[R-sig-ME] Why lme4 doesn't throw an error for illegitimate an model

[Simon Harmel]

Thank you Phillip. The data structure is exactly the way you understood it.
Another nonsensical model without warning would be m2. Where `ses` is a
predictor that varies both within and across `sch.id` (clusters), and
`sector` is a binary variable that only varies across the `sch.id`
(clusters).

The cross-level interaction is set by the software syntax to AGAIN vary
across the levels of a grouping variable. But the model runs without
warning.

hsb <- read.csv('
https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')
m2 <- lmer(math ~ ses+sector + (ses:sector | sch.id), data = hsb)

On Wed, Oct 7, 2020 at 3:58 PM Phillip Alday <phillip.alday using mpi.nl> wrote:

> Without knowing the structure of the data, it's hard to answer the
> question ... there are ways for me explore and find out what the
> nesting/grouping structure is, but that takes time I don't have. So
> here's a quick attempt just using general principles.
>
> I think the first trick is to stop thinking of thinking as an ith-level
> predictor. For one thing, the levels don't have to be strictly nested.
> Personally, I find the i-th level terminology confusing because I can
> never remember which direction we're counting from.
>
> Dropping the lm/ler calls for convenience in typing:
>
> math ~ 1 + ses
>
> this estimates a model with a slope for ses and an intercept.
>
> math ~ 1 + ses + (1|sch.id)
>
> this estimates a model with a slope for ses and an intercept and an
> offset for each sch.id. (The estimated offsets are technically
> "predictions", because the variance of the offsets is what's being
> estimated, but we'll leave that be for now.)
>
> An offset to what? Well the population-level/fixed effect corresponding
> to the intercept. So you can think of this random effect as providing an
> adjustment to the intercept for each sch.id
>
>
> math ~ 1 + ses + (1+ses|sch.id)
>
> this estimates a model with a slope for ses and an intercept; as well as
> per-sch.id adjustments for the intercept and ses.
>
> Note by the way that the model
>
> math ~ 1
>
> is a special case of
>
> math ~ 1 + ses
>
> with the slope of ses set / assumed to be zero.
>
> This will help in the next step.
>
> math ~ 1 + (1+ses|sch.id)
>
> this estimates a model with a slope an intercept; as well as per-sch.id
> adjustments for the intercept and ses. But where is ses in the fixed
> effects? Well, you can think of it as being zero (see previous point),
> so the adjustments will be from the assumed slope of zero, instead of
> the estimated slope.
>
> This brings us to
>
> math ~ 1 + ses + (1 + sector | sch.id)
>
> this estimates a model with a slope an intercept; as well as per-sch.id
> adjustments for the intercept and sector.
>
> This is mathematically well-defined, even if there is only one value of
> sector observed for each sch.id (which is the case when sch.id is nested
> within sector), because the shrinkage of the random effects deals with
> the rank deficiency. (If you didn't understand that sentence: it's still
> possible to estimate these quantities.) In the case that sector doesn't
> vary within sch.id, you'll get an estimate that reflects this: either it
> will be perfectly correlated with the intercept or shrunk to zero. In
> other words, that's one way to get a singular/boundary fit.
>
> Now mathematically well-defined doesn't mean that it makes sense
> inferentially. And that's where it's incumbent upon the user to think
> about their inferential question, their data, and their phrasing of the
> inferential question as a statistical model.
>
> Phillip
>
> On 7/10/20 9:30 pm, Simon Harmel wrote:
> > correction:
> >
> > As far as I understand, in a 2-level model, the use of a level-2
> predictor
> > (here "sector") in the ***random part*** is illegitimate.
> >
> > But I wonder why in the following model `lmer` doesn't throw an error to
> > indicate that? What does the random part estimates in the output?
> >
> > library(lme4)
> > hsb <- read.csv('
> > https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')
> >
> > mn <- lmer(math ~ ses + (sector | sch.id), data = hsb)
> >
> >
> >
> > On Wed, Oct 7, 2020 at 2:24 PM Simon Harmel <sim.harmel using gmail.com>
> wrote:
> >
> >> Dear All,
> >>
> >> As far as I understand, in a 2-level model, the use of a level-2
> predictor
> >> (here "sector") is illegitimate.
> >>
> >> But I wonder why in the following model `lmer` doesn't throw an error to
> >> indicate that?
> >>
> >> library(lme4)
> >> hsb <- read.csv('
> >> https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')
> >>
> >> mn <- lmer(math ~ ses + (sector | sch.id), data = hsb)
> >>
> >
> >       [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>

	[[alternative HTML version deleted]]