[R-sig-ME] Random effects estimation in Lmer

Hester Lingsma h.lingsma at erasmusmc.nl
Tue Dec 15 09:09:20 CET 2009

Dear R-users,
>> I have a question on how the random effects are estimated in Lmer

>> I have a dataset with families with women who have breastcancer. The age
>> of cancer diagnosis is highly variable between the families. We want to
>> predict the age of cancer diagnosis (for screening purposes) for 'new'
>> family members. I have fitted a linear random effects model with lmer (model
>> 1)  with age at diagnosis as outcome, a random intercept for family, and
>> cancer type (three subtypes, on family level) in the fixed part.
>> I now want to make a regression formula (for a predction rule) which is of
>> course easy for the fixed part of the model (intercept + coefs for type) but
>> more difficult for the random effect part.
>> My practical solution was the following: I fitted a new model (model 2) on
>> the familiy level aggregated dataset with the estimated random effect as an
>> outcome, and number of fam members and the distance between the expected age
>> for the family based on type (the fixed part of model) and the observed mean
>> age, as predictors.
>> Model 2 has an R2 of 0.85 and the predicted ages (fixed part + the random
>> part as 'estimated' in model 2) for some families are 4 years away from the
>> posterior estimate (from model 1). So we want to do better. I tried some
>> polynomials in model 2, since we do not expect the effect of the parameters
>> to be linear, but it did not help a lot. I also included the within family
>> variance (the sd) in model 2 since I noticed that the predicted ages got
>> worse in families with high within family variance, also without much
>> succes.
>> So basically my question is: is there a (better) way to approximate the
>> random effects estimated in model 1, to formulate a 'random' part of the
>> regression formula/a predction rule?
>> Thank you very much in advance.
>> Hester Lingsma

Hester F. Lingsma, MSc
Dept of Public Health
Room AE-141
Erasmus MC
P.O. Box 2040
3000 CA Rotterdam
The Netherlands
Phone: (+31) (0)10 7038458/7038460
Mobile: (+31) (0)6 26467338

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