[R-sig-ME] Large mixed & crossed-effect model looking at educational spending on crime rates with error messages

[Ades, James]

Thanks, Philip.

I took some time to read more about covariance/multicollinearity. I found two papers pretty informative/easy to digest, for anyone interested in or struggling with this topic. The second papers concerns mostly hierarchical models.

https://www.ncbi.nlm.nih.gov/pubmed/23017962
https://www.sciencedirect.com/science/article/pii/S0049089X15000885?via%3Dihub

I’ve had some experience with BRMS, so maybe that is something to try in order to implement priors. I also looked into linear growth curve analysis.

Re my last question, I think you understand most of what I’m saying. Referring to my dataset, crime counts are the dv. If a police department reports crime counts for some years but not for others, would that be imputable? As it is now, I’ve filtered out all rows for which there is no crime count, under the impression that there was little to be done for predictors/explanatory variables with no dv. Am I mistaken?

I know that lme4 drops incomplete cases (winnowing the sample), but is the information for some of these predictors imputable, such that I maintain more rows that do have a dependent variable—let’s say I’m missing one value for median income for one city for one year…lme4 would remove this entire row; but is that information imputable, such that lme4 doesn’t remove that row?

Re the unreliability of Nelder Mead…what’s weird is that whereas the lme4 default optimizer fails to converge, Nelder Mead does. I know that that doesn’t necessarily imply accuracy, but in such situations would the results of Nelder Mead be questionable? Would it be better to opt for a simpler model, perhaps with a random slope without intercepts that works with the default--something like ( 0 + year | place_id )?

As always, thanks much!

James



On Oct 1, 2019, at 12:15 AM, Phillip Alday <phillip.alday using mpi.nl<mailto:phillip.alday using mpi.nl>> wrote:



On 01/10/2019 08:25, Ades, James wrote:
I see what you’re saying
with regard to the actual source of variation, but can’t it be the case
that one thing isn’t vaguely related to another, and that the actual
source of variation is the two variables. In such a case, aren’t there
ways to parse that covariance, such that you gain a better understanding
of each variable’s effect on variance?

This is non trivial in the general case. If you know something about the
latent structure, then things like structural equation models may help,
see e.g.

https://www.johnmyleswhite.com/notebook/2016/02/25/a-variant-on-statistically-controlling-for-confounding-constructs-is-harder-than-you-think/

which provides an alternative presentation of

Westfall, J. & Yarkoni, T. (2016): Statistically Controlling for
Confounding Constructs Is Harder than You Think PLoS ONE, , 11 , 1-22

Remember, linear regression -- fixed or mixed effect -- isn't sufficient
to make causal conclusions without additional assumptions. The issue
with collinearity (as long as its not perfect / leads to rank
deficiency) is not so much in the estimates as in the standard errors,
which get inflated by the covariance. There are several classical
approaches to dealing with this (such as residualization), but they all
have pros and cons. (Oversimplifying a bit) Residualization for example
attributes only the residual variance from the first predictor to the
second predictor -- i.e. all of the shared variance is attributed to the
first predictor. Regularized regression (e.g. LASSO, ridge, elastic net)
may help, especially with prediction. Equivalently, in a Bayesian
framework, appropriate choice of priors may help to pull the estimates
apart.

But all of these comments aren't specific to the mixed-model case, so
that opens up the set of resources you can turn to. ;)


Also, just want to make sure: if you don’t have a dependent observation
for a given condition, you would have to remove that entire row,
correct? The mixed-model wouldn’t be able to work around that? This is
what i learned in stats class, but if I’m doing this wrong, I think this
might also be affecting correlation.

If I understand you correctly, you're asking what happens when your
response variable (y) is missing for a given combination of predictors
(x's)? Depending on the exact structure of the missing data, multiple
imputation might help you there, but generally if a particular case
never occurs (say "12 hours of sunlight but with winter temperatures"
for a model predicting plant growth derived from observations taken
outside but which you want to use to predict in a greenhouse), it's hard
to make inferences about that complete interaction. lme4 by default
drops incomplete cases (i.e. any rows in the dataframe where there is an
NA *for variables used in the model*).

Phillip


Thanks, Philip!

James



On Sep 29, 2019, at 3:06 AM, Phillip Alday <phillip.alday using mpi.nl<mailto:phillip.alday using mpi.nl>
<mailto:phillip.alday using mpi.nl>> wrote:

The default optimizer in lme4 is the default for a reason. :) While
there's no free lunch or single best optimizer for every situation, the
default was chosen based on our experience about which optimizer works
performs well across a wide range of models and datasets.

Multicollinearity in mixed-effects models works pretty much exactly the
same way as it does in fixed-effects (i.e. regular/not mixed) regression
and so the way it's addressed (converting to PC basis, residualization,
etc.) In your case, you could omit one race and then the remaining races
will be linearly independent, albeit still correlated with another. This
correlation isn't great and will inflate your standard errors, but then
at least your design matrix won't be rank deficient.

Regarding year-spending: Are you using 'correlated' in a strict sense,
e.g. that spending tends to go up year-by-year? Or do just mean that
including spending in the model changes the effect of year? (I think the
latter weakly implies the former, but it's a different perspective.)
Either way, the changing coefficient isn't terribly surprising. In
'human' terms: if you don't have the option of attributing something to
the actual source of variation, but you do have something that is
vaguely related to it, then you will attribute it to that. However, if
you're ever given the chance to attribute it to the actual source, you
will do that and your attribution to the vaguely-related thing will
change.

Best,
Phillip

On 29/09/2019 03:20, Ades, James wrote:
Thanks, Ben and Philip!

So I think I was conflating having a continuous dependent variable,
which could then be broken up into different categories with dummy
variables (for instance, if I wanted to look at how wealth affects the
distribution of race in an area, I could create a model like lmer(total
people ~ race + per capita income + …) with creating something similar
with a fixed factor (which I guess can’t be done).

I did try running the variables independently, which worked, I just
thought there was a way to combine races, and then per that logic,
thought that since race variables repeated within place (city/town), I
could nest it within PLACE_ID. But realized that the percent race as a
fixed effect (as an output) didn’t really make sense…hence my confusion.
So I guess somewhere in there my logic was afoul.

Regarding Nelmed-Mead: that’s odd...I recall reading somewhere that it
was actually quicker and more likely to converge. Good to know. I read
through the lme4 package details here:
https://cran.r-project.org/web/packages/lme4/lme4.pdf Would you
recommend then optimx? Or Nloptr/bobyqa? (which I think is the default).

Regarding multicollinearity: is there an article you could send me on
dealing with multicollinearity in mixed-effect models? I’ve perused the
internet, but haven’t been able to find a great how to and dealing with
it, such that you can better parse the effects of different variables (I
know that one can use PCA, but that fundamentally alters the process,
and isn’t there a way of averaging variables such that you minimize
collinearity?).

One thing I’m currently dealing with in my model is that year as a fixed
effect is correlated with a district’s spending, such that if I remove
year, district spending has a negative effect on crime, but including
year as a fixed effect alters the spending regression coefficient to be
positive (just north of zero). Though here, specifically, I’m not sure
if this is technically collinearity, or if time as a fixed factor is
merely controlling, here, for crime change over time, where a model
without year as a fixed factor would be looking at the effect of
district spending on crime (similar to a model where years are averaged
together). Does that make sense? Is that interpretation accurate?

Thanks much!

James


On Sep 28, 2019, at 8:09 AM, Phillip Alday <phillip.alday using mpi.nl<mailto:phillip.alday using mpi.nl>
<mailto:phillip.alday using mpi.nl>
<mailto:phillip.alday using mpi.nl>> wrote:

ink the answer to your proximal question about per_race is that
you would need five *different* numerical varia


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