Multicollinearity test before fitting the INLA model

[Babu Lawrence]

Hi all,

Is it recommended to perform a multicollinearity test to filter out variables with high VIF values before fitting the INLA model?

Many thanks and best wishes,

Lawrence

[Helpdesk (Haavard Rue)]

In general, this is not needed, as the prior will regularize this automatically.

however, with multicollinearity, there is an issue about the interpretation of
marginal distributions, since the uncertainty will be inflated.

here is an example

> n=100
> x=rnorm(n)
> xx = x + rnorm(n, sd=0.01)
> y = x + xx + rnorm(n, sd=0.1)

if you do not do anything, the 'sd' for 'x' and 'xx' is high due to co-lin

> r=inla(y ~ x + xx, data=data.frame(x,xx,y),
control.fixed=list(correlation.matrix=TRUE))
> r$misc$lincomb.derived.correlation.matrix
> r$summary.fixed[, c("mean", "sd")]
mean sd
(Intercept) -0.002613851231 0.01046462064
x -1.048997163900 1.01893598347
xx 3.033589783438 1.01915485993


if we simply skip 'xx' then its all good

> rr=inla(y ~ x, data=data.frame(x,xx,y),
control.fixed=list(correlation.matrix=TRUE))
> rr$misc$lincomb.derived.correlation.matrix
(Intercept) x
(Intercept) 1.0000000000 -0.1397949111
x -0.1397949111 1.0000000000
> rr$summary.fixed[, c("mean", "sd")]
mean sd
(Intercept) -0.004610456321 0.01084912133
x 1.983788524350 0.01061801634

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--
Håvard Rue
he...@r-inla.org

[Helpdesk (Haavard Rue)]

to add here, with co-lin, we can interpret

beta.x * x + beta.xx * xx

but not each term individually

so, in practice you may want to do something about it

--
Håvard Rue
he...@r-inla.org