What predicts a school's ties to outside organizations

The eight organizations: parents' groups, civic groups, local businesses, churches, social services, mental-health providers, juvenile justice agencies, and the police.

Figures

Tables

<!-- generated by scripts/paper_tables.py; do not edit by hand -->

Table 1. Bipartite exponential random graph model of schools and the eight organizations, 2015-16 wave (n = 1,805 schools)

Note: A coefficient is the change in the log odds of a school working with a given organization. The first two terms describe the shape of the network. The rest ask whether schools with more of that characteristic hold more ties, which this kind of model calls an activity effect. Column 1 puts the neighborhood in on its own; column 2 adds the three things the school runs for itself, and the neighborhood coefficient falls to nothing, which is the paper's direct-and-indirect result inside the model. Unweighted, since exponential random graph models do not take survey weights. The neighborhood coefficient in column 1 is +0.051 at a decay of 0.2 and +0.036 at 0.8, so it does not turn on that parameter. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 2. How many organizations a school works with

Note: Survey-weighted least squares within grade level, controlling for size, location and wave. Standard errors clustered on the sampling stratum within wave. Parent process and security equipment are standardized; the index row enters the three as one standardized index, built within the grade level. The three columns cover 12,620 of the 13,167 school-years; the 547 schools spanning several grade levels are a mixed category and are not shown. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 3. The crime level the principal reports, and how many organizations a school works with

Note: Per standard deviation of the principal's description of the crime level in the area where the school is located, reversed so that higher means more crime, and standardized. Controlling for size, grade level and urbanicity, and wave in the pooled row. Standard errors clustered on the sampling stratum within wave. The variation across waves is larger than sampling noise: a joint test of crime by wave interactions gives F = 3.53, p = 0.0040. The pooled estimate does not depend on any single wave. Dropping 2021-22 gives +0.164* and dropping 2015-16 gives +0.095. In the two waves carrying the fifty replicate weights, a jackknife standard error on the pooled specification gives 0.023 against 0.029 here. The sample excludes the 2,028 school-years that work with all eight organizations or with none; putting them back gives +0.125*** on 15,195 school-years, and the exclusion rate does not vary with the crime measure (low 12.6%, moderate 12.6%, high 11.6%). \\\p < 0.001, \\p < 0.01, \p < 0.05.

<!-- descriptives, weighted analyzed panel: mean count 4.00; shares police 81%; parent_groups 71%; social_services 65%; mental_health 63%; civic 40%; juvenile_justice 32%; business 26%; church 22%; juvenile justice 40% to 26%; mental health 52% to 76% -->

Table 10. The reported crime level with the student body added

Note: Survey-weighted least squares, standard errors clustered on the sampling stratum within wave, in brackets. All predictors standardized, so a coefficient is the change in the count of organizations for a school one standard deviation higher on that measure. The neighborhood coefficient barely changes when the student body is added, and only one of the five separates from zero, students who transferred in, and at p < 0.05. This is H4. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 4. What the reported crime level does to each of the eight ties

Note: One model per organization, per standard deviation of the reported crime level, controlling for size, grade level, urbanicity and wave, with standard errors clustered on the sampling stratum within wave. The last column gives the share of schools reporting the tie, which bounds how far a coefficient can go. The two negative coefficients rest on different amounts of evidence. Estimated within wave, parents' groups is 2005-06 -0.007, 2007-08 -0.030*, 2015-16 -0.009, 2017-18 -0.013, 2019-20 -0.012, 2021-22 -0.032**, negative in 6 of the six waves, and the pooled estimate stays significant in 6 of the six samples that leave one wave out. The police coefficient is 2005-06 +0.000, 2007-08 -0.017, 2015-16 -0.001, 2017-18 -0.005, 2019-20 -0.010, 2021-22 -0.035*, negative in 5 of the six, and the pooled estimate stays significant in 3 of the six leave-one-out samples. The police estimate should not be read as a within-period regularity. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 5. Two readings of the environment, and the two combined

Note: n = 11,335, the schools answering both readings on a scale. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. Each column is a separate model; the three measures are never entered together except where the note says so. The two readings correlate at 0.79 and the two-item scale has an alpha of 0.88, which is why averaging them is reasonable. Entered together the catchment reading takes the association: +0.150 against +0.018 for the school's own area. Splitting schools four ways by whether the principal calls each area high or moderate rather than low, and taking schools calling neither as the comparison, gives 2 the school's area only -0.054, 3 the students' areas only +0.264, 4 both +0.357***. The two do not interact: entered as a product the interaction is +0.009 (p = 0.72). Across single surveys, the combined scale separates from zero in 5 of six and the school's own area in 3. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 6. The same estimate with the enforcement organizations taken out of the count

Note: n = 13,167. Per standard deviation of the reported crime level, survey-weighted, with standard errors clustered on the sampling stratum within wave and the same controls throughout. If the association were police arriving in schools under another name, it should weaken as the enforcement organizations are removed. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 9. Whether the extra organizations fall on one side

Note: n = 13,167. Per standard deviation of the reported crime level, survey-weighted, with standard errors clustered on the sampling stratum within wave and the same controls throughout. Both sides rise. The balance between them does not change, with or without the number of organizations held constant, which is H5: a rougher area is associated with a school reaching further out rather than with a school reaching in a particular direction. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 11. The two organizations that changed, by the crime level the principal reports

Note: Survey-weighted shares, n = 13,167. Crime level is the principal's description of the area. The two rows that changed over the period are shown; the other six organizations barely changed. On mental health, high-crime schools led low-crime schools by 15 points in 2005-06 and the two were level by 2021-22. Between 106 and 144 schools report a high level of crime in any one wave, so a single cell carries a standard error of roughly four points and the wave-to-wave movement in that row should not be read closely. Interacting the crime measure with time, the association with the count of organizations falls across the six waves by -0.144 (p = 0.026). The fall sits in the pandemic year, not in a gradual narrowing: estimated without 2021-22 it is -0.040 (p = 0.54), and on the four pre-pandemic waves -0.016 (p = 0.79). So the convergence in the levels shown above does not appear as a downward trend in the association before the closures. Taken one organization at a time the trend does not separate from zero either, at p = 0.10 and p = 0.08. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 7. The same estimate inside each kind of place

Note: Per standard deviation of the reported crime level, survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, grade level and wave. The rows compare high-crime with low-crime schools inside the same kind of place, so a difference in how many organizations exist in cities against rural areas cannot produce them. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 8. The reported crime level with the school's own arrangements added in sequence

Note: n = 13,167. The first three rows are survey-weighted with standard errors clustered on the sampling stratum within wave. The fourth drops the weights, as the exponential random graph model in Table 1 does. These are adjusted estimates in sequence rather than a formal decomposition: the fall from the first row to the third measures what the school's own arrangements account for, not an estimated indirect effect. The last row gives the outcome the sequence presumes, that schools in rougher areas employ more security staff; it is a probability, so it is not on the same scale as the rows above it but is on the same scale as the per-organization ties. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 17. The two sources of reach

Note: n = 13,167. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. All predictors standardized, so each coefficient is the difference in the count of organizations between two schools one standard deviation apart. What the school has built is an index of the three standing arrangements the survey carries in every wave: security staffing (harmonized to any-versus-none across a wording change in 2015-16), the formal parent process, and security equipment; each is standardized, the three are averaged, and the average is restandardized. The capacity coefficient carries the scrutiny the environmental one does. Estimated within wave it is 2005-06 +0.506, 2007-08 +0.467, 2015-16 +0.474, 2017-18 +0.411, 2019-20 +0.482, 2021-22 +0.486, significant in all six; leaving any one wave out keeps the pooled estimate between +0.463 and +0.487. It is not an artefact of overlap between the index and the ties (the staffing measure includes sworn officers; one tie is law enforcement): on the six ties excluding the police and parents' groups it is +0.367 (0.019), the same rate per organization. The index measures how much machinery, not which kind: at a fixed count, security staffing goes with the government side of the field (+0.075) and the parent process with the community side (-0.098), while equipment goes with neither (-0.015). In the joint rows the two main effects come from the additive model; the product row comes from the model that adds it, whose main effects are +0.479 and +0.077. The interaction implies an environmental slope of +0.113 (0.032) at -1, +0.077 (0.027)** at +0, +0.042 (0.032) at +1, +0.006 (0.043) at +2 standard deviations of capacity: the first two separate from zero and the last two do not, so the environmental route is clear at and below average capacity and cannot be distinguished from zero in the sixth of schools more than one standard deviation above it. The last three rows test whether advantage builds reach. Entered alone, the share expected to go to college and the share testing at the bottom carry the wrong sign for a position account; entered together neither separates from zero, and with the crime reading and all five student-body measures present they are -0.017 and +0.002. Nothing here suggests that advantage builds reach. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 16. Whether the single dimension looks the same in every kind of school

Note: Survey-weighted, on all school-years including those working with all eight organizations or with none, because the restriction used elsewhere removes exactly the tails whose spread the first column measures. The first column compares how much schools' totals actually vary against how much they would vary if every school decided about each organization on its own; a value of 1 would mean the eight are independent. The last two columns describe the relations among the eight. If different kinds of school organized these relationships differently, the rows would not agree. Every row falls between 2.6 and 2.9 on the first column and between 0.23 and 0.27 on the second, and not one of the 28 pairs is negative in any subgroup. This is H2(b).

Table 15. Whether the data have the shape a reversed arrow would give them

Note: n = 13,167, except the parent-turnout row, which uses the 8,774 school-years in the four waves carrying those items. Survey-weighted, standard errors clustered on the sampling stratum within wave. The top panel asks whether the principal's reading tracks anything beyond the ties it is used to predict. The bottom panel reverses the regression: if a school came to describe its area as rougher because its partners told it so, the partners with a crime remit would be the ones going with a higher reading. The middle panel gives the police relationship on the margins the survey records beyond the tie itself, carried from 2015-16 on; the agreement rows apply only to schools with officers, and the discipline row only to those with an agreement, which is why their samples shrink. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 14. Why the tie to parents' groups falls

Note: The first four rows use n = 8,774: the parent-participation items are carried by 2005-06, 2007-08, 2015-16 and 2017-18 but not by the last two waves. The last two rows use all 13,167. Parent turnout averages four items, how many parents attend open house, parent-teacher conferences and subject-area events and how many volunteer, each on a four-point scale; schools not offering an event are held out of it. Survey-weighted, standard errors clustered on the sampling stratum within wave. Parents turn up substantially less where the principal reports more crime, and the fall in the tie to organized parents does not survive controlling for it. The last two rows test whether schools reach out to other organizations because parents or police are unavailable: if so, schools lacking those ties would hold more of the rest. They hold fewer. The fourth row conditions a single tie on the count that contains it, which turns the question from whether the tie is held into whether it is held at a given reach; the small negative that returns there says that at a fixed count, rougher-reading schools are slightly less likely to include organized parents in the set. Turnout accounts for the level of the tie, not entirely for its place in the composition. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 13. The reading of the outside against what happens inside

Note: n = 13,167. Survey-weighted, standard errors clustered on the sampling stratum within wave, in brackets. The outcome is the count of organizations except in the last two rows. Reported trouble is how often the principal says bullying, harassment and verbal abuse occur; recorded incidents is the count of crime and violence the school recorded that year. Both describe what the school is dealing with inside. Entered together with the reading of the outside, reported trouble no longer separates from zero. The reading of the outside does. On parents' groups the reading of the school's own area is accounted for by what happens inside, but the reading of the areas where the students live is not: it is -0.019** (0.006) in the same specification. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 12. Every measure, as the questionnaire asked it

Note: Wording from the 2015-16 codebook, which is the wave the two-mode model uses. The eight tie items and the two crime items are worded the same way in all six waves; the year named in a stem changes with the wave. The crime item on where students live carries a fourth answer that the item on the school's own area does not, which is why the two are not on the same scale and are not treated as though they were. Read off the codebook by scripts/paper_tables.py, not transcribed.

<!-- pandemic-wave figures quoted in the results: mean ties 4.40 to 3.83; share reporting high crime 7.6% to 6.4%; recorded incidents 15.8 to 15.4; reported trouble 2.07 to 2.03; every one of the eight fell, Parents' groups -14; Civic organizations -11; Local businesses -7; Police -7; Social services -6; Churches -5; Juvenile justice -5; Mental-health providers -3 -->

Table 18. The mix at a fixed count: each tie with the total number held constant

Note: Linear probability models, one per organization, per standard deviation of the reported crime level, survey-weighted, standard errors clustered on the sampling stratum within wave, controlling for size, grade level, urbanicity, wave and the total count of organizations. Because the count is held constant, a coefficient reads as a change in the share of schools holding that tie at a given number of ties: the mix, not the amount. The turnout row uses the four surveys carrying the attendance items. The two negative coefficients are negative in every wave and significant on every leave-one-out sample. The shift does not change the balance between the community and government sides, and it comes on top of the rise in the count, not in place of it. \\\p < 0.001, \\p < 0.01, \p < 0.05.

Table 19. The faint second structure: within-side pairing at fixed margins, by wave

Note: Each z compares the observed number of schools holding both ties in a pair (summed over the twelve within-side pairs in the first column, single pairs in the others) against 300 curveball randomizations that hold every school's count of ties and every organization's prevalence exactly fixed, so the margins explain none of it. The structure is present in every wave and it is small: the first two eigenvalues of the tetrachoric correlation matrix are 2.9 and 1.5, so the count's dimension is roughly twice the size of the sides dimension, and at a fixed count the within-pair residual correlations sit near +0.06 against a compositional baseline of −0.14. A varimax rotation of the two factors reproduces the community and government sides used throughout the paper. Randomization seed 7; reproduce.R rechecks the observed totals exactly and the z-scores with independent draws.