Computation of the AIC and Mallows's \(Cp\) criteria for univariate PLSR models (Lesnoff et al. 2021). This function may receive modifications in the future (work in progress).
aicplsr(
X, y, nlv, algo = NULL,
meth = c("cg", "div", "cov"),
correct = TRUE, B = 50,
print = FALSE, ...)
dataframe with \(n\), and the etimated criteria (\(df\), \(ct\), \(ssr\), \(aic\), \(cp1, cp2\)) for 0 to \(nlv\) latent variables in the model.
dataframe with the differences between the estimated values of \(aic\), \(cp1\) and \(cp2\), and those of the model with the lowest estimated values of \(aic\), \(cp1\) and \(cp2\), for models with 0 to \(nlv\) latent variables
vector with the optimal number of latent variables in the model (i.e. minimizing aic, cp1 and cp2 values)
A \(n x p\) matrix or data frame of training observations.
A vector of length \(n\) of training responses.
The maximal number of latent variables (LVs) to consider in the model.
a PLS algorithm. Default to NULL (plskern is used).
Method used for estimating \(df\). Possible values are "cg" (dfplsr_cg), "cov" (dfplsr_cov)or "div" (dfplsr_div).
Logical. If TRUE (default), the AICc corection is applied to the criteria.
For meth = "div": the number of observations in the data receiving perturbation (maximum is \(n\); see dfplsr_cov). For meth = "cov": the number of bootstrap replications (see dfplsr_cov).
Logical. If TRUE, fitting information are printed.
Optionnal arguments to pass in algo.
For a model with \(a\) latent variables (LVs), function aicplsr calculates \(AIC\) and \(Cp\) by:
\(AIC(a) = n * log(SSR(a)) + 2 * (df(a) + 1)\)
\(Cp(a) = SSR(a) / n + 2 * df(a) * s2 / n\)
where \(SSR\) is the sum of squared residuals for the current evaluated model, \(df(a)\) the estimated PLSR model complexity (i.e. nb. model's degrees of freedom), \(s2\) an estimate of the irreductible error variance (computed from a low biased model) and \(n\) the number of training observations.
By default (argument correct), the small sample size correction (so-called AICc) is applied to AIC and Cp for deucing the bias.
The functions returns two estimates of Cp (\(cp1\) and \(cp2\)), each corresponding to a different estimate of \(s2\).
The model complexity \(df\) can be computed from three methods (argument meth).
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Lesnoff, M., Roger, J.M., Rutledge, D.N., Submitted. Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data. Journal of Chemometrics.
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data(cassav)
Xtrain <- cassav$Xtrain
ytrain <- cassav$ytrain
nlv <- 25
res <- aicplsr(Xtrain, ytrain, nlv = nlv)
names(res)
headm(res$crit)
z <- res$crit
oldpar <- par(mfrow = c(1, 1))
par(mfrow = c(1, 4))
plot(z$df[-1])
plot(z$aic[-1], type = "b", main = "AIC")
plot(z$cp1[-1], type = "b", main = "Cp1")
plot(z$cp2[-1], type = "b", main = "Cp2")
par(oldpar)
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