[R-sig-ME] Modelling random effects for only part of the observations (in lme4)

Mitchell Maltenfort mmalten at gmail.com
Thu Jan 15 19:34:04 CET 2015

What about nested random effects...where you only have one group within no
treatment, and multiple groups within treatment?  Or would R crash?

On Thursday, January 15, 2015, Hufthammer, Karl Ove <
karl.ove.hufthammer at helse-bergen.no> wrote:

> Dear list members,
> I have a seemingly easy problem, though it turned out to be more difficult
> in practice. Basically, I'm wondering if it is possible in lme4 to model
> random effects for only *some* of the observations?
> Here's my problem (somewhat simplified). Individuals are randomised to
> either treatment or no treatment. The treatment consists of group therapy,
> where the individuals are (randomly) assigned to groups. It is reasonable
> to expect some sort of group/cluster effect - e.g. a therapist effect
> and/or a within-group interaction effect for the individuals - and this
> effect can be modelled as a random effect. So far so good.
> However, for the individuals randomised to no treatment, there are no
> groups, and thus no group effects. So basically (I think!) I can use the
> linear model (in mathematical notation)
>   y_ij = intercept + b*x_ij + eps_ij
> for the untreated individuals, and
>   y_ij = intercept + b*x_ij + treatment + B_i + eps_ij
> for the treated indivduals, where i are group indices, j are indices for
> the individuals, x_ij is some (baseline) covariate(s) and B_i are the
> random effects. (i is of course not really defined for the control
> individuals, so you can assume that all j indices are different for
> different individuals, and replace ij with j and i with i(j), if that makes
> the syntax easier to understand.)
> Or, in lme4/lm syntax:
>   y ~ x + treat_factor + (1|group) # Treated individuals
>   y ~ x + treat_factor             # Untreated individuals
> where treat_factor is a two-level factor (control/treatment).
> The two *mathematical* linear predictor formulas are easy to combine into
> one:
>   y_ij = intercept + b*x_ij + arm_ij*treatment + arm_ij*B_i + eps_ij
> where arm_ij (indicating treatment/control arm) is 1 if the individual
> (i,j) was randomised to the treatment arm and 0 if he/she was randomised to
> the control arm.
> But how do I write this in lme4 syntax?
> I have thought about letting each individual in the control arm being its
> own cluster/group. But this doesn't seem realistic. Why would the variance
> between groups (in the treatment arm) be similar to the variance between
> individuals in control arm? It doesn't seem like a realistic model, and I
> believe it would bias the estimated treatment effect.
> Is it even possible to fit these types of models? Or are there other R
> packages that can be used instead? (Note that for my actual data set I have
> a logistic, not a linear, model, but I doubt this makes things *easier* .)
> Any help would be appreciated.
> --
> Karl Ove Hufthammer
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