Random intercept and slope model with lmer

[I am taking the liberty of forwarding back to r-sig-mixed-models ...
you may feel this is 'too basic', but (as I always tell my classes)
there are probably quite a few people lurking on the list who wouldn't
mind knowing the answers -- or at least knowing my answers (which may
not be "the" answers.]

  The standard deviations of the random effects are interpretable on the
same scale as the corresponding fixed effects, and hence directly
comparable.  For example, your intercept is approx. 43 (in whatever
units); the standard deviation of the variation in intercepts among
localities (?) is 47; and the standard deviation of the residual
variation among observations is 21.  Hence, while the average value at
time=0 is strongly different from zero (t-score approx. 7), this
difference from zero is quite a bit smaller than the variation among
individual observations (think about +/- 2 std. dev.), which is in turn
smaller than the variation among localities.  The other random effect
(time|localidad) describes the variation in slope among localities (a
similar comparison to that above applies to the strongly negative
average slope with great variation in slopes among localities).

  However, there is also something a bit funny with your model, because
the correlation between the random effects is listed as being -1: the
random variation in slopes and intercepts is perfectly (negatively)
correlated.  Possibly your experimental/observational design is
insufficient (you only have an average of about 4 observations per
group); it might also help to center your time variable at the midpoint
time.

  I also think that looking at Ch. 4 of Bates's book draft
<http://lme4.r-forge.r-project.org/book/Ch4.pdf>, or at the equivalent
examples (Orthodont etc.) in PB2000, would be helpful.

 cheers
   Ben

Dear Ben,

Sorry to bother you with this again, but what do you look for at the 
output of a mixed model in R?  I know what to do with the fixed effect, 
but what about the random effects?:

 > modelo7 = lmer(ipa ~ time + (time | localidad), data=ipa)
 > summary(modelo7)

Linear mixed model fit by REML
Formula: ipa ~ time + (time | localidad)
   Data: ipa
  AIC  BIC logLik deviance REMLdev
 1917 1937 -952.4     1913    1905
Random effects:
 Groups    Name        Variance Std.Dev. Corr  
 localidad (Intercept) 2232.31  47.247         
           time         545.97  23.366   -1.000
 Residual               450.92  21.235         
Number of obs: 196, groups: localidad, 49

Fixed effects:
            Estimate Std. Error t value
(Intercept)   42.852      6.918   6.194
time         -19.746      3.603  -5.480

Correlation of Fixed Effects:
     (Intr)
time -0.904

Thank you very much in advance.
Best,

Manuel


Ben Bolker wrote:

Manuel Sp?nola wrote:
  

Dear Ben,

I am trying to fit a random intercept and slope model with lme4 using 
function lmer.
Is my formulation correct?

 > names(ipa)

[1] "localidad" "time"    "ipa"

 > modelo7 = lmer(ipa ~ time + (time | localidad), data=ipa)

Thank you very much in advance.
Best,

Manuel

    

  That looks reasonable.
  See

http://lme4.r-forge.r-project.org/book/

 especially chapter 4.

(Why not send these questions to r-sig-mixed-models at r-project.org ?)

  

Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc