What predicts a school's ties to outside organizations

Results

Schools differ in how many organizations they work with

Schools differ mainly in how many of the eight organizations they work with: parents' groups, civic groups, local businesses, churches, social services, mental-health providers, juvenile justice agencies and the police. The particular ones a school picks are close to unpredictable. Knowing the count barely narrows them down, and nothing else the survey records narrows them either: not the size of the school, not its grade level, not whether it sits in a city or the countryside, not the make-up of its student body.

A statistical model of the whole network says the same thing. The uneven spread of ties across schools comes out at -1.33, and the minus sign means some schools hold far more ties than chance would give them. Schools vary far more than they would if each relationship were decided on its own.

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.

One faint pattern does survive. Among the eight organizations, three pairs turn up together slightly more often than chance: social services with mental health, juvenile justice with police, and civic groups with businesses. The effect is small, and it sorts the organizations rather than the schools, so the finding that schools have no types still stands.

Table 19. Co-occurrence of organizations on the same side, against randomizations holding the margins fixed, by survey

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.

These figures cover the 13,167 school-years that work with between one and seven of the eight. The 2,028 that work with all eight or with none are set aside, and putting them back leaves the main estimate at +0.125 instead of +0.126.

Security staff, parent processes and equipment predict most

Schools that have security staff, a formal process for consulting parents, and security equipment work with more outside organizations. This is the strongest pattern in the data. Two schools one standard deviation apart on those three differ by about half an organization out of the eight.

It holds in all six surveys, from +0.41 in 2017-18 to +0.51 in 2005-06. Drop any single survey and the overall figure stays between +0.463 and +0.487. It holds at every grade level too: +0.52 in primary schools, +0.42 in middle schools and +0.33 in high schools.

You might worry that this is circular, because security staff can include police officers and one of the eight organizations is the police. It is not. Leave out both the police and parents' groups and count only the other six, and the figure is +0.367, the same rate per organization.

The index counts how much a school runs, not which kind of organization it favors. Hold the count fixed and security staffing leans slightly towards the government organizations (+0.075), the parent process towards the community ones (-0.098), and equipment towards neither (-0.015).

Table 17. Security staff, the parent process and equipment, and the crime level, entered alone and entered together

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.

How the principal describes the neighborhood

The survey asks principals to describe the crime level in the area around the school as low, moderate or high. Schools whose principals say high work with more outside organizations. The gap between the schools called low-crime and those called high-crime is about a third of one organization, on a count that averages 4.0. It shrinks to about a tenth once the school's own staff, parent process and equipment are accounted for, and it is still there.

That is the point where the two explanations can be told apart. Resource dependence predicts it. Social capital predicts the opposite, because it reads a wide network as a sign of an organization doing well.

The effect is not the same in every survey. Pooled across all six it is +0.126, but a test says the surveys genuinely differ from each other rather than wobbling by chance (F = 3.53, p = 0.004). So treat +0.126 as an average over six years that differ, not as one stable number.

Which organizations schools in rougher areas add

When a school in a high-crime area works with more organizations, the extra ones are spread across community groups and government agencies alike. They are not concentrated on the police and the courts. The count of community partners and the count of government partners both rise by about the same amount, and the balance between the two sides does not change.

Drop the police from the count altogether and the link between the principal's description of the area and the number of organizations gets stronger, not weaker. Whatever is going on, it is not policing under another name.

Table 18. Each of the eight organizations against the crime level, holding the total number 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.

Two ways of asking about the area

The survey asks principals about crime twice. Once about the area where the school sits, and once about the areas where its students live. The second question predicts the number of organizations better than the first: +0.165 against +0.126.

The two questions do not share a response scale. Reading them as though they did reversed one of this project's results before the error was caught.

It also matters that the reading is the principal's, not a recorded crime statistic. Put the school's own recorded incidents into the model and the principal's description keeps predicting. Put in how much trouble is reported inside the school and that washes out while the reading of the outside does not. The reading of the surrounding area does the work, not what has already happened in the building.

The two that do not rise: parents' groups and the police

Six of the eight organizations become more common as the reported crime level rises, once school size, grade level, where the school sits and which survey are allowed for. Two do not.

Parents' groups become less common, at -0.016 per standard deviation. The survey suggests why. It also asks how many parents turn up to school events, and in the areas principals call high-crime, fewer do. The schools are not turning away from parents. There are fewer organized parents there to work with.

Work with the police is no more common, at -0.012. We report that and do not build on it. It holds in 2021-22 alone, and the pooled figure does not survive dropping any of three of the six surveys. The argument about enforcement rests on the counts instead.

What changed over the sixteen years

Between 2005-06 and 2021-22, the share of schools working with juvenile justice agencies fell from 40% to 26%. The share working with mental-health providers rose from 52% to 76%. The other six barely changed.

Through all of it the average number of organizations a school works with stayed in a narrow band, between 3.8 and 4.4. Which organizations schools worked with changed. How many they worked with did not.

Table 11. Share of schools working with juvenile justice and with mental-health providers, by survey and 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.

The change did not happen evenly everywhere. Split the two organizations that changed by the crime level the principal reports and the shift shows up in both, but it runs further in the schools whose principals call the area high-crime.