Correct specification of random coefficients in lme4

by Mainard   Last Updated September 13, 2017 14:19 PM

Can anyone help me understand the difference in the following two model parameterizations please?

I have a repeated measures from clusters, over several years, and I expect the cluster effect to vary each year. Year is coded as a factor, with '1' as reference level. I have tried the following:

mod1<-lmer(y ~ x + year + (year|cluster))

and

mod2<-lmer(y ~x + year + (1|cluster:year))

My first example specifies the following random effects:

ranef(mod1)
$cluster
    (Intercept)  year2         year3        year4         year5
AA   0.03721015  0.0573160920 -0.114709171  0.1588302187  0.125329740
AB  -0.12958994 -0.0458997003  0.216455596  0.2345170893  0.248950509
AC  -5.10692972 -0.1311546328  1.130347798  2.5215580167  5.070106525
AD   0.10087455 -0.2677088515 -0.345583355 -0.2442831982 -0.257074662
....

Second one specifies:

ranef(mod2)
$`cluster:year`
              (Intercept)
AA:year2  0.0838186244
AA:year3 -0.1197284361
AA:year4  0.1944488619
AA:year5  0.1562090690

I assumed they would be equivalent, given year is a factor, but I must not understand the random effect specification of lme4 well enough. Any suggestions would be appreciated



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