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

[Jarrod Hadfield]

Hi,

Create a binary vector (lets call it b) with 0 for observations where  
you don't want random effects and a 1 where you do. Then fit:

(b|group)

Cheers,

Jarrod



Quoting Mitchell Maltenfort <mmalten at gmail.com> on Thu, 15 Jan 2015  
13:34:04 -0500:

> 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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>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
>
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