + k(log(n) + 1) + 2C(F^{-1})$$

\(F\) is the fisher information matrix. \(F^{-1}\) is the reverse Fisher information matrix. \(C\) is the complexity measure. Four variants are available:

\(C_1\) (Bozdogan, 2010) is

$$C_1(F^{-1}) = s/2*log(lambda_a / lambda_g)$$

\(C_F\) (Bozdogan, 2010) is

$$C_F(F^{-1}) = 1/s*sum_i^s(lambda_i - lambda_a)$$

\(C_1F\) (Bozdogan, 2010) is

$$C_1F(F^{-1}) = 1/(4lambda_a^2)*sum_i^s(lambda_i - lambda_a)$$

\(C_1R\) (Bozdogan, 2000) is

$$C_1R(F^{-1}) = 1/2*log(|R|)$$

Here, \(R\) is the correlation matrix of the model, \(lambda_1, ..., lambda_s\) are eigenvalues of \(F\), \(lambda_a\) and \(lambda_g\) are arithmetic and geometric mean of eigenvalues of \(F\), respectively. \(s\) is the dimension of \(F\). While calculating the Fisher information matrix (\(F\)), we used the joint parameters (\(beta,sigma^2\)) of the models. In \(C1R(.)\) function, we utilized the usual variance-covariance matrix \(Cov(beta)\) of the models. beta is the vector of regression coefficients.

References

Bozdogan, H. (2003). Intelligent Statistical Data Mining with Information Complexity and Genetic Algorithms Hamparsum Bozdogan University of Tennessee, Knoxville, USA. In Statistical data mining and knowledge discovery (pp. 47-88). Chapman and Hall/CRC.

Koc, E. K., & Bozdogan, H. (2015). Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function. Machine Learning, 101(1), 35-58.

Bozdogan, H. (2010). A new class of information complexity (ICOMP) criteria with an application to customer profiling and segmentation. <U+0130>stanbul <U+00DC>niversitesi <U+0130><U+015F>letme Fak<U+00FC>ltesi Dergisi, 39(2), 370-398.

Pamuk<U+00E7>u, E., Bozdogan, H., & <U+00C7>al<U+0131>k, S. (2015). A novel hybrid dimension reduction technique for undersized high dimensional gene expression data sets using information complexity criterion for cancer classification. Computational and mathematical methods in medicine, 2015.

Bozdogan, H. (2000). Akaike's information criterion and recent developments in information complexity. Journal of mathematical psychology, 44(1), 62-91.

Examples

# NOT RUN {
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")

ICOMP_IFIM_CF(m1)
ICOMP_IFIM_CF(m2)
ICOMP_IFIM_CF(m3)
CICOMP_C1(m1)
CICOMP_C1(m2)
CICOMP_C1(m3)
ICOMP(m1, type = "PEU", C = "C1R")


# }