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Effects of Education Spending on Crime, multi-level mixed-model structure

由 不问归期 提交于 2020-02-07 04:04:49

问题


I’m looking at the effect of education_expenditure per school district on crime rate within the cities and towns those school districts serve over a fifteen year period. (The DV has 1,676,191 observations of city/town crime data over those fifteen years).

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, overlap with counties.

Cities are nested within county, but given that each city/town has a distinct PLACE_ID, my understanding is that this could be represented as (1|PLACE_ID) + (1|COUNTY_ID) or (1|PLACE_ID/COUNTY_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 ; however, I’m still a little stuck with whether I can create a crossed effect model like the one below:

glmer.total <- glmer(CRIME_TOTAL ~ cent.log.pop + cent.log.pop.dens + year + cent.log.unemployment_rate + cent.schooldist.prop5.17.pov + cent.log.per.cap + diff.dem + cent.log.enforcement +cent.EXP_STUDENT + (year|PLACE_ID/COUNTY_ID) + (year|full_district_id) + (1|STATE), family = "poisson", control = glmerControl(optimizer = "nloptwrap", calc.derivs = FALSE), REML = FALSE, total.years, na.action = "na.omit")

Variables 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.

  • Would I need to choose to average expenditure per city by year, or is the above code legitimate? I’m receiving the following error:
extra argument(s) ‘REML’ disregardedError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GHrule(0L), compDev = compDev,  : 
  (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate

I’ve provided a brief snippet of the data below (but selected only a number of variables to make it much smaller, as a dput.

Thanks!

structure(list(STATE = c("alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama", "alabama", "alabama", 
"alabama", "alabama", "alabama", "alabama"), state = c("AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", "AL", 
"AL"), full_district_id = c("0100510", "0100510", "0100510", 
"0100510", "0100090", "0100540", "0101860", "0102635", "0102760", 
"0100090", "0100540", "0101860", "0102635", "0102760", "0100090", 
"0100540", "0101860", "0102635", "0102760", "0100090", "0100540", 
"0101860", "0102635", "0102760", "0100090", "0100540", "0101860", 
"0102635", "0102760", "0100090", "0100540", "0101860", "0102635", 
"0102760", "0100090", "0100540", "0101860", "0102635", "0102760", 
"0100090", "0100540", "0101860", "0102635", "0102760", "0100090", 
"0100540", "0101860", "0102635", "0102760", "0100090", "0100540", 
"0101860", "0102635", "0102760", "0100090", "0100540", "0101860", 
"0102635", "0102760", "0100090", "0100540", "0101860", "0102635", 
"0102760", "0100090", "0100540", "0101860", "0102635"), SCHOOL_DISTRICT.x = c("butler county school district", 
"butler county school district", "butler county school district", 
"butler county school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district", "piedmont city school district", 
"anniston city school district", "calhoun county school district", 
"jacksonville city school district", "oxford city school district", 
"piedmont city school district", "anniston city school district", 
"calhoun county school district", "jacksonville city school district", 
"oxford city school district"), COUNTY = c("butler ", "butler ", 
"butler ", "butler ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", 
"calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun ", "calhoun "
), year = c(2006, 2007, 2008, 2009, 2006, 2006, 2006, 2006, 2006, 
2007, 2007, 2007, 2007, 2007, 2008, 2008, 2008, 2008, 2008, 2009, 
2009, 2009, 2009, 2009, 2010, 2010, 2010, 2010, 2010, 2011, 2011, 
2011, 2011, 2011, 2012, 2012, 2012, 2012, 2012, 2013, 2013, 2013, 
2013, 2013, 2014, 2014, 2014, 2014, 2014, 2015, 2015, 2015, 2015, 
2015, 2016, 2016, 2016, 2016, 2016, 2017, 2017, 2017, 2017, 2017, 
2007, 2007, 2007, 2007), COUNTY_ID = c("01013", "01013", "01013", 
"01013", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015", "01015", "01015", "01015", "01015", "01015", 
"01015", "01015"), SCHOOL_DISTRICT.y = c("BUTLER CO SCH DIST", 
"BUTLER CO SCH DIST", "BUTLER COUNTY SCHOOL DISTRICT", "BUTLER COUNTY SCHOOL DISTRICT", 
"ANNISTON CTY SCH DST", "CALHOUN CO SCH DIST", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCH DIST", "PIEDMONT CTY SCH DIST", "ANNISTON CTY SCH DST", 
"CALHOUN CO SCH DIST", "JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCH DIST", 
"PIEDMONT CTY SCH DIST", "ANNISTON CTY SCH DST", "CALHOUN COUNTY SCHOOL DISTRICT", 
"JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCHOOL DISTRICT", 
"PIEDMONT CITY SCHOOL DISTRICT", "ANNISTON CITY SCHOOL DISTRICT", 
"CALHOUN COUNTY SCHOOL DISTRICT", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCHOOL DISTRICT", "PIEDMONT CITY SCHOOL DISTRICT", 
"ANNISTON CITY SCHOOL DISTRICT", "CALHOUN COUNTY SCHOOL DISTRICT", 
"JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCHOOL DISTRICT", 
"PIEDMONT CITY SCHOOL DISTRICT", "ANNISTON CITY SCHOOL DISTRICT", 
"CALHOUN COUNTY SCHOOL DISTRICT", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCHOOL DISTRICT", "PIEDMONT CITY SCHOOL DISTRICT", 
"ANNISTON CITY SCHOOL DISTRICT", "CALHOUN COUNTY SCHOOL DISTRICT", 
"JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCHOOL DISTRICT", 
"PIEDMONT CITY SCHOOL DISTRICT", "ANNISTON CITY SCHOOL DISTRICT", 
"CALHOUN COUNTY SCHOOL DISTRICT", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCHOOL DISTRICT", "PIEDMONT CITY SCHOOL DISTRICT", 
"ANNISTON CITY SCHOOL DISTRICT", "CALHOUN COUNTY SCHOOL DISTRICT", 
"JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCHOOL DISTRICT", 
"PIEDMONT CITY SCHOOL DISTRICT", "ANNISTON CITY SCHOOL DISTRICT", 
"CALHOUN COUNTY SCHOOL DISTRICT", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCHOOL DISTRICT", "PIEDMONT CITY SCHOOL DISTRICT", 
"ANNISTON CITY SCHOOL DISTRICT", "CALHOUN COUNTY SCHOOL DISTRICT", 
"JACKSONVILLE CITY SCHOOL DISTRICT", "OXFORD CITY SCHOOL DISTRICT", 
"PIEDMONT CITY SCHOOL DISTRICT", "ANNISTON CITY SCHOOL DISTRICT", 
"CALHOUN COUNTY SCHOOL DISTRICT", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCHOOL DISTRICT", "PIEDMONT CITY SCHOOL DISTRICT", 
"ANNISTON CTY SCH DST", "CALHOUN CO SCH DIST", "JACKSONVILLE CITY SCHOOL DISTRICT", 
"OXFORD CITY SCH DIST"), EXPENDITURE_PER_STUDENT = c(7593, 8334, 
9281, 9147, 8240, 7216, 6822, 7554, 7155, 8758, 8186, 7323, 8380, 
7710, 9070, 8707, 8070, 8853, 8054, 9364, 8212, 7787, 8560, 7760, 
10006, 8264, 7964, 8771, 8442, 10154, 8209, 7955, 8967, 7911, 
10661, 8157, 8096, 9097, 7660, 11480, 8415, 9351, 8829, 8102, 
12057, 8479, 8708, 8965, 8443, 10988, 8930, 8932, 9118, 8706, 
11277, 9134, 9223, 9347, 8524, 11277, 9134, 9223, 9347, 8524, 
8758, 8186, 7323, 8380), PLACE_ID = c("0101345496", "0101345496", 
"0101345496", "0101345496", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101501852", "0101501852", "0101501852", 
"0101501852", "0101501852", "0101529992", "0101529992", "0101529992", 
"0101529992"), CITY = c("mckenzie", "mckenzie", "mckenzie", "mckenzie", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"anniston", "anniston", "anniston", "anniston", "anniston", "anniston", 
"glencoe", "glencoe", "glencoe", "glencoe"), POPULATION.EST = c(548, 
542, 536, 526, 23470, 23470, 23470, 23470, 23470, 23360, 23360, 
23360, 23360, 23360, 23313, 23313, 23313, 23313, 23313, 23262, 
23262, 23262, 23262, 23262, 23106, 23106, 23106, 23106, 23106, 
22849, 22849, 22849, 22849, 22849, 22644, 22644, 22644, 22644, 
22644, 22457, 22457, 22457, 22457, 22457, 22280, 22280, 22280, 
22280, 22280, 22107, 22107, 22107, 22107, 22107, 21926, 21926, 
21926, 21926, 21926, 21770, 21770, 21770, 21770, 21770, 32, 32, 
32, 32), CRIME_VIOLENT = c(1, 0, 2, 1, 521, 521, 521, 521, 521, 
541, 541, 541, 541, 541, 572, 572, 572, 572, 572, 584, 584, 584, 
584, 584, 0, 0, 0, 0, 0, 411, 411, 411, 411, 411, 504, 504, 504, 
504, 504, 461, 461, 461, 461, 461, 536, 536, 536, 536, 536, 607, 
607, 607, 607, 607, 735, 735, 735, 735, 735, 754, 754, 754, 754, 
754, 9, 9, 9, 9), CRIME_PROPERTY = c(6, 9, 9, 7, 3044, 3044, 
3044, 3044, 3044, 2912, 2912, 2912, 2912, 2912, 2429, 2429, 2429, 
2429, 2429, 2379, 2379, 2379, 2379, 2379, 2038, 2038, 2038, 2038, 
2038, 2323, 2323, 2323, 2323, 2323, 2484, 2484, 2484, 2484, 2484, 
1988, 1988, 1988, 1988, 1988, 1711, 1711, 1711, 1711, 1711, 1645, 
1645, 1645, 1645, 1645, 1712, 1712, 1712, 1712, 1712, 1352, 1352, 
1352, 1352, 1352, 106, 106, 106, 106), CRIME_TOTAL = c(7, 9, 
11, 8, 3565, 3565, 3565, 3565, 3565, 3453, 3453, 3453, 3453, 
3453, 3001, 3001, 3001, 3001, 3001, 2963, 2963, 2963, 2963, 2963, 
2038, 2038, 2038, 2038, 2038, 2734, 2734, 2734, 2734, 2734, 2988, 
2988, 2988, 2988, 2988, 2449, 2449, 2449, 2449, 2449, 2247, 2247, 
2247, 2247, 2247, 2252, 2252, 2252, 2252, 2252, 2447, 2447, 2447, 
2447, 2447, 2106, 2106, 2106, 2106, 2106, 115, 115, 115, 115), 
    prop.5.17.pov = c(30.2, 33.1, 28.1, 33.4, 25.6, 25.6, 25.6, 
    25.6, 25.6, 24, 24, 24, 24, 24, 20.1, 20.1, 20.1, 20.1, 20.1, 
    23.7, 23.7, 23.7, 23.7, 23.7, 30.8, 30.8, 30.8, 30.8, 30.8, 
    31.1, 31.1, 31.1, 31.1, 31.1, 30.5, 30.5, 30.5, 30.5, 30.5, 
    27, 27, 27, 27, 27, 25.4, 25.4, 25.4, 25.4, 25.4, 29.8, 29.8, 
    29.8, 29.8, 29.8, 24.2, 24.2, 24.2, 24.2, 24.2, NA, NA, NA, 
    NA, NA, 24, 24, 24, 24)), row.names = c(NA, -68L), class = c("tbl_df", 
"tbl", "data.frame"))

回答1:


A very partial answer:

  • (year|PLACE_ID/COUNTY_ID) looks backwards (the nesting syntax is larger/smaller), but given your description of the coding, either (year|PLACE_ID) + (year|COUNTY_ID) or (year|COUNTY_ID/PLACE_ID) would work. (Or (year|STATE/COUNTY_ID/PLACE_ID) ?)
  • crossing districts and states/counties seems reasonable, although I can imagine things getting a bit weird if some PLACE_IDs constitute a single school district ...
  • it should be fine to give expenditure per district

It's hard to say what's going wrong with the full model. How small a subsample can you take of the data and replicate the problem? Does the model work as a linear mixed model? If so, does the fitted model give you any hints about what might be weird with the data/model?



来源：https://stackoverflow.com/questions/56812571/effects-of-education-spending-on-crime-multi-level-mixed-model-structure

标签
r
time-series
mixed-models
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