Monotonically increasing RW2

[John Molitor]

Hello,

Suppose I fit a model (using simplified notation):

ER ~ 1 + f(heat,model="rw2")

However, I want the "dose-response" relationship between heat and ER to be monotonically increasing, so if heat increases, the ER value will either stay the same or increase, but not decrease.

Is this possible?

Thanks,

John

[John Molitor]

To to follow up on my own post, what I'm really after is a model with a monotonic relationship between heat and ER (as heat goes up ER goes up), but I want the effect of heat to vary by zipcode (zip) with some besag-like spatial smoothing on "intercepts" and "slopes" (effects), similar in spirit to Spatially Varying Coefficient (SVC) models but with a "spline" (RW2) relationship between heat and ER.

[Håvard Rue]

there is no way of doing exactly this. the the case you need this, you need to
write something spesific (using 'rgeneric' or 'cgeneric')

essentially, you need to put the coefficients into the hyperparameters and do
the spline, similar to the 'linear regression' example in 'rgeneric'

Best
Havard

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[John Molitor]

Suppose I fit a polynomial model, something like:

ER ~ 1 + f(zip0,model="bym2") + heat + f(zip,heat,model="besag") + heat^2 + f(zip2, heat^2,model="besag")

Can I induce a monotonic relationship with this simpler approach?

John

[Helpdesk (Haavard Rue)]

If this how you want to use it, then yes.

its important to have

heat + f(zip, heat, ...)

as the besag has default sum-to-zero constraints.

also, you need to make sure 'heat' is centered at zero.

you can also expand it using a increasing function of 'heat', and go along this
line

he...@r-inla.org

[Helpdesk (Haavard Rue)]

there is no guarentee that you'll get something increasing though...

you can define something spline-like that is ok, but when you wrap it in the
'besag' framework, then no