stan_gamm4: bug with polynomial parameter

[DominiqueMakowski]

rstanarm appears to fail when entering a polynomial parameter:

This works

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + s(Petal.Width), random=~(1|Species), data=iris)

This doesn't

rstanarm::stan_gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

Error in poly(Sepal.Length, 2) : object 'Sepal.Length' not found

Note that the same using gamm4 works:

gamm4::gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

Is there a way to fix it?

[bgoodri]

We'll look into it, but

Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random = ~(1 | Species), data = iris)

should at least get it going.

On Tue, Jul 24, 2018 at 6:48 AM Dominique Makowski [email protected] wrote:

rstanarm appears to fail when entering a polynomial parameter: This works

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + s(Petal.Width), random=~(1|Species), data=iris)

This doesn't

rstanarm::stan_gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

Error in poly(Sepal.Length, 2) : object 'Sepal.Length' not found

Note that the same using gamm4 works:

gamm4::gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

Is there a way to fix it?

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[DominiqueMakowski]

@bgoodri Thanks, the workaround works (although I am wondering if it's possible to set orthogonal polynomials this way).

[bgoodri]

With QR = TRUE

On Mon, Oct 8, 2018 at 1:16 PM Dominique Makowski [email protected] wrote:

@bgoodri https://github.com/bgoodri Thanks, the workaround works (although I am wondering if it's possible to set orthogonal polynomials this way).

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[DominiqueMakowski]

It seems that setting QR to TRUE does not change raw polynomials to orthogonal polynomials:

GAMM4 - Orthogonal

gamm4::gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 3.26 and -1.2.

GAMM4 - Raw

gamm4::gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 1.8 and -0.1.

rstanarm - QR FALSE

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 1.7 and -0.1.

rstanarm - QR TRUE

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris, QR=TRUE)

The fixed coefs are roughly the same as just above.

[bgoodri]

The parameters are estimated under an orthogonal rotation (the Q matrix from the X=QR decomposition) and then after the initial posterior distribution has been obtained the coefficients are re-rotated back to the original coordinates so that they pertain to the columns of X. So, you get the efficiency benefits of orthogonalization without changing the interpretation of the output.

On Tue, Oct 9, 2018 at 3:42 AM Dominique Makowski [email protected] wrote:

It seems that setting QR to TRUE does not change raw polynomials to orthogonal polynomials: GAMM4 - Orthogonal

gamm4::gamm4(Sepal.Width ~ poly(Sepal.Length, 2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 3.26 and -1.2. GAMM4 - Raw

gamm4::gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 1.8 and -0.1. rstanarm - QR FALSE

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris)

The fixed coefs are roughly 1.7 and -0.1. rstanarm - QR TRUE

rstanarm::stan_gamm4(Sepal.Width ~ Sepal.Length + I(Sepal.Length^2) + s(Petal.Width), random=~(1|Species), data=iris, QR=TRUE)

The fixed coefs are roughly the same as just above.

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[DominiqueMakowski]

Thanks for the clarification! (Although in my case I needed the interpretation of orthogonal polynomials ☺️, but I managed to compute them beforehand and feed them directly in the model.)