# Akaike Information Criterion (AIC) Calculation Function Calculates the AIC value(s) of the object(s) obtained from using the `fitIPEC` function. ```r 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). ## Returns There is an AIC value corresponding to one object, and there is a vector of AIC values corresponding to the multiple objects. ## 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. tools:::Rd_expr_doi("10.1186/1471-2210-10-6") ## Author(s) Peijian Shi pjshi@njfu.edu.cn , Peter M. Ridland p.ridland@unimelb.edu.au , David A. Ratkowsky d.ratkowsky@utas.edu.au , Yang Li yangli@fau.edu . ## 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. ## See Also `bic`, `AIC` in package `stats`, and `BIC` in package `stats` ## Examples ```r #### 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) ################################################################################################## ```

aic function