1d:T7d6,# Prediction Band Calculate a prediction band for a fitted growth curve. ```r pred_band(age, model, level = 0.95) ``` ## Arguments - `age`: a vector of ages to calculate the prediction band. - `model`: a fitted growth model. - `level`: significance level. ## Returns A data frame containing five columns: - **age**: age - **Lhat**: predicted length - **sigma**: growth variability - **lower**: lower limit of prediction band - **upper**: upper limit of prediction band ## Note The variability of length at age (`sigma`) increases linearly with length: $$ \sigma_L ~=~ \alpha \,+\, \beta \hat Lsigma_L = alpha + beta * Lhat $$ This calculation of `sigma` is demonstrated in the example below. The `lower` and `upper` limits of the prediction band are calculated as $Lhat +/- 1.96 * sigma_L$ at the 95% significance level. ## Examples ```r # Fit a model init <- list(log_L1=log(20), log_L2=log(70), log_k=log(0.1), log_sigma_min=log(3), log_sigma_max=log(3)) dat <- list(Aoto=otoliths_had$age, Loto=otoliths_had$len, t1=1, t2=10) model <- vonbert(init, dat) fit <- nlminb(model$par, model$fn, model$gr, control=list(eval.max=1e4, iter.max=1e4)) # Calculate 95% prediction band x <- seq(1, 18, 0.5) band <- pred_band(x, model) # Plot 95% prediction band areaplot::confplot(cbind(lower,upper)~age, band, xlim=c(0,18), ylim=c(0,100), ylab="len", col="mistyrose") points(len~age, otoliths_had, pch=16, col="#0080a010") lines(Lhat~age, band, lwd=2, col=2) lines(lower~age, band, lty=1, lwd=0.5, col=2) lines(upper~age, band, lty=1, lwd=0.5, col=2) # Calculate sigma by hand report <- model$report() alpha <- report$sigma_intercept beta <- report$sigma_slope Lhat <- band$Lhat alpha + beta * Lhat # same values as band$sigma calculated by pred_band() ``` ## See Also `gcm`, `gompertz`, `gompertzo`, `richards`, `richardso`, `schnute3`, `vonbert`, and `vonberto` are alternative growth models. `fishgrowth-package` gives an overview of the package.

pred_band function