random slope for categorical predictor

[szm...@stanford.edu]

Hello!

I was wondering if it is possible model random slope for categorical predictor in INLA. In lme4 syntax, it will be

lme.res <- lmer(BETA ~ 1 + POPULATION + (0 + POPULATION|VARID), data=data)

where VARID and POPULATION are both factors. I tried

inla.res <- inla(BETA ~ 1 + POPULATION + f(VARID, POPULATION, model='iid'),

                 control.compute=list(config = TRUE), data=data)

It runs, but gave a warning message:

Warning message in `[<-.factor`(`*tmp*`, is.na(www), value = 0):

“invalid factor level, NA generated”

[Helpdesk]

population has to be numeric in f(varid, population), as this term is
like

u[i] * population[i]


where u is a random effect indexed by varid

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[Thierry Onkelinx]

You'll need one of the "iidnd" models to fit this if you want to
replicate the (0 + POPULATION|VARID) model from lme4. The lme4 model
also fits the correlation among the random slopes. See
https://www.math.ntnu.no/inla/r-inla.org/doc/latent/iid123d.pdf

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry....@inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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[Mamie Wang]

Thanks, Thierry! POPULATION has four levels and I made them dummy variables using model.matrix. And here is the updated model using iid4d: 

nod2.data$VARID.int <- as.numeric(as.factor(nod2.data$VARID))

population <- model.matrix(~0+POPULATION, data=nod2.data)

nod2.data <- cbind(nod2.data, population)

n.loc <- max(nod2.data$VARID.int)

nod2.data$VARID2.int <- nod2.data$VARID.int + n.loc

nod2.data$VARID3.int <- nod2.data$VARID.int + 2 * n.loc

nod2.data$VARID4.int <- nod2.data$VARID.int + 3 * n.loc

inla.res <- inla(BETA ~ 1 + POPULATION + f(VARID.int, POPULATIONaj, model='iid4d', n=n.loc * 4) +

                                          f(VARID2.int, POPULATIONfc, copy='VARID.int') +

                                          f(VARID3.int, POPULATIONfin, copy='VARID.int') +

                                          f(VARID4.int, POPULATIONnfe, copy='VARID.int'),

                 control.compute=list(config = TRUE), 

                 data=nod2.data)

The estimates for fixed effect and the variance for the random effects are quite similar between lme4 and INLA, but the INLA estimate for the correlation seems to be more conservative compared with the lme4 as shown in the image attached below. I also compared the same model in brms which uses rstan as backend and same syntax for formula interface to fit multilevel models, which also gives lower estimate. I was wondering why is the likelihood method gives higher correlation estimate compared to the Bayesian methods?

In addition, I was wondering if it is possible to implement LKJ prior for the correlation matrix between random effects in INLA as in Stan? 

Mamie

Mamie Wang

Biomedical Informatics MS Candidate, 2018

Stanford University, School of Medicine

E-mail | szm...@stanford.edu

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