aic {IPEC}

Akaike Information Criterion (AIC) Calculation Function

Description

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

Usage

aic( object, ... )

Arguments

object

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

...

Optionally more fitted model objects

Details

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

Value

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

Note

When there are sample.size and n in object at the same time, the default of the sample size is sample.size, which is superior to n. With the sample size increasing, the number of model parameter(s) has a weaker influence on the value of AIC assuming that ln(RSS/n) is a constant.

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. doi:10.1186/1471-2210-10-6

See Also

bic, 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)

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