Large mixed & crossed-effect model looking at educational spending on crime rates with error messages

Mon, Sep 9, 2019 2:58 AM

Dear James,

Since all ID's are unique, you can rely on the implicit nesting of random
effects. (1|STATE_ID/COUNTY_ID) is equivalent to (1|STATE_ID) +
(1|COUNTY_ID) when each COUNTY_ID is unique (not reused among states).

There is a huge overlap between PLACE_ID and full_district_id. The model
will have a hard time separating both effects. Especially since you have
the same random slope.

You should also center the year variable. Now your model is estimating the
random intercept at year 0.

So in terms of basic model I would

- drop either PLACE_ID or full_district_id
- center year
- add year to the fixed effects or add it as a separate random intercept

Furthermore, I'm not sure it the Poisson distribution is the most relevant
distribution for your response. I've seen a case were the Poisson
distribution failed. The response was an area in hectares rounded to an
integer value. The model fitted well with a Gamma distribution.

Best regards,

Thierry

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
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<https://www.inbo.be>

Op zo 8 sep. 2019 om 07:40 schreef Ades, James <jades at ucsd.edu>:

Okay, sorry for the delay; I was waiting to hear back from a couple people
at the census regarding a question on school district info in the dataset.

I?ve uploaded the dataset as a zip and an xs:

https://drive.google.com/file/d/1hyJYVg0x_-dIHfZdjWzdRuQS_H365buK/view?usp=sharing

https://drive.google.com/file/d/1qKU7vvzsqzrD58lcu6HWlMALwy4mm6RF/view?usp=sharing

There is one important thing to note, here, which is that there is more
city overlap between counties than I thought. The easiest way to explain
this is by checking distinct values: using distinct(PLACE_ID, COUNTY_ID,
year), you should get 107,515; however, with distinct(PLACE_ID, year),
you?ll only get 99,832. So essentially, there are ~8000 times that a city
will overlap in two counties (this likely includes the same city repeating
this overlap every year?though it all depends on what years the city/town
police department reports crime to the FBI). I can figure out the
respective populations in each of the two counties where the city overlaps.
It?s a bit of leg work, but it is possible. Still, it seems that it would
not be principled to include the city/town in both counties because there
would be the assumption that the crime occurring in each corresponding
county is tied solely to population. Still, I left in all cities/towns
overlapping with two counties, in case you have some ideas about how a
mixed-model might be used to account for these (I don?t think a
crossed-effect structure would do it). So pretty much any city with
duplicate values where that value lies within the same county should be
counted (these are just separate school districts), but any city with
duplicate values where one of those values happens to be in another county,
yet the school district is still the same, shouldn't be counted; unless, of
course, there is a way for mixed-modeling in lme4 to account for that
(PLACE_ID will be the same, but COUNTY_ID will be different, but
full_district_id will be the same). Does that make sense? I'll soon send an
email to the group with more clarification.

Use IDs vs names. I included names for reference, but city/towns might not
always be recorded exactly the same, so IDs are the safer bet.

I have tried lmer?originally, my intention was to preserve counts of zero
crime (whether it?s weariness or sanity that has changed my view, the
difference between one and zero doesn?t seem so important anymore. I get
the boundary (singular) warning (if a warning is what it can be called). No
doubt there are many here that know more than me, but my understanding of
this message is that it mostly warns against overfitting. To me,
controlling for time through a fixed effect and as a random slope seems
warranted?different cities/towns have different rates of change in crime
from year to year.

I still think fitting with glmer would be ideal, but I also lack an
understanding of the nuances on the backend with regard to how the two
functions differ. It seems that lmer is faster and more efficient in
modeling, though I?m not sure why?mathematically or programmatically?that?s
the case. If you can point me to an explanation, I?d appreciate that.

Thanks much for your messages and your help.

James

On Sep 4, 2019, at 12:54 AM, Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote:

Dear James,

Your mail contains only a part of the dput() output. Given the size of
your data, I suggest that you place it somewhere online and send us a link
to the data.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be/>

Op di 3 sep. 2019 om 21:34 schreef Ades, James <jades at ucsd.edu>:

I posted my question at Stack Overflow, where it didn?t get much of a
response, and I was pointed in this direction by Ben Bolker. I?m happy to
send the whole dataset to anyone who wants but thought that it would be
presumptuous to include an enormous dput() here.

I?m looking at the effects of education spending per school district on
crime rate (FBI crime data/UCR) within the cities and towns those school
districts serve over a fifteen year period. The DV now has 203,410
observations of city/town crime data over those fifteen years. (I use that
figure with some reticence, because there are so many moving parts and
things to account for, but having employed over 100 datasets and hours
passing through the code again, I think that figure is correct.)

Cities are technically crossed with school district, in that one city
might attend multiple school districts. This means that one city could have
multiple values for expenditure per student. School districts, however,
also overlap with counties. As if things weren?t complicated enough, cities
are mostly nested within county (though there are cities that exist in two
counties, but it?s not often, and it?s usually by a small amount). Given
that each city/town has a distinct PLACE_ID, my understanding is that this
could be represented as (1|PLACE_ID) + (1|STATE/COUNTY_ID) or
(1|STATE/COUNTY_ID/PLACE_ID).

I?m pretty familiar with mixed-effect models, and I?ve looked through
clear and informative posts such as this one:
https://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specified.
I believe things would remain sane to include school district
(full_district_id) as another crossed effect, as below:
glmer.total <- glmer(CRIME_TOTAL ~ 1 + (year|PLACE_ID) +
(1|STATE/COUNTY_ID) + (year|full_district_id), family = "poisson", control
= glmerControl(optimizer = "nloptwrap", calc.derivs = FALSE), REML = FALSE,
total.years, na.action = "na.omit")

Variables (not included in this model, to keep things null and simple)
are centered and logged: pop per city, pop.dens per city, year,
unemployment rate per county, proportion children living in poverty per
school district, per capita income per county, difference in those who
voted democrat in presidential elections per county, log enforcement per
city/town, centered expenditure per student/ 1000 (per school district).
PLACE_ID corresponds to cities and towns, COUNTY_ID to counties,
full_district_id to school districts, and state.

First, if I try to run the full model, using UCSD?s supercomputer, I get
the error that the job was killed, presumably because it got to a point
where it consumed too much ram (I think 125mb).

I then tried to create a small subsection of data with arrange(STATE,
COUNTY_ID, PLACE_ID) and then slicing by the first ten states (up through
Delaware), so that I have 26,599 values. If I run this null model with the
above code, I get the following error:

```
Error in getOptfun(optimizer) :
  optimizer function must use (at least) formal parameters ?fn?, ?par?,
?lower?, ?control?
```

Then I tried with the optimx, with these configurations: control =
glmerControl(optimizer = "optimx?,
optCtrl = list(method = "nlminb?,
maxit=10000,
iter.max=10000,
eval.max=10000,
lower = c(0,0,0),
upper = c(Inf,10,1)))

and I received the following warning?since this is a null model, there
aren?t any variables to really rescale.\

```
Warning messages:
1: In nlminb(start = par, objective = ufn, gradient = ugr, lower =
lower,  :
  unrecognized control elements named ?lower?, ?upper? ignored
2: In nlminb(start = par, objective = ufn, gradient = ugr, lower =
lower,  :
  unrecognized control elements named ?lower?, ?upper? ignored
3: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge with max|grad| = 0.00102386 (tol = 0.001,
component 1)
4: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model is nearly unidentifiable: very large eigenvalue
 - Rescale variables?
```

I then tried more values (to 92,486, through Missouri). First, I tried
the optimizer nloptr, and then I tried the optimix. I still received the
same above errors.

I?ve checked and rechecked everything, so I wanted to solicit advice,
either for where I might be going wrong, or for what I could do to resolve
these error messages.

I?ve provided a brief snippet of the data below (randomly pulling a
number of cities within counties of Arkansas, Arizona, and Alabama, as a
dput.

Thanks!



231, 206, 935, 1070, 974, 1108, 1244, 1095, 1131, 1151, 1420,
1316, 1321, 1414, 1484), full_district_id = c("0100240", "0100240",
"0100240", "0100240", "0100240", "0100240", "0100240", "0100240",
"0100240", "0100240", "0100240", "0100240", "0100240", "0100240",
"0100240", "0100240", "0100240", "0100240", "0100240", "0100240",
"0100240", "0100240", "0100240", "0100240", "0100240", "0100240",
"0100240", "0100240", "0100240", "0100240", "0100240", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0100270", "0100270", "0100270", "0100270",
"0100270", "0100270", "0407130", "0407130", "0407130", "0407130",
"0407130", "0407130", "0407130", "0407130", "0407130", "0407130",
"0407130", "0407130", "0407130", "0407130", "0408080", "0408080",
"0408080", "0408080", "0408080", "0407130", "0407130", "0407130",
"0407130", "0407130", "0407130", "0407130", "0407130", "0407130",
"0407130", "0407130", "0407130", "0407130", "0400212", "0408020",
"0400212", "0408020", "0400212", "0408020", "0400212", "0408020",
"0400212", "0408020", "0400212", "0408020", "0401180", "0401180",
"0401180", "0401180", "0401180", "0401180", "0401180", "0401180",
"0401180", "0402530", "0402530", "0402530", "0402530", "0402530",
"0402530", "0402530", "0402530", "0408600", "0408600", "0408600",
"0408600", "0408600", "0408600", "0408600", "0408600", "0408600",
"0403150", "0401460", "0403150", "0401460", "0403150", "0401460",
"0403150", "0401460", "0403150", "0401460", "0403150", "0401460",
"0401460", "0403150", "0401460", "0403150", "0401460", "0403150",
"0401460", "0401460", "0401460", "0401460", "0408600", "0408600",
"0408600", "0408600", "0409250", "0409250", "0409250", "0409250",
"0409250", "0409250", "0409250", "0409250", "0409250", "0409250",
"0409250", "0409250", "0409250", "0402860", "0402860", "0402860",
"0402860", "0402860", "0402860", "0402860", "0402860", "0402860",
"0402860", "0402860", "0402860", "0402860", "0402860", "0402860",
"0403080", "0403080", "0403080", "0403080", "0403080", "0403080",
"0403080", "0403080", "0403080", "0403080", "0403080", "0403080",
"0403080", "0403080", "0405820", "0403080", "0405820", "0403080",
"0405820", "0403080", "0405820", "0403080", "0405820", "0403080",
"0405820", "0403080", "0405820", "0403080", "0405820", "0403080",
"0405820", "0403080", "0405820", "0402860", "0402860", "0402860",
"0402860", "0402860", "0402860", "0402860", "0402860", "0402860",
"0402860", "0402860", "0409310", "0409310", "0409310", "0409310",
"0409310", "0409310", "0409310", "0409310", "0409310", "0409310",
"0409310", "0403500", "0405030", "0403500", "0405030", "0403500",
"0405030", "0403500", "0405030", "0403500", "0405030", "0403500",
"0405030", "0403500", "0405030", "0403500", "0405030", "0403500",
"0405030", "0403500", "0405030", "0403500", "0405030", "0403730",
"0405030", "0405030", "0405030", "0405030", "0405030", "0405030",
"0405030", "0405030", "0405030", "0405030", "0405030", "0405030",
"0405030", "0406070", "0406070", "0406070", "0406070", "0406070",
"0406070", "0406070", "0406070", "0406070", "0406070", "0406070",
"0406070", "0406440", "0406440", "0406440", "0406440", "0406440",
"0406440", "0406440", "0406440", "0406440", "0406440", "0406440",
"0406440", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0407240", "0408410", "0407240", "0408410", "0407240",
"0408410", "0402110", "0405320", "0402110", "0405320", "0402110",
"0405320", "0402110", "0405320", "0402110", "0405320", "0402110",
"0405320", "0405320", "0402110", "0405320", "0402110", "0405320",
"0405980", "0405980", "0405980", "0405980", "0405980", "0405980",
"0405980", "0509000", "0509000", "0509000", "0509000", "0509000",
"0509000", "0509000", "0509000", "0509000", "0509000", "0509000",
"0509000", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0509000", "0511850", "0509000", "0511850", "0509000",
"0511850", "0509000", "0511850", "0509000", "0511850", "0509000",
"0511850", "0509000", "0511850", "0509000", "0511850", "0509000",
"0511850", "0509000", "0511850", "0509000", "0511850", "0509000",
"0511850", "0509000", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0511850", "0511850", "0511850", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0510680", "0511850", "0510680", "0511850", "0510680", "0511850",
"0500009", "0500009", "0500009", "0500009", "0500009", "0500009",
"0500009", "0500009", "0500009", "0500009", "0509270", "0509270",
"0509270", "0513080", "0513080", "0513080", "0513080", "0513080",
"0513080", "0513080", "0513080", "0513080", "0513080", "0513080",
"0513080", "0513080", "0511610", "0511610", "0511610", "0511610",
"0511610", "0511610", "0511610", "0511610", "0511610", "0511610",
"0512480", "0512480", "0512480", "0512480", "0506270", "0506270",
"0506270", "0506270", "0506270", "0506270", "0506270", "0506270",
"0506270", "0506270", "0508040", "0508040", "0508040", "0508040",
"0508040", "0508040", "0503690", "0503690", "0502790", "0502960",
"0503690", "0507320", "0502790", "0502960", "0503690", "0507320",
"0502790", "0502960", "0503690", "0507320", "0502790", "0502960",
"0503690", "0507320", "0502790", "0502960", "0503690", "0507320",
"0502790", "0502960", "0503690", "0507320", "0502790", "0502960",
"0503690", "0507320", "0502790", "0502960", "0503690", "0507320",
"0502790", "0502960", "0503690", "0507320", "0502790", "0502960",
"0503690", "0507320", "0502790", "0502960", "0503690", "0507320",
"0502790", "0502960", "0503690", "0507320", "0502790", "0502960",
"0503690", "0507320", "0503690", "0503690", "0503690", "0503690",
"0503690", "0503690", "0503690", "0503690", "0503690", "0503690",
"0503690", "0506420", "0506420", "0506420", "0506420", "0506420",
"0506420", "0506420", "0506420", "0506420", "0506420", "0506420",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0503690", "0511850", "0503690",
"0511850", "0503690", "0511850", "0503690", "0511850", "0500015",
"0500015", "0500015", "0500015", "0500015", "0500015", "0500015",
"0500015", "0500015", "0500015", "0500015", "0500015", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850",
"0511850", "0511850", "0511850", "0511850", "0511850", "0511850"
), COUNTY = c("autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"autauga county", "autauga county", "autauga county", "autauga county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "baldwin county",
"baldwin county", "baldwin county", "baldwin county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "apache county",
"apache county", "apache county", "apache county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"cochise county", "cochise county", "cochise county", "cochise county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "coconino county", "coconino
county",
"coconino county", "coconino county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "gila county", "gila county", "gila county", "gila county",
"gila county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "graham county", "graham county", "graham county",
"graham county", "greenlee county", "greenlee county", "greenlee county",
"greenlee county", "greenlee county", "greenlee county", "greenlee
county",
"greenlee county", "greenlee county", "greenlee county", "greenlee
county",
"greenlee county", "greenlee county", "greenlee county", "greenlee
county",
"greenlee county", "greenlee county", "la paz county", "la paz county",
"la paz county", "la paz county", "la paz county", "la paz county",
"la paz county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"pulaski county", "pulaski county", "pulaski county", "pulaski county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"randolph county", "randolph county", "randolph county", "randolph
county",
"st. francis county", "st. francis county", "st. francis county",
"st. francis county", "st. francis county", "st. francis county",
"st. francis county", "st. francis county", "st. francis county",
"st. francis county", "st. francis county", "st. francis county",
"st. francis county", "st. francis county", "st. francis county",
"st. francis county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
"saline county", "saline county", "saline county", "saline county",
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"05125", "05125", "05125", "05125", "05125", "05125", "05125",
"05125", "05125", "05125", "05125", "05125"), DISTRICT = c("Autauga
County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Autauga County School District", "Autauga County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
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"Baldwin County School District", "Baldwin County School District",
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"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Baldwin County School District",
"Baldwin County School District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "St. Johns Unified District",
"St. Johns Unified District", "St. Johns Unified District", "St. Johns
Unified District",
"St. Johns Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Round Valley Unified District", "Round Valley Unified District",
"Benson Unified School District", "St. David Unified District",
"Benson Unified School District", "St. David Unified District",
"Benson Unified School District", "St. David Unified District",
"Benson Unified School District", "St. David Unified District",
"Benson Unified School District", "St. David Unified District",
"Benson Unified School District", "St. David Unified District",
"Bisbee Unified District", "Bisbee Unified District", "Bisbee Unified
District",
"Bisbee Unified District", "Bisbee Unified District", "Bisbee Unified
District",
"Bisbee Unified District", "Bisbee Unified District", "Bisbee Unified
District",
"Douglas Unified District", "Douglas Unified District", "Douglas Unified
District",
"Douglas Unified District", "Douglas Unified District", "Douglas Unified
District",
"Douglas Unified District", "Douglas Unified District", "Tombstone
Unified District",
"Tombstone Unified District", "Tombstone Unified District", "Tombstone
Unified District",
"Tombstone Unified District", "Tombstone Unified District", "Tombstone
Unified District",
"Tombstone Unified District", "Tombstone Unified District", "Fort
Huachuca Accommodation District",
"Sierra Vista Unified District", "Fort Huachuca Accommodation District",
"Sierra Vista Unified District", "Fort Huachuca Accommodation District",
"Sierra Vista Unified District", "Fort Huachuca Accommodation District",
"Sierra Vista Unified District", "Fort Huachuca Accommodation District",
"Sierra Vista Unified District", "Fort Huachuca Accommodation District",
"Sierra Vista Unified District", "Sierra Vista Unified District",
"Fort Huachuca Accommodation District", "Sierra Vista Unified District",
"Fort Huachuca Accommodation District", "Sierra Vista Unified District",
"Fort Huachuca Accommodation District", "Sierra Vista Unified District",
"Sierra Vista Unified District", "Sierra Vista Unified District",
"Sierra Vista Unified District", "Tombstone Unified District",
"Tombstone Unified District", "Tombstone Unified District", "Tombstone
Unified District",
"Willcox Unified District", "Willcox Unified District", "Willcox Unified
District",
"Willcox Unified District", "Willcox Unified District", "Willcox Unified
District",
"Willcox Unified District", "Willcox Unified District", "Willcox Unified
District",
"Willcox Unified District", "Willcox Unified District", "Willcox Unified
District",
"Willcox Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
"Flagstaff Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
"Flagstaff Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
"Flagstaff Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
"Flagstaff Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
"Flagstaff Unified District", "Fredonia-Moccasin Unified District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Fredonia-Moccasin Unified
District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
"Fredonia-Moccasin Unified District", "Page Unified District",
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Unified District",
"Flagstaff Unified District", "Flagstaff Unified District", "Flagstaff
Unified District",
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"Williams Unified District", "Williams Unified District", "Williams
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"Williams Unified District", "Williams Unified District", "Williams
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"Williams Unified District", "Williams Unified District", "Williams
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"Williams Unified District", "Globe Unified District", "Miami Unified
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"Miami Unified District", "Globe Unified District", "Miami Unified
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"Miami Unified District", "Globe Unified District", "Miami Unified
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Large mixed & crossed-effect model looking at educational spending on crime rates with error messages

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