Solved – How to fit data with nonlinear partial least squares in R

partial least squaresr

I am looking for a way to do nonlinear partial least squares in R or matlab. I thought kernel pls was a way to do it but it is not directly related to nonlinear pls. Do I have to calculate my own nonlinear kernel matrix and pass it to kernel pls? Any hint would be appreciated.

Update: I don't think there is any direct way to do nonlinear pls in R or matlab. But I found a package kernlab that can be useful when you deal with kernels for nonlinearity. I think this can be a good start point.

Best Answer

Have you checked the package pls.pcr from the CRAN?

Here is a link to the help page.

The mvr function has an option method="kernelPLS" that seem fairly easy to use.

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Solved – Calculate log-likelihood “by hand” for generalized nonlinear least squares regression (nlme)

Let's start with the simpler case where there is no correlation structure for the residuals:

fit <- gnls(model=model,data=data,start=start)
logLik(fit)

The log likelihood can then be easily computed by hand with:

N <- fit$dims$N
p <- fit$dims$p
sigma <- fit$sigma * sqrt((N-p)/N)
sum(dnorm(y, mean=fitted(fit), sd=sigma, log=TRUE))

Since the residuals are independent, we can just use dnorm(..., log=TRUE) to get the individual log likelihood terms (and then sum them up). Alternatively, we could use:

sum(dnorm(resid(fit), mean=0, sd=sigma, log=TRUE))

Note that fit$sigma is not the "less biased estimate of $\sigma^2$" -- so we need to make the correction manually first.

Now for the more complicated case where the residuals are correlated:

fit <- gnls(model=model,data=data,start=start,correlation=correlation)
logLik(fit)

Here, we need to use the multivariate normal distribution. I am sure there is a function for this somewhere, but let's just do this by hand:

N <- fit$dims$N
p <- fit$dims$p
yhat <- cbind(fitted(fit))
R <- vcv(tree, cor=TRUE)
sigma <- fit$sigma * sqrt((N-p)/N)
S <- diag(sigma, nrow=nrow(R)) %*% R %*% diag(sigma, nrow=nrow(R))
-1/2 * log(det(S)) - 1/2 * t(y - yhat) %*% solve(S) %*% (y - yhat) - N/2 * log(2*pi)

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Solved – Calculate log-likelihood “by hand” for generalized nonlinear least squares regression (nlme)

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