The Role of Classroom Seating Arrangements in Friendship Formation and Persistence

Portinari Maranca, Alessandra Rister

doi:10.21307/connections-2019.043

Figures & Tables

A visualization of the research question with classroom number 4 (TA). Here, white nodes represent White students and black nodes represent Black students. The friendship network, before the semester, is compared to the friendship network at the end of the semester, taking into consideration the seating arrangement in between. (Node positions are maintained across three pictures). TA, teacher-assigned.

Differences between before and after semester network statistics: of network density, mean degree, mean distance, race assortativity, gender assortativity, and grade assortativity, with slopes, correlation coefficients, and p-values for the sake of comparison. SC, student-chosen; TA, teacher-assigned.

Goodness of fit tests for the 24 networks.

Results comparing the STERGM estimates of factors governing tie formation (right) and persistence (left). The results are separated by seating type (SC or TA). SC, student-chosen; TA, teacher-assigned.

Results of STERGM formation and persistence for teacher-chosen classrooms_

Class	Type	Formation (estimate, p-value)	Persistence (estimate, p-value)
1	TA	edges (−4.6697, < 1e-04 ^*), racial homophily (1.5218, 0.00391 ^), triadic closure (0.01252^*)
2	TA	edges (−4.66039, 0.000298^**), non-white outdegree (0.99882, 0.028678^), mutuality (2.16343, 0.000236^***)	edges (1.15196, 0.087114+), seating (2.27947, 0.032804^*)
3	TA	edges (−2.53740,<1e-04^*), mutuality (1.51807, 0.000251^*), triadic closure (NA, 0.095127+)	edges (5.54313, 0.003879^*), girl outdegree (−1.87382,0.024540^)
4	TA	edges (−4.756824,<1e-04^*), mutuality (1.325573, 0.008302 ^), triadic closure (NA, 0.000146^***)
5	TA	edges (−3.43292, <1e-04 ^**), non-white indegree (0.40454, 0.0890+), girl indegree (0.50478, 0.0483 ^), mutuality (1.81821, <1e-04 ^**), triadic closure (0.40458, 0.0233 ^)
6	TA	edges (−2.87312, <1e-04 ^*), non-white outdegree (0.62196, 0.00597 ^), mutuality (1.54773, <1e-04 ^***), triadic closure (0.51810, 0.06822+)	mutuality (1.69691, 0.00669 ^**)
7	TA	edges (−3.45125, <1e-04 ^*), mutuality (1.20579, 0.000859 ^), triadic closure (0.90554, 0.000117 ^**)	edges (1.62969, 0.055371+)
8	TA	edges (−3.23157, <1e-04 ^*), 11 grader outdegree (−1.81279, 0.0908+), mutuality (2.16172, <1e-04 ^*)	triadic closure (0.83281,0.0105+)
9	TA	edges (4.3701, < 1e-04 ^**), seating (0.4754, 0.02471 ^), non-white outdegree (0.8559, 0.00311 ^), mutuality (2.5804, < 1e-04 ^), triadic closure (1.2353, 0.00538 ^*)
23	TA	edges (−5.06002, <1e-04 ^**), non-white indegree (−0.83548, 0.014202 ^), non-white outdegree (1.58795, <1e-04 ^*), mutuality (1.38504, 0.001826 ^), triadic closure (1.40902, 0.000776 ^***)	edges (1.53861, 0.078322+), racial homophily ( −1.15963, 0.063901+), mutuality (1.46604, 0.048401 ^), triadic closure (0.58833, 0.032323 ^ )
24	TA	edges (−4.63762, <1e-04 ^*), gender homophily (0.87172, 0.00820 ^), 9th grader indegree (1.18034, 0.01947 ^), girl outdegree (0.68859, 0.03343 ^), triadic closure (0.95337, <1e-04 ^***)	triadic closure (1.33068, 0.00343 ^**)

Results of STERGM formation and persistence for SC classrooms_

Class	Type	Formation (estimate, p-value)	Persistence (estimate, p-value)
10	SC	edges (−3.94281, < 1e-04^**), gender homophily (−0.66842, 0.01785^), mutuality (2.35829, < 1e-04^*), triadic closure (0.69331, 0.00367^)
11	SC	edges (−4.3457168, <1e-04 ^*), mutuality (1.7479738,<1e-04 ^* ), triadic closure (1.0083759, 0.0231 ^*)	seating (2.2146689, 0.0740+)
12	SC	edges (−2.03702,0.03316 ^), mutuality (1.83455, 0.00444 ^*)	triadic closure (1.50379, 0.05099+)
13	SC	edges (−3.85863, < 1e-04^*), mutuality (1.57682, < 1e-04^), triadic closure (1.00728, 0.000146^**)	mutuality (3.11584, 0.001632^**)
14	SC	gender homophily (2.2956, 0.00223 ^*) girls outdegree (−1.8065, 0.01609 ^) seating (1.1260, 0.06051+)
15	SC	grade homophily (−2.7301, 0.0258 ^*)
16	SC	edges (−4.27543, <1e-04 ^**), grade homophily (1.77210, 0.0270 ^), mutuality (1.40598, 0.0450 ^*)	mutuality (2.71069, 0.0107 ^*)
17	SC	edges (−3.400596, < 1e-04 ^**), 11 grader indegree (−1.999271, 0.04689 ^), triadic closure (0.891412, 0.00687 ^**)
18	SC	edges (−3.93163, < 1e-04 ^**), seating (−0.77997, 0.031878 ^), mutuality (1.41718, 0.001916 ^*), triadic closure (0.97603, 0.035833 ^)	triadic closure (0.68382, 0.035833 ^*)
19	SC	edges (−4.02308, <1e-04 ^*), gender homophily (0.58180, 0.0784 +), mutuality (2.00926, <1e-04 ^) triadic closure (0.59734, 0.0108 ^)	gender homophily (1.64543, 0.0572+), mutuality (2.16391, 0.0440 ^*)
20	SC	edges (−1.05228, 0.0117 ^), girl outdegree (−0.84408, 0.0323 ^)
21	SC	edges (−3.86354, <1e-04 ^**), gender homophily (0.86038, 0.0128 ^), grade homophily (1.69354, <1e-04 ^***)
22	SC	edges (−3.549671, 0.000752 ^***), girl outdegree (1.532272, 0.064955 +)	grade homophily (−2.967090, 0.023639 ^*)

STERGM terms tested for the formation and for the persistence of ties_ Note that not all terms were tested for all networks due to size or other constraints (for instance, racial homophily could not be tested for white-only networks)_

Variables	STERGM term	Definition
Edges	edges	The number of edges in the network.
Mutuality	mutual	Probability of bidirectional edge to be formed or mantained
Homophily	nodematch	Probability of formation and persistence of edges within nodes sharing the same attribute (in this case, gender, race, and grade).
Seating proximity	edgecov(seating)	Sum of seating proximity for all edges in the network.
Triadic closure	gwesp.fixed.0.5	Geometrically weighted edge shared partners. Tests if students form (and keep) edges when they share many common friends.
In-degree	nodeifactor	Differences in in-degree by nodal attribute (in this case, gender, race, and grade).
Out-degree	nodeofactor	Differences in out-degree by nodal attribute (in this case, gender, race, and grade).

Network attributes changes_

Class	Type	n	e(S1)	e(S2)	Δ density	Δ mean dist.	Δ mean deg.	Δ centralization
1	TA	14	35	47	0,0659341	−0,146808	1,714286	0,051282
2	TA	14	64	96	0,152381	−0,323341	4,266667	0,0357142
3	TA	17	49	99	0,1838235	−0,93939	5,882354	0,1083334
4	TA	18	55	91	0,117647	−1,075059	3,999999	−0,03308823
5	TA	24	72	142	0,1268116	−0,765732	5,83333	0,04940714
6	TA	24	89	185	0,173913	−0,722117	8,000003	−0,04743086
7	TA	22	70	142	0,1558441	−1,420978	6,545454	0,07142858
8	TA	18	65	88	0,0751634	−0,283273	2,555556	0,0569852
9	TA	24	97	201	0,1884058	−0,744438	8,666667	0,0158103
10	SC	20	51	104	0,1394737	−0,493138	5,3	0,06871347
11	SC	18	67	131	0,2091504	−0,591145	7,111116	−0,0183823
12	SC	13	35	53	0,1153846	0,004831	2,769231	0,030303
13	SC	24	82	165	0,1503623	−1,26794	6,916667	0,01284585
14	SC	11	20	36	0,1454545	0,253086	2,909091	−0,0277777
15	SC	8	14	19	0,0892857	−0,209184	1,25	0,13095238
16	SC	16	50	54	0,0166667	0,463289	0,5	−0,0095238
17	SC	18	57	82	0,0816994	−0,608628	2,777778	0,0202206
18	SC	22	79	110	0,0670995	−0,898577	2,818182	0,0154762
19	SC	18	47	72	0,0816993	−0,281671	2,777778	−0,01286769
20	SC	15	41	77	0,1714286	−0,767532	4,800003	0,02472531
21	SC	26	70	96	0,04	−1,1696	2	0
22	SC	14	37	30	−0,038462	−0,637253	−1	−0,0673077
23	TA	19	77	121	0,128655	−0,32748	4,631577	0,0212418
24	TA	20	60	81	0,0552632	−0,826451	2,1	−0,001462

Network assortativity changes_

Class	Type	Δ gender assortativity	Δ race assortativity	Δ grade assortativity
1	TA	−0,12992152	−0,1138759	NA
2	TA	−0,2800093	−0,0044844	NA
3	TA	0,010200081	−0,27768636	NA
4	TA	0,07025436	0,0120824	NA
5	TA	−0,21661889	−0,0863014	NA
6	TA	−0,19435523	−0,28064122	NA
7	TA	−0,05244456	NA	−0,1888698
8	TA	−0,2323466	NA	0,01198873
9	TA	−0,14999934	−0,223815	NA
10	SC	−0,450792526	−0,4044041	NA
11	SC	−0,17527807	−0,059338	NA
12	SC	−0,1508002	−0,349391	−0,2033669
13	SC	−0,079262478	−0,4754838	NA
14	SC	0,2349064	NA	−0,8430588
15	SC	−0,5266441	NA	−0,74261296
16	SC	−0,1831539	NA	0,1267994
17	SC	−0,3295782	NA	−0,1149261
18	SC	−0,239163	NA	−0,0921452
19	SC	0,0296049	NA	−0,3941588
20	SC	−0,1588119	NA	NA
21	SC	−0,1311118	NA	−0,1616417
22	SC	0,13544486	NA	−0,2851677
23	TA	−0,006702639	−0,00981007	NA
24	TA	0,0101957	NA	−0,3874417

Descriptive characteristics of the classrooms studied, including the name of the class, aimed grade, seating type, number of respondents, number of missing longitudinal data, percentage non-white, percentage woman, and percentage not in the aimed grade level for the class_

Class	Name	Aimed grade	Type	Respondents	Missing	Non-white (%)	Woman (%)	Not in aimed level (%)
1	Biology	10th	TA	14	2	35,7	64,28	7,1
2	Biology	12th	TA	14	0	35,7	64,28	0
3	English	12th	TA	17	3	52,9	58,8	0
4	English	10th	TA	18	1	38,8	72,2	0
5	Trigonometry	10th	TA	24	1	37,5	54,1	0
6	English	10th	TA	24	3	41,6	54,1	0
7	Chemistry	10th	TA	22	1	0	50	18,1
8	Chemistry	10th	TA	18	0	5,5	50	5,5
9	AP English	12th	TA	24	1	37,5	79,1	0
10	Discrete Mathematics IB	12th	SC	20	2	55	55	0
11	Calculus IB	12th	SC	18	3	33,3	27,77	0
12	Algebra II	10th	SC	13	0	46,1	61,5	15,3
13	US History II IB	12th	SC	24	3	41,6	79,1	0
14	Precalculus	12th	SC	11	0	0	63,6	27,3
15	Precalculus	12th	SC	8	2	12,5	62,6	75
16	Biology II	12th	SC	16	0	5,5	68,7	31,2
17	Trigonometry	10th	SC	18	2	5,5	55,5	22,2
18	Chemistry	10th	SC	22	3	4,5	50	31,8
19	Physics	12th	SC	18	3	5,5	66,6	22,2
20	Calculus	12th	SC	15	1	6,6	60	0
21	Geometry	10th	SC	26	2	7,6	50	50
22	Algebra B	10th	SC	14	2	0	50	35,7
23	Biology	10th	TA	19	0	42,1	63,1	0
24	Geometry	10th	TA	20	1	0	45	45

The Role of Classroom Seating Arrangements in Friendship Formation and Persistence

Figures & Tables

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Figure 5:

Figure 4:

Results of STERGM formation and persistence for teacher-chosen classrooms_

Results of STERGM formation and persistence for SC classrooms_

STERGM terms tested for the formation and for the persistence of ties_ Note that not all terms were tested for all networks due to size or other constraints (for instance, racial homophily could not be tested for white-only networks)_

Network attributes changes_

Network assortativity changes_

Descriptive characteristics of the classrooms studied, including the name of the class, aimed grade, seating type, number of respondents, number of missing longitudinal data, percentage non-white, percentage woman, and percentage not in the aimed grade level for the class_

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