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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