bic: Bayesian Information Criterion (BIC) Calculation Function

In IPEC: Root Mean Square Curvature Calculation

Bayesian Information Criterion (BIC) Calculation Function

Description

Calculates the BIC value(s) of the object(s) obtained from using the fitIPEC function.

Usage

bic( object, ... )

Arguments

object	A fitted model object for which there exists the sample size (n), estimate(s) of model parameter(s) (par), and residual sum of squares (RSS)
...	Optionally more fitted model objects

Details

BIC = p ln(n) - 2 ln(L), where p represents the number of model parameter(s) plus 1 for the error, n represents the sample size, and ln(L) represents the maximum log-likelihood of the estimated model (Spiess and Neumeyer, 2010).

Value

There is a BIC value corresponding to one object, and there is a vector of BIC values corresponding to the multiple objects.

Note

The BIC gives a higher penalty on the number of model parameters than the AIC.

Author(s)

Peijian Shi [e-mail], Peter M. Ridland [e-mail], David A. Ratkowsky [e-mail], Yang Li [e-mail].

References

Spiess, A-N and Neumeyer, N. (2010) An evaluation of R squared as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach. BMC Pharmacol. 10, 6. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1186/1471-2210-10-6")}

See Also

aic, AIC in package stats, and BIC in package stats

Examples

#### Example #####################################################################################
data(leaves)
attach(leaves)
# Choose a geographical population (see Table S1 in Wang et al. [2018] for details)
# Wang, P., Ratkowsky, D.A., Xiao, X., Yu, X., Su, J., Zhang, L. and Shi, P. 
#   (2018) Taylor's power law for leaf bilateral symmetry. Forests 9, 500. doi: 10.3390/f9080500
# 1: AJ; 2: HN; 3: HW; 4: HZ; 5: JD; 
# 6: JS; 7: SC; 8: TC; 9: TT; 10: TX
ind <- 1
L   <- Length[PopuCode == ind]
W   <- Width[PopuCode == ind] 
A   <- Area[PopuCode == ind]

# Define a model y = a*(x1*x2), where a is a parameter to be estimated
propor <- function(theta, x){
    a  <- theta[1]
    x1 <- x[,1]
    x2 <- x[,2]
    a*x1*x2
}

# Define a model y = a*(x1^b)*(x2^c), where a, b and c are parameters to be estimated    
threepar <- function(theta, x){
    a  <- theta[1]
    b  <- theta[2]
    c  <- theta[3]
    x1 <- x[,1]
    x2 <- x[,2]
    a*x1^b*x2^c
}

# Define a model y = a*x^b, where a and b are parameters to be estimated    
twopar <- function(theta, x){
    a  <- theta[1]
    b  <- theta[2]
    a*x^b
}


  A1 <- fitIPEC(propor, x=cbind(L, W), y=A, fig.opt=FALSE,
            ini.val=list(seq(0.1, 1.5, by=0.1)))
  B1 <- curvIPEC(propor, theta=A1$par, x=cbind(L, W), y=A)    
  A2 <- fitIPEC(threepar, x=cbind(L, W), y=A, fig.opt=FALSE,
            ini.val=list(A1$par, seq(0.5, 1.5, by=0.1), seq(0.5, 1.5, by=0.1)))    
  B2 <- curvIPEC(threepar, theta=A2$par, x=cbind(L, W), y=A)
  A3 <- fitIPEC(twopar, x=L, y=A, fig.opt=FALSE,
                ini.val=list(1, seq(0.5, 1.5, by=0.05)))    
  B3 <- curvIPEC(twopar, theta=A3$par, x=L, y=A)
  A4 <- fitIPEC(twopar, x=W, y=A, fig.opt=FALSE,
                ini.val=list(1, seq(0.5, 1.5, by=0.05)))    
  B4 <- curvIPEC(twopar, theta=A4$par, x=W, y=A)
  aic(A1, A2, A3, A4)
  bic(A1, A2, A3, A4)

##################################################################################################

IPEC documentation built on Nov. 2, 2023, 6:14 p.m.