Solved – Mixed model (Multilevel) with two INDEPENDENT Random Effects [lmer]

mixed modelmultilevel-analysisrandom-effects-model

I like to estimate a mixed model with two Random Effects, that are independent of each other and among themselves.

I use Panel data with a nested structure (counties $j$ nested within regions $i$). The error component should decompose in the following way:

$$E_{ijt} = \alpha_i + \mu_{ij} + e_{ijt}$$

$\alpha_i$ is an unobservable region specific time-invariant effect (normal distributed)

$\mu_{ij}$ is a nested effect of county $j$ within region $i$ (normal distributed)

$e_{ijt}$ is a remainder disturbance (normal distributed)

I read somewhere that "lmer" is capable to fit such specifications with idenpendent Random Effects.

lmer(y~.... + (1|region) + (1|county)

Is the lmer-model adequate for my task?

Yes, lme4 should be fine in here. The formula you are asking is:

y ~ 1 + (1|region) + (1|region:county)

because in model you described country is nested in region.

For an extended description and examples see here, here or here.

Even if the model is quite complicated, interpretation of the effect of A on the response variable is straightforward, as is any other linear model: according to your output, all other things being equal, a variation of magnitude $x$ in your independent variable A is associated with a variation of $ e^{ x * 0.008585}$ of your response variable. However, standard error is not at play when making prediction from your fitted model. It gives you informations about the accuracy of your coefficient estimate and allows you to compute a confidence interval around your estimate, but cannot be referred as a "more or less modifier" of the prediction.
Regarding the interpretation of the intercept, it's a bit more complicated to translate it clearly, because it's related to the Region random effect. Here you have a random effect on the intercept, hence its value depends on the value of the categorical Region variable. The value -1.112047 showed in your output is the intercept value for the base value of the Region variable (i.e. Region category encoded as 0). In any case, there is no need for the intercept to be equal to the mean of the reponse variable, intercept is simply the expected value of your response variable when all other dependent variables are equal to zero.

Try rescaling your predictor variable FilingFee, e.g.,

lmerfit <- lmer(evictionfilingrate ~ I(FilingFee/10) + 
                  (1 + I(FilingFee/10) | state), data = d)

and also using nlme::lme(), i.e.,

 lmefit <- lme(evictionfilingrate ~ FilingFee, data = d,
               random = ~ FilingFee | state)

 lmefit <- lme(evictionfilingrate ~ I(FilingFee/10), data = d,
               random = ~ I(FilingFee/10) | state)

And also possibly changing the optimization algorithm to optim in lme(); see lmeControl() for more info.