[R-sig-ME] Specifying random effects for multiple covariates via lmer

Douglas Bates bates at stat.wisc.edu
Thu Sep 6 04:22:00 CEST 2007

On 9/5/07, Andy Bush <ajbush at bellsouth.net> wrote:
> While working through the text "Applied Longitudinal Analysis" by
> Fitzmaurice, Laird and Ware, I encountered a fairly simple case study (pp
> 210-7) in which a longitudinal model specifies three random effects: (1)
> random intercepts for id, (2) random slopes for covariate1 (Age | id), and
> (3) random slopes for covariate2 (log(ht) | id).  I've had no difficulty
> formulating lmer models with correlated random intercepts and slopes for
> either of the covariates individually but have not succeeded when I try to
> compose a model with correlated random intercepts and slopes for two
> covariates.

> Following is code that works well with the individual covariates separately:

> m1=lmer(LFEV1~Age + loght + InitAge + logbht + (1 + Age | id),data=fev,
>        na.action=na.omit, method="REML")

> m2=lmer(LFEV1~Age + loght + InitAge + logbht+(1 + loght | id),data=fev,
>        na.action=na.omit, method="REML")

Maybe I am missing the point but wouldn't the model you are
considering be written as

lmer(LFEV1 ~ Age + loght + InitAge + logbht + (loght + Age|id), data =
fev, na.action = na.omit, method = "REML")

That provides correlated random effects for the intercept, the
coefficient for loght and the coefficient for Age at each level of the
id factor.

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