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It Takes Two Shining Lights to Brighten the Room: Peer Effects with Random Roommate Assignments

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Title: It Takes Two Shining Lights to Brighten the Room: Peer Effects with Random Roommate Assignments
Language: English
Authors: Zhang, Liang, Pu, Shi
Source: Education Economics. 2017 25(1):3-21.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 19
Publication Date: 2017
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: College Housing, Grades (Scholastic), Grade Point Average, College Freshmen, Interpersonal Relationship, Statistical Analysis, Gender Differences, Asians, Correlation, Foreign Countries, Academic Achievement, Peer Influence
Geographic Terms: China
DOI: 10.1080/09645292.2016.1203867
ISSN: 0964-5292
Abstract: We used housing assignment data from a college in China to investigate peer effects on college grades. Study results provided some evidence for peer effects in college housing units. First, peer effects through means occurred during both fall and spring semester of the first year in college, with estimated effect much larger than that in previous studies. Second, students are also influenced by the mix of roommates. Finally, having more than one roommate in the top quartile has large and significant effects for female students; however, this positive effect is not statistically significant for male students.
Abstractor: As Provided
Number of References: 33
Entry Date: 2016
Accession Number: EJ1122235
Database: ERIC
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  Value: <anid>AN0120040857;ede01feb.17;2019Feb20.14:06;v2.2.500</anid> <title id="AN0120040857-1">It takes two shining lights to brighten the room: peer effects with random roommate assignments. </title> <p>We used housing assignment data from a college in China to investigate peer effects on college grades. Study results provided some evidence for peer effects in college housing units. First, peer effects through means occurred during both fall and spring semester of the first year in college, with estimated effect much larger than that in previous studies. Second, students are also influenced by the mix of roommates. Finally, having more than one roommate in the top quartile has large and significant effects for female students; however, this positive effect is not statistically significant for male students.</p> <p>Keywords: College; peer effects; academic performance</p> <hd id="AN0120040857-2">1. Introduction</hd> <p>A substantial body of research has explored peer effects in education since the publication of the Coleman Report (Coleman et al. [<reflink idref="bib8" id="ref1">8</reflink>]). Although this literature is large and varied, at the core of the debate is whether students exert externalities onto their peers (Sacerdote [<reflink idref="bib28" id="ref2">28</reflink>]). In colleges and universities, peer effects have usually been investigated in housing units, perhaps because the organization of classes in higher education is loose and ad hoc in nature. Quite a few studies have used quasi-experimental strategies to estimate the effects of peers in the same housing unit on own academic and social outcomes. When college Grade Point Averages (GPAs) especially freshman year GPAs are used as the outcome, having roommates with high academic ability yields a positive albeit small effect (Carrell, Fullerton, and West [<reflink idref="bib5" id="ref3">5</reflink>]; Lyle [<reflink idref="bib19" id="ref4">19</reflink>]; Sacerdote [<reflink idref="bib27" id="ref5">27</reflink>]; Zimmerman [<reflink idref="bib33" id="ref6">33</reflink>]).</p> <p>In this study, we extend the literature on peer effects in higher education by using administrative data from a Chinese college to investigate effects of peer composition in quadruple rooms. In doing so, the current study expands and contributes to the literature in several important ways. First, most previous studies have used colleges in the United States as their empirical settings. It is not obvious whether their empirical findings could be generalized to other educational contexts. From a theoretical point of view, roommates matter because they spend more time together than with other students (Stinebrickner and Stinebrickner [<reflink idref="bib30" id="ref7">30</reflink>]); thus the strength of peer effects may well depend on the importance of roommates and residence life on collegiate experiences and vary considerably across national contexts. Studying peer effects in different nations could improve our understanding on the role of educational contexts within which peer effects take place.</p> <p>The Chinese context is interesting in several respects. For example, in many Chinese colleges, students live in designated residence zones on campus, and roommates spend an extensive amount of time together in studying and other activities. As a result, peer effects could be larger in Chinese colleges than in the United States. Chinese colleges are also unique in their admission process, which affects the distribution of student abilities within an institution. For example, in the United States, Scholastic Aptitude Test (SAT) scores are used in the college admission process as one of many factors including high school GPAs, class rank, and sometimes demographic and family characteristics. As a result, the distribution of SAT scores in a particular US college is quite dispersed. In China, however, students take the College Entrance Examination (CEE) at the end of their 12th grade, and the CEE scores are then used as the sole criterion for college admission. Not surprisingly, the range of CEE scores at any particular Chinese college is quite narrow, presenting a different empirical setting to study peer effects.</p> <p>Second, studies on roommate effects often rely on random assignment of students into rooms to identify peer effects. Unfortunately, the observational data on roommate assignment are rarely random; this clouds the generalizability of identified peer effects. In many cases students have the opportunity to 'choose' their future roommates by revealing their housing preferences, usually including the number of occupants in a room (i.e. single, double, etc.), smoker, preference regarding noise (i.e. listen to music while studying), neatness, and sleep patterns (i.e. night owl vs. early bird). Students are either matched based on these self-reported preferences (e.g. Zimmerman [<reflink idref="bib33" id="ref8">33</reflink>]) or pre-screened into a series of piles before randomly assigned into rooms within each pile (e.g. Sacerdote [<reflink idref="bib27" id="ref9">27</reflink>]). Prescreening effectively reduces the within-room variation in student preferences, although it is not clear whether more homogeneous peers would experience larger or smaller peer effects (Sacerdote [<reflink idref="bib28" id="ref10">28</reflink>]). Further, prescreening could also result in biased estimates for peer effects in that the impact of these shared preferences on academic performance becomes part of the estimates, in addition to any causal peer effects (Zimmerman [<reflink idref="bib33" id="ref11">33</reflink>]). In a few studies, random assignments without prescreening were used to estimate roommate effects (e.g. Stinebrickner and Stinebrickner [<reflink idref="bib30" id="ref12">30</reflink>]). The room assignment rule at our study site also did not involve prescreening students into different groups based on their revealed preferences. As a result, roommates in our sample are less homogenous in their living habits than students in many of US studies.[<reflink idref="bib1" id="ref13">1</reflink>] This setting helps to reveal how peer effects operate in less homogenous peer groups.</p> <p>Last but not least, dorm rooms on US college campuses are typically either doubles or triples. For example, in Sacerdote ([<reflink idref="bib27" id="ref14">27</reflink>]), 53% of freshmen in the final sample were in doubles and 44% were in triples. All students in the final sample in Zimmerman ([<reflink idref="bib33" id="ref15">33</reflink>]) lived in doubles. These particular room settings limit our understanding of the effect of peer composition in relatively large rooms, for example, quadruple occupancy rooms, where dynamics among roommates may be quite different than in smaller rooms. Other studies have used large groups to examine peer effects. For example, Carrell, Fullerton, and West ([<reflink idref="bib5" id="ref16">5</reflink>]) used squadrons of about 30 students at the United States Air Force Academy to examine the effect of peers' quality on own academic achievement. Peer composition is difficult to measure in such large groups.</p> <p>The quadruple rooms used in this study allowed the effect of roommate composition to emerge. We argue that the composition of the roommate mix, in addition to average roommate performance, might have significant peer effects on own academic performance. This cannot be done in double-occupancy rooms. This is important from a policy perspective because when peer effects operate through the composition of students, students may be rearranged to improve both individual and overall academic performance.</p> <hd id="AN0120040857-3">2. Peer effects in higher education</hd> <p>The study of peer effects dates back to Coleman ([<reflink idref="bib7" id="ref17">7</reflink>]) and recently has undergone a renaissance with works by Sacerdote ([<reflink idref="bib27" id="ref18">27</reflink>]), Zimmerman ([<reflink idref="bib33" id="ref19">33</reflink>]), Lyle ([<reflink idref="bib19" id="ref20">19</reflink>]), Ost ([<reflink idref="bib25" id="ref21">25</reflink>]), and Carrell, Sacerdote, and West ([<reflink idref="bib6" id="ref22">6</reflink>]). Sacerdote ([<reflink idref="bib28" id="ref23">28</reflink>]) conducted an excellent overview of peer effects in higher education. Not only were the results of peer effects important for academic and theoretical purposes, but they might also provide an effective and potentially free tool for colleges and universities to use in redesigning their residential housing assignment rules in ways that improve student academic and social outcomes. Since the literature on higher education is varied both in terms of outcome variables and definitions of peer groups, we focused our discussion on those studies most relevant to the current study, that is, peer effects of roommates on academic outcomes.[<reflink idref="bib2" id="ref24">2</reflink>]</p> <p>A number of studies used academic performance, including first-semester and first-year cumulative GPAs, as the outcome variables. These studies' findings were not totally unequivocal. While some studies demonstrated significant peer effects, these effects appeared to be small and moderated by a variety of factors. For example, Sacerdote ([<reflink idref="bib27" id="ref25">27</reflink>]) used a sample of freshmen at Dartmouth College to examine the effect of roommates' academic ability on own freshman year GPAs. Results suggested modest and statistically significant peer effects, especially when a student was assigned a roommate who was in the top 25% of academic ability; however, the peer effect from a roommate who was in the bottom 25% of academic ability was not statistically significant. The non-significant peer effect was probably due to the pool of high-ability students at Dartmouth, including those rated as in the bottom 25% of academic ability.</p> <p>Using freshmen from another highly selective private institution, Williams College, Zimmerman ([<reflink idref="bib33" id="ref26">33</reflink>]) found strong peer effects when evaluated using roommate's verbal SAT scores rather than math SAT scores. In addition, this peer effect was most pronounced for mid-range students who shared rooms with students who were in the bottom 15% of the verbal SAT distribution. There was also evidence that peer effects varied by fields of study and gender. Using roommate assignments data from an Italian university, Brunello, De Paola, and Scoppa ([<reflink idref="bib4" id="ref27">4</reflink>]) found marked differences among fields of study. While peer effects were positive and strong in the hard sciences, the effects in the social sciences and humanities were non-existent. In a study involving data from the University of Maryland, Foster ([<reflink idref="bib11" id="ref28">11</reflink>]) found no evidence of peer effects. Data from a Chinese college indicated stark differences by gender, according to Han and Li ([<reflink idref="bib13" id="ref29">13</reflink>]). In particular, female students were more likely to be influenced by their peers than their male counterparts. Taken together, these studies seem to provide rather limited evidence on peer effects when academic performance is used as the outcome variable. In cases in which peer effects are observed, they tend to occur to certain subgroups of students (McEwan and Soderberg [<reflink idref="bib22" id="ref30">22</reflink>]).</p> <hd id="AN0120040857-4">3. Empirical strategy</hd> <p>Estimating peer effects is not an easy task. As Sacerdote ([<reflink idref="bib29" id="ref31">29</reflink>]) noted, the formation of an individual's peer group is anything but random: parents spend considerable energy and money in choosing children's schools, so that they could have high-quality teachers and peers, and students tend to hang out with individuals with shared interests, for example, reading, playing video games, similar preference of food, etc. Given the considerable self-selection in the process of peer group formation, it is natural to expect that individuals within a peer group are more similar than individuals across peer groups. These similarities become the main confounder in peer effect studies: when we observe an academically competent friend increasing an individual's test scores (Sacerdote [<reflink idref="bib27" id="ref32">27</reflink>]; Zimmerman [<reflink idref="bib33" id="ref33">33</reflink>]), it is important to learn whether the effect is due to students' inclination to make friends with similar study habits and similar inherent ability, or due to peer tutoring, acquiring learning strategies from friends, being pressured to spend more time on study, etc. While the latter is the effect of peers from social interaction, the former is merely that birds of a feather flocking together.</p> <p>Mouw ([<reflink idref="bib23" id="ref34">23</reflink>]) and Sacerdote ([<reflink idref="bib29" id="ref35">29</reflink>]) provided thorough reviews of existing practices to disentangle peer effect from the inherent similarities within each peer group. In most cases, researchers have relied on an exogenous formation of peer group to eliminate selection bias. For example, Sacerdote ([<reflink idref="bib27" id="ref36">27</reflink>]) and Zimmerman ([<reflink idref="bib33" id="ref37">33</reflink>]) used randomly assigned roommates to study the effect of peer's academic quality on college students' first-year GPA. Duncan et al. ([<reflink idref="bib9" id="ref38">9</reflink>]) used the same setting to study peer effects on students' alcohol consumption. Lyle ([<reflink idref="bib19" id="ref39">19</reflink>]) utilizes the randomly formed company in West Point, which contain 35 students in each class, to study peer effects on GPA and major preference.</p> <p>The second popular strategy is to utilize the variation of student demographics characteristics, especially gender composition, across cohorts. The intuition is that adjacent cohort variation in demographics, for example gender, is not foreseeable by parents, thereby their choice of schools is not likely to be related to this cohort variation (Sacerdote [<reflink idref="bib29" id="ref40">29</reflink>]). Hoxby ([<reflink idref="bib14" id="ref41">14</reflink>]) is among the first studies that applied this strategy. Lavy and Schlosser ([<reflink idref="bib16" id="ref42">16</reflink>]) also used cohort gender variation to study peer effects in Israeli's primary and secondary schools. And Anelli and Peri ([<reflink idref="bib1" id="ref43">1</reflink>]) use gender variation between high school teaching classes in Milan, Italy, to study the effects of gender composition on students' choice of college majors. The last common practice to control peer group unobserved similarities is through peer group-level fixed effects. For example, Lin ([<reflink idref="bib18" id="ref44">18</reflink>]) used school-cohort fixed effects to control for school-level selection bias. Arcidiacono and Nicholson ([<reflink idref="bib2" id="ref45">2</reflink>]) use school fixed effects to eliminate across school sorting. Nanda and Sorensen ([<reflink idref="bib24" id="ref46">24</reflink>]) controlled firm fixed effects to eliminate employees' sorting across companies. Since our data provide students' housing information, we will use the first strategy to deal with selection bias.</p> <p>We used a similar estimating framework in studies on roommate peer effects (Han and Li [<reflink idref="bib13" id="ref47">13</reflink>]; Sacerdote [<reflink idref="bib27" id="ref48">27</reflink>]; Zimmerman [<reflink idref="bib33" id="ref49">33</reflink>]). Using double-occupancy rooms as an example, a student's own outcome (a student's GPA) is a function of her roommate's outcome , her own characteristics , and roommate' characteristics. As a mathematical notation:</p> <p>(<reflink idref="bib1" id="ref50">1</reflink>)</p> <p>Graph</p> <p>(<reflink idref="bib2" id="ref51">2</reflink>)</p> <p>Graph</p> <p>Equations (<reflink idref="bib1" id="ref52">1</reflink>) and (<reflink idref="bib2" id="ref53">2</reflink>), however, are subject to endogeneity bias, that is, the outcome of roommate is simultaneously determined by a similar equation that involves as an independent variable. This reflection problem (Manski [<reflink idref="bib21" id="ref54">21</reflink>]) could cause serious upward bias in the estimated effect of roommate outcomes on own outcomes. Therefore, we estimate the following reduced form equation after substituting out in Equation (<reflink idref="bib1" id="ref55">1</reflink>):</p> <p>(<reflink idref="bib3" id="ref56">3</reflink>)</p> <p>Graph</p> <p>Whenever the roommate size is greater than two, the average of roommates' characteristics is used instead, that is:</p> <p>(<reflink idref="bib4" id="ref57">4</reflink>)</p> <p>Graph</p> <p>The literature typically differentiates roommates' academic ability from other individual characteristics including gender, race/ethnicity, and major fields of study, assuming that peer effects operate through roommates' academic ability but not through other characteristics. Therefore, instead of using peers' every average quality, we focus on their average academic ability.[<reflink idref="bib3" id="ref58">3</reflink>]</p> <p>(<reflink idref="bib5" id="ref59">5</reflink>)</p> <p>Graph</p> <p>where represents the impact of roommates' academic ability on own academic performance, that is, peer effects.</p> <p>One feature of Equation (<reflink idref="bib5" id="ref60">5</reflink>) is that all peer effects operate through the mean of roommates' academic ability. In other words, the distribution of roommates' academic ability is not considered. Any mean-preserving transformation of roommates' academic ability has no effect on own academic performance. This empirical strategy might have precluded other types of peer effects based on the composition of roommates. Previous studies have examined peer effects beyond the mean of peers. For example, the bad apple model in Lazear ([<reflink idref="bib17" id="ref61">17</reflink>]) proposes that one disruptive student or the least able student in a class could hurt everyone in a class. The same might be true in the residential housing setting, where one low-ability or disruptive roommate might have a detrimental effect on everyone's academic performance. The opposite (i.e. the shining light model) might also work: one high-ability or hardworking student could set a good example for everyone in a room, hence improving their academic performance. Hoxby and Weingarth ([<reflink idref="bib15" id="ref62">15</reflink>]) provided an excellent discussion and empirical test of these varied models regarding the effect of race in classrooms. Lyle ([<reflink idref="bib20" id="ref63">20</reflink>]) used companies at West Point as peer groups and examined the effect of group heterogeneity on individual academic outcomes. Results suggested that more heterogeneous peer groups have positive effects on individual grades. The heterogeneity of large peer groups was typically measured by dispersion, for example, interquartile range in Lyle ([<reflink idref="bib20" id="ref64">20</reflink>]). The empirical setting of this study, discussed in the next section, provides an excellent opportunity to study peer effects beyond those operating through means in college housing units.</p> <p>For Equation (<reflink idref="bib5" id="ref65">5</reflink>) to yield unbiased estimates for , the usual ordinary least squares (OLS) assumptions apply. Specifically, the average academic ability of roommates should not be correlated with own error terms. For example, when a high-performing student shares a room with other high-ability students, a positive correlation between and will be created, resulting in an upward bias in estimated peer effects. The orthogonality condition can be satisfied when roommates are randomly assigned, that is, characteristics of roommates are not correlated with own idiosyncratic error terms. In some cases, because researchers possess information on student preference and assignment process, they may use covariate adjustment to eliminate potential bias caused by this non-random assignment (Rubin [<reflink idref="bib26" id="ref66">26</reflink>]). That is, the prevailing method in estimating roommate peer effects is based on conditional random assignment. In the next section, we discuss our data and test for conditional random assignment.</p> <hd id="AN0120040857-5">4. Data</hd> <p>We collected student-level administrative data from a 4-year, tier-two regional college located in southwest China.[<reflink idref="bib4" id="ref67">4</reflink>] The college mainly enrolls resident students from its host province, with approximately a quarter from other provinces in China. The data were from the freshman class of 2012, with an overall sample size of 2993 students from both science and humanity tracks[<reflink idref="bib5" id="ref68">5</reflink>] and 78% from the host province. For both groups from the host and other provinces, about 60% were on the humanity track and the rest were on the science track. The disaggregation of students between academic tracks and by province was important in this study because the admission criteria varied by these two factors.</p> <p>Students in our sample lived in 11 dorm buildings and a total of 782 quadruple or sextuple rooms, including 172 quadruples with three students, 587 fully occupied quadruples, 9 sextuples with five students, and 14 fully occupied sextuples. According to the Director of the Residence Life, these quadruples with three students and sextuples with five students might also be fully occupied, because it is possible that our data do not include all students who lived in these rooms. For example, one possibility is that students in more senior cohorts who lived with the freshmen are not included in the freshmen cohort data set; another possibility is that some freshmen dropped out by the end of the first year so that their records have been removed, which could be a potentially serious threat to the validity of our results if many students dropped out for academic reasons. However, additional administrative data requested from the college suggest that only 16 students dropped out during their first year in this college. The average CEE scores of these 16 students were 0.017 standard deviation above the average. Among these 16 students, only two dropped out due to poor academic performance; other students quit school due to health reasons (six students), to start up their own companies (three students), for family reasons (two students), to retake the CEE exam next year in the hope that they might obtain better scores (two students), and to study abroad (one student).</p> <p>Since we used students' CEE scores as a measure of their academic ability, a brief discussion of the exam and especially the distribution of CEE scores among our sample are in order. College admission in China is solely based on CEE scores. The exams differ for students on science and humanity tracks and sometimes vary by province. The vast majority of students take CEE just once on June 7–9 of their senior year in high school. Based on their test scores, an automated system matches students' college preferences with the availability of college seats in each college. Each admissible student (i.e. whose test score is above the admission threshold) is admitted into one and only one college, resulting in an unusually high matriculation rate. Only a very small proportion of admitted students choose not to enroll; they might choose to study abroad, not continue college education, or simply wait one more year and take the exam again. This highly regulated and uniform college admission process, although undesirable in many aspects, eliminates many confounding factors when CEE scores are used as a measure for student ability. For example, in the United States, students may re-take SAT/ACT tests to improve their scores; however, the probability of re-taking is related to a host of non-academic factors (Vigdor and Clotfelter [<reflink idref="bib31" id="ref69">31</reflink>]).</p> <p>Not surprisingly, this highly streamlined admission procedure results in a positively skewed distribution of CEE scores within any particular college. Since students from the host province constitute the majority of our sample, we use these students as an illustration. Figure 1 presents the distribution of CEE scores for all high school seniors in the host province who participated in CEE in June 2012 and the CEE scores of those who eventually enrolled in the college. In June 2012, slightly over 295,000 high school seniors took the CEE tests for the science track; their test scores ranged from 4 to 650, with 750 total possible points. The dotted line, using a left vertical axis, presents the distribution of CEE scores for these students. Those students who scored at least 445, which is equivalent to the 66th percentile of the entire distribution, are qualified for slots at tier-two colleges. (The tier-one threshold is 518 points or about the 90th percentile.) The solid line, using the right vertical axis, presents the distribution of CEE scores for the 898 science students in our sample. Not surprisingly, the majority of these students were concentrated within a relatively narrow range right above the tier-two threshold. For example, 95% of students in our college sample were between 445 points (i.e. 66th percentile in the population distribution) and 480 points (i.e. 80th percentile in the population distribution). Panel B presents distributions in the humanity track for over 220,000 students in the host province who took the CEE exam in June 2012 (dotted line) and the 1428 students who registered for the college. Similarly, 95% of students in our college sample ranged between 454 points (i.e. 84th percentile in the population distribution) and 496 points (i.e. 94th percentile in the population distribution). Since CEE tests differ by academic track and sometimes vary by province, we standardized the CEE score by academic track and province to make these scores comparable across provinces and tracks. The exclusive role of CEE scores in college admission in China and the relatively narrow range of student academic ability measured by CEE scores present a very different research context than in studies that use colleges and universities in the United States as their empirical context. In our study, the low-ability students are not far from the high-ability students.</p> <p>Graph: Figure 1. Distribution of CEE scores for high school seniors. Panel A: Students on the science track. Panel B: Students on the humanities track.</p> <p>Besides CEE scores, we also collected a variety of student-level information, including student background, room assignments, and academic performance in their first year in college. Students' background information included gender, minority status, and high school location (urban vs. rural). In addition, we identified the high school each student attended. We also obtained very detailed dormitory assignment information, including types of registration (online vs. onsite), time of registration with one-second accuracy, room types (triple, quadruples, quintuples). Student academic performance was measured by their GPAs in both fall and spring semester of the 2012–13 academic year. GPAs in this particular school are based on a 0–100 scale. Figure 2 presents the distribution of cumulative GPAs for first-year students in our sample, which had a mean of 75.75 and a standard deviation of 7.60. Finally, at this particular college, there are a total of 21 major fields of study. Students within the same major take very similar compulsory courses in their first year. To the extent that grade assignment rules may differ across majors, we used a series of dummies to account for major differences.</p> <p>Graph: Figure 2. Distribution of cumulative GPAs for first-year college students.</p> <hd id="AN0120040857-6">5. Room assignment</hd> <p>To gain a good understanding of the room assignment rule for this particular college, we engaged in extensive interviews with the Director of Residence Life at the college. We learned that the room assignment process followed two simple rules with minor twists. First, male and female students are placed into different buildings. Other than the obvious fact that this limits our study of peer effect to the same gender, it does not create any problems in terms of random assignments of roommates within each gender type. Second, students may choose to register early online or register onsite right before the academic year begins. For those who register online, the registration system offers eight random rooms (with building and room numbers) from which to choose. It is noteworthy that the registration system only randomly selects rooms from some but not all buildings. This information suggests that there might be differences across buildings. The Director of Residence Life also informed us that a software bug allows students to refresh screens to obtain more room selections if, for whatever reason, they are not happy with any of the eight rooms offered. This could be a potential source of non-random assignment because friends may be able to choose the same room if they spend time refreshing screens. To the extent that friends may share similar unobserved characteristics such as study habits, having them in the same room may give rise to biased estimates. For those who register onsite, available beds are queued (not randomly), and students are assigned to the next available bed when they register. This could be another potential source of non-random assignment because friends – whether they know this room assignment rule or not – are likely to register at the same time and thus increase the likelihood of being assigned to the same room. Once students are assigned to rooms, they remain in those rooms during their first year. In extremely rare cases, the college allows room changes.[<reflink idref="bib6" id="ref70">6</reflink>] Our interviews with the Director of Residence Life did not raise any other red flags about potentially non-random assignments. For example, unlike the common practice at US colleges and universities, students are not asked about preferences regarding rooms, smoking, noise, neatness, or sleep patterns.</p> <p>Before proceeding to the peer effects estimation, it is important to evaluate the potential impact of these room assignment rules on the random assignment of students in our sample. For the beginning class of 2012, the overall sample of 2993 students was from 820 high schools. The number of students from each high school was highly positively skewed, ranging from a low of 1 and high of 36, for an average of 3.65 students per high school. Among these students, about 45% registered online; the remaining 55% did so onsite. For both registration types, we obtained information on the time of their registration with one-second accuracy, allowing us to test several scenarios. The main concern here was that students who knew each other before coming to this college might be able to game the room assignment rules so that they could select the same room in the case of online registration or be assigned to the same room in the case of onsite registration. Unfortunately, we did not observe the personal relationships among students, so there was no way to directly verify whether friends were indeed more likely to be roommates. However, due to long school days in Chinese high schools and the prevalence of interpersonal relationships occurs within rather than between high schools, high schools can serve as a proxy for unobserved interpersonal relationships. In addition, because students from the same high school may share similar unobserved characteristics even if they are not friends, it is important to check whether students from the same high school are more likely to be roommates.</p> <p>Recall that our data included the name of the high school from which each student graduated. We conducted two tests using that information. In the first test, we sorted all students by their time of registration and checked whether students from the same high schools were likely to show up in pairs. Indeed, we observed quite a few students with the same high school identifier who registered within a couple of minutes of each other. This was especially true among students who registered online, confirming our earlier suspicion that students might be able to select their roommates by refreshing room selection screens. To formally test this pattern, we conducted a runs test to examine whether each of the 820 high school identifiers appeared randomly in the registration sequence. Among these 820 high schools, 330 had at least 2 female and/or 2 male students in our overall sample. The runs test was separately conducted for female and male students. Results indicated that 44 of these 330 high schools presented patterns of non-randomness at the 5% significance level, suggesting non-random appearances of students from the same high schools.</p> <p>In the second test, we simulated a process by randomly assigning all students into all beds in our data, again separated by gender. This simulation would tell us that under perfect random assignment, the number of rooms housing roommates from the same high schools. We repeated this simulation 3000 times[<reflink idref="bib7" id="ref71">7</reflink>]; results are presented in Figure 3. The simulation indicated that the number of rooms with roommates from the same high school ranged from 4 to 32, with a mean value of 15.4 and a standard deviation of 3.7. These results suggest that a perfect random assignment is highly unlikely to produce more than 26 rooms (i.e. 3 standard deviations above the mean) containing students from the same high schools. However, our real data contained 126 such rooms, suggesting that quite a few students might have gamed the room assignment rules. In other words, some students in these 126 rooms may not have been randomly assigned. Assuming that friends are similar in their study habits and academic performance, this creates a positive correlation between own academic performance and friends' characteristics. Consequently, we decided to drop those 126 rooms. This reduction resulted in a sample size of 2502 students in a total 656 rooms, including 153 quadruples with three students, 484 fully occupied quadruples, 7 sextuples with five students, and 12 fully occupied sextuples. Because we are interested in understanding how roommate composition affects own academic performance, having rooms of different sizes may complicate the analysis. For example, having two roommates in the top quartile means quite different between rooms with three and four roommates. In addition, it is possible that these quadruples with three students actually had a fourth roommate whose information was not available to us. Finally, as discussed above, because only two students dropped out college due to poor academic performance, removing those rooms with three students is not likely to create a sample selection problem. Therefore, for the main analyses in this paper, we focused on those 484 quadruple rooms, for a total of 1936 students. Table 1 reports descriptive statistics for this final sample of 1936 students. It is noteworthy that we have standardized both GPA data and CEE scores in this final analytic sample to make our results comparable to other studies.</p> <p>Graph: Figure 3. A simulation of number of rooms with roommates from the same high school.</p> <p>Table 1. Descriptive statistics for main variables.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Variable</td><td>Mean</td><td>SD</td></tr></thead><tbody><tr><td>First-semester GPA</td><td char=".">0</td><td char=".">1.000</td></tr><tr><td>Second-semester GPA</td><td char=".">0</td><td char=".">1.000</td></tr><tr><td>First-year GPA</td><td char=".">0</td><td char=".">1.000</td></tr><tr><td>CEE score</td><td char=".">0</td><td char=".">1.000</td></tr><tr><td>Roommates average CEE</td><td char=".">0.000</td><td char=".">0.579</td></tr><tr><td>Female</td><td char=".">0.661</td><td char=".">0.473</td></tr><tr><td>Humanities track</td><td char=".">0.608</td><td char=".">0.488</td></tr><tr><td>Minority</td><td char=".">0.025</td><td char=".">0.157</td></tr><tr><td>Host province</td><td char=".">0.760</td><td char=".">0.427</td></tr><tr><td>Online registration</td><td char=".">0.402</td><td char=".">0.491</td></tr><tr><td>Room size</td><td char=".">4</td><td char="." /></tr><tr><td>Sample size</td><td char=".">1936</td><td char="." /></tr></tbody></table> </ephtml> </p> <p>Once the final sample was determined, we conducted three additional tests to ascertain whether students in these rooms were indeed randomly assigned in terms of their academic ability conditional on several identified factors, including whether one registered online or not, registration sequence, and building. The inclusion of building is necessary because it accounts for the separation of males and females into separate buildings and selection of only certain buildings to accommodate those who registered online. In the first test, we examined whether a student's CEE score was related to the academic quality of his or her roommates. Table 2 shows that after controlling for registration type, registration sequence, and dorm building, a student's CEE score was not significantly related to the average CEE score for one's roommates. It also was not related to the distribution of the roommates' CEE within a room in terms of the number of roommates in the bottom and top quartiles. It is interesting to note that because male and female students were assigned into different buildings and because female students on average out-performed male students, there were significant differences in student academic performance across buildings. However, this difference largely reflected the gender difference in academic performance. In other words, these building fixed effects became small and statistically insignificant when examined separately for male and female students.</p> <p>Table 2. Relationship between own and roommates' CEE scores.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td></tr></thead><tbody><tr><td>Roommates avg. CEE</td><td>−0.0301</td><td /><td /><td /><td /></tr><tr><td>(0.0399)</td><td /><td /><td /><td /></tr><tr><td>1 Roommate in bottom 25%</td><td /><td>−0.0270</td><td /><td /><td /></tr><tr><td /><td>(0.0468)</td><td /><td /><td /></tr><tr><td>1 Roommate in top 25%</td><td /><td /><td>0.0453</td><td /><td /></tr><tr><td /><td /><td>(0.0462)</td><td /><td /></tr><tr><td>>1 Roommate in bottom 25%</td><td /><td /><td /><td>−0.00621</td><td /></tr><tr><td /><td /><td /><td>(0.0626)</td><td /></tr><tr><td>>1 Roommate in top 25%</td><td /><td /><td /><td /><td>−0.0338</td></tr><tr><td /><td /><td /><td /><td>(0.0625)</td></tr><tr><td>Register online</td><td>0.144</td><td>0.140</td><td>0.144</td><td>0.139</td><td>0.142</td></tr><tr><td>(0.102)</td><td>(0.101)</td><td>(0.101)</td><td>(0.102)</td><td>(0.101)</td></tr><tr><td>Register sequence (1000)</td><td>0.0376</td><td>0.0332</td><td>0.0354</td><td>0.0338</td><td>0.0351</td></tr><tr><td>(0.0609)</td><td>(0.0607)</td><td>(0.0607)</td><td>(0.0608)</td><td>(0.0607)</td></tr><tr><td>Building fixed effects</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td><italic>N</italic></td><td>1936</td><td>1936</td><td>1936</td><td>1936</td><td>1936</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.013</td><td>0.013</td><td>0.013</td><td>0.012</td><td>0.013</td></tr></tbody></table> </ephtml> </p> <p>Note: All models also include constant terms. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < .1.</p> <p>In the second test, we asked whether peer quality was related to own characteristics. To conduct this test, we used peer quality (i.e. roommates' average CEE) as the dependent variable and started with the set of controls (i.e. registration type, registration sequence, and building dummies) that we believed necessary to get as-good-as-random assignment. Then we added observed own characteristics one by one. Both a t-test and F-test were used to determine whether these individual characteristics explained peer quality. Results are reported in Table 3. Model 1 represents our minimum model in which known assignment rules were controlled. In subsequent models to which additional variables were added, none of these variables were statistically significant. Using Model 1 as the restricted model and each of the subsequent models as the unrestricted model, F-tests suggested these additional variables in various combinations do not explain the peer quality of one's roommates.</p> <p>Table 3. Relationship between peer quality and own characteristics.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td></tr></thead><tbody><tr><td>Std CEE</td><td>−0.00980</td><td>−0.0190</td><td>−0.0175</td><td>−0.0177</td><td>−0.0165</td></tr><tr><td>(0.0130)</td><td>(0.0149)</td><td>(0.0150)</td><td>(0.0150)</td><td>(0.0150)</td></tr><tr><td>Registration online</td><td>0.151**</td><td>0.150**</td><td>0.150**</td><td>0.150**</td><td>0.157**</td></tr><tr><td>(0.0579)</td><td>(0.0579)</td><td>(0.0579)</td><td>(0.0579)</td><td>(0.0585)</td></tr><tr><td>Host province</td><td /><td>0.0446</td><td>0.0419</td><td>0.0446</td><td>0.0434</td></tr><tr><td /><td>(0.0351)</td><td>(0.0352)</td><td>(0.0356)</td><td>(0.0358)</td></tr><tr><td>Humanities track</td><td /><td /><td>−0.0295</td><td>−0.0295</td><td>−0.0297</td></tr><tr><td /><td /><td>(0.0269)</td><td>(0.0269)</td><td>(0.0270)</td></tr><tr><td>Minority</td><td /><td /><td /><td>0.0466</td><td>0.0461</td></tr><tr><td /><td /><td /><td>(0.0834)</td><td>(0.0836)</td></tr><tr><td>Building fixed effects</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Registration sequence</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Major fixed effects</td><td /><td /><td /><td /><td>Yes</td></tr><tr><td><italic>N</italic></td><td>1936</td><td>1936</td><td>1936</td><td>1936</td><td>1936</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.040</td><td>0.041</td><td>0.042</td><td>0.042</td><td>0.053</td></tr><tr><td><italic>F</italic>-statistics</td><td /><td>2.004</td><td>2.005</td><td>1.336</td><td>1.086</td></tr><tr><td><italic>P</italic>-value</td><td /><td>0.157</td><td>0.135</td><td>0.261</td><td>0.352</td></tr></tbody></table> </ephtml> </p> <p>Note: All models also include constant terms. <emph>F</emph>-tests use Model 1 as the restricted model. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < .1.</p> <p>Lastly, because students in consecutive positions or close to each other in the registration sequence are likely to be roommates, we wondered whether students with similar academic quality would be registered about the same time. We treated students' CEE test scores as time series data and tested whether they were autocorrelated (Box, Jenkins, and Reinsel [<reflink idref="bib3" id="ref72">3</reflink>]). After controlling for gender and registration type, students' CEE scores were not significantly autocorrelated from lag 1 to lag 3 at the 5% level. (More lags up to 10 were not significant either. But because our room size was four, only the first three lags were meaningful in this study.) These three additional tests suggested that our final sample – conditional on registration types, sequence, and building – was as good as random assignment.</p> <hd id="AN0120040857-7">6. Peer effects</hd> <p>Table 4 presents our baseline model as in Equation (<reflink idref="bib5" id="ref73">5</reflink>), where a student's semester academic performance was regressed on his/her own CEE scores (and its square terms to control for possible non-linear relationship), roommates' average CEE, and a host of control variables including registration type, registration sequence, dorm building fixed effects, host province, humanities students, minority status, and college major fixed effects. In this table, these control variables were added to the model sequentially so that we could check for the robustness of peer effects for different specification. We estimated the same model by using fall semester GPA, spring semester GPA, and first-year cumulative GPA as dependent variables. It is important to note that because the treatment is applied at the room level and that within-room spillovers are almost inevitable, the standard errors in this and following tables are all clustered at the room level. In addition, since both GPA and CEE scores are standardized, the estimated coefficients reported here reflect the effect of an increase of one standard deviation in CEE scores on college GPA in terms of standard deviations.</p> <p>Table 4. Estimates of peer effects based on roommates' average CEE scores.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Fall Semester</td><td>(1)</td><td>(2)</td><td>(3)</td><td>(4)</td><td>(5)</td><td>(6)</td></tr></thead><tbody><tr><td>Std CEE</td><td>0.275***</td><td>0.246***</td><td>0.124***</td><td>0.137***</td><td>0.139***</td><td>0.138***</td></tr><tr><td>(0.0218)</td><td>(0.0191)</td><td>(0.0216)</td><td>(0.0215)</td><td>(0.0216)</td><td>(0.0218)</td></tr><tr><td>Std CEE squared</td><td>−0.0146</td><td>−0.0182+</td><td>−0.00239</td><td>0.00132</td><td>0.00150</td><td>0.000881</td></tr><tr><td>(0.0127)</td><td>(0.0111)</td><td>(0.0112)</td><td>(0.0119)</td><td>(0.0120)</td><td>(0.0122)</td></tr><tr><td>Roommates' avg. CEE</td><td>0.171***</td><td>0.0946*</td><td>0.0829*</td><td>0.0780*</td><td>0.0796*</td><td>0.0798*</td></tr><tr><td>(0.0470)</td><td>(0.0372)</td><td>(0.0354)</td><td>(0.0353)</td><td>(0.0351)</td><td>(0.0353)</td></tr><tr><td>Spring Semester</td></tr><tr><td>Std CEE</td><td>0.227***</td><td>0.201***</td><td>0.119***</td><td>0.127***</td><td>0.128***</td><td>0.128***</td></tr><tr><td>(0.0224)</td><td>(0.0187)</td><td>(0.0210)</td><td>(0.0212)</td><td>(0.0213)</td><td>(0.0210)</td></tr><tr><td>Std CEE squared</td><td>0.00395</td><td>−0.00204</td><td>0.00869</td><td>0.0111</td><td>0.0113</td><td>0.0117</td></tr><tr><td>(0.0118)</td><td>(0.00987)</td><td>(0.00951)</td><td>(0.00991)</td><td>(0.01000)</td><td>(0.0105)</td></tr><tr><td>Roommates' avg. CEE</td><td>0.141**</td><td>0.0835*</td><td>0.0756*</td><td>0.0723+</td><td>0.0736*</td><td>0.0728*</td></tr><tr><td>(0.0499)</td><td>(0.0383)</td><td>(0.0370)</td><td>(0.0369)</td><td>(0.0369)</td><td>(0.0355)</td></tr><tr><td>Cumulative</td></tr><tr><td>Std CEE</td><td>0.268***</td><td>0.239***</td><td>0.131***</td><td>0.142***</td><td>0.144***</td><td>0.144***</td></tr><tr><td>(0.0220)</td><td>(0.0183)</td><td>(0.0206)</td><td>(0.0207)</td><td>(0.0208)</td><td>(0.0209)</td></tr><tr><td>Std CEE squared</td><td>−0.00466</td><td>−0.0100</td><td>0.00401</td><td>0.00726</td><td>0.00743</td><td>0.00749</td></tr><tr><td>(0.0128)</td><td>(0.0109)</td><td>(0.0107)</td><td>(0.0112)</td><td>(0.0113)</td><td>(0.0118)</td></tr><tr><td>Roommates' avg. CEE</td><td>0.165***</td><td>0.0948*</td><td>0.0845*</td><td>0.0802*</td><td>0.0817*</td><td>0.0816*</td></tr><tr><td>(0.0495)</td><td>(0.0375)</td><td>(0.0357)</td><td>(0.0355)</td><td>(0.0355)</td><td>(0.0350)</td></tr><tr><td>Register online</td><td /><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Register sequence</td><td /><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Building fixed effects</td><td /><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Host province</td><td /><td /><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Humanities</td><td /><td /><td /><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Minorities</td><td /><td /><td /><td /><td>Yes</td><td>Yes</td></tr><tr><td>Major fixed effects</td><td /><td /><td /><td /><td /><td>Yes</td></tr></tbody></table> </ephtml> </p> <p>Note: Also included in models are constant terms. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < .1.</p> <p>We began in the first column by estimating a model that excluded those three random assignment conditions, that is, register on line, register sequence, and buildings. To the extent that student unobserved characteristics could vary along these conditions, the estimates of peer effects would be biased if these conditions were not controlled. As expected, there was a considerable drop in the estimated peer effects – from 0.171 to 0.095 standard deviation – once those three conditions were controlled in model 2. From model 2 to model 3, there is a noticeable jump in the coefficient of own CEE score, which is understandable in that CEE tests may vary across provinces. The estimates for peer effects, that is, the coefficients for roommates' average CEE, were fairly consistent across all five specifications from model 2 to model 6. Since even in the case of conditional random assignment, it is probably safer to control for variables that might affect academic performance, we used the last specification, that is, model 6, in our interpretation here. Results from model 6 indicated that the effect of student's own CEE scores was positive and significant, but the magnitude was modest at best. For one standard deviation increase in one's CEE score, the fall semester GPA increased by 0.14 standard deviation. Its effect on spring semester and cumulative GPAs were about the same. The square terms for CEE scores were mostly insignificant across all columns, except marginally significant at the.1 level in model 2. Roommates' average CEE had a positive and modest effect on own academic performance. One standard deviation increase in roommates' average CEE improved own fall semester GPA by 0.08 standard deviation, which was significant at the.05 level. The estimated effect was positive and similar in magnitude for both spring semester and cumulative GPA. Although the effect size (i.e. 0.08 standard deviation) was not large in an absolute sense, it was quite large when considering that the effect of own CEE on own GPA was only 0.14 standard deviation.</p> <p>In order to compare the magnitude of peer effects across studies, we calculated peer effects as a percentage of own ability effects because the magnitude of absolute peer effects may depend on the measurement of ability in different educational contexts. Our estimates suggested that the influence of roommates' average CEE score was about 60% as strong as that of own CEE scores, a magnitude very similar to Han and Li ([<reflink idref="bib13" id="ref74">13</reflink>]) who also used data from a Chinese college to study roommate effects. These effects seem to be much higher than estimates in other educational contexts. For example, Brunello, De Paola, and Scoppa ([<reflink idref="bib4" id="ref75">4</reflink>]) found that in hard sciences a one-point increase in own academic ability was associated with an increase of 0.203 point in college GPA, suggesting an effect size of 0.49 after adjusting for standard deviations. However, in terms of peer effects, the effect was about 0.096 standard deviation after adjusting for standard deviations, suggesting that the peer effect was about 20% of own ability effect. This relative magnitude is even lower in other studies. For example, Zimmerman ([<reflink idref="bib33" id="ref76">33</reflink>]) found that peer effect was approximately 5% of own ability effect, while Stinebrickner and Stinebrickner ([<reflink idref="bib30" id="ref77">30</reflink>]) found the percentage somewhere between 7% and 19% (Brunello, De Paola, and Scoppa [<reflink idref="bib4" id="ref78">4</reflink>]). The large variation in the relative magnitude of peer effects across countries seems to suggest the importance of educational contexts in determining peer effects.</p> <p>Table 5 uses model 6 in Table 4 as our preferred model and presents estimates separately for female and male students. Most findings from pooled models in Table 4 held true for these two subgroups although actual estimates differ slightly. For example, own GPAs were positively affected by own CEE scores, although the relationship seemed tighter for male than for female students. For example, when cumulative GPA is used as the outcome variable, the coefficient for own GPA is 0.185 standard deviation for male students and 0.113 standard deviation for female students, although the difference (<emph>t</emph> = 1.48) is not statistically significant. The main focus of our study, that is, the effects of roommates' average CEE on own GPAs, was very similar for female and male students – both around 0.08 standard deviation – although due to reduced sample sizes, coefficients for the female students are only significant at the.1 level, and the coefficients for male group was not statistically significant.</p> <p>Table 5. Estimates of peer effects based on roommates' average CEE scores, by gender.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Female students</td><td>Male students</td></tr><tr><td /><td>Fall</td><td>Spring</td><td>Cumulative</td><td>Fall</td><td>Spring</td><td>Cumulative</td></tr></thead><tbody><tr><td>Std CEE</td><td>0.0894***</td><td>0.117***</td><td>0.113***</td><td>0.221***</td><td>0.128**</td><td>0.185***</td></tr><tr><td>(0.0236)</td><td>(0.0231)</td><td>(0.0227)</td><td>(0.0421)</td><td>(0.0432)</td><td>(0.0419)</td></tr><tr><td>Std CEE squared</td><td>0.0145+</td><td>0.0246**</td><td>0.0217*</td><td>−0.0153</td><td>−0.00989</td><td>−0.0132</td></tr><tr><td>(0.00848)</td><td>(0.00922)</td><td>(0.00894)</td><td>(0.0228)</td><td>(0.0194)</td><td>(0.0221)</td></tr><tr><td>Roommates' avg. CEE</td><td>0.0710+</td><td>0.0757+</td><td>0.0788+</td><td>0.0816</td><td>0.0789</td><td>0.0863</td></tr><tr><td>(0.0420)</td><td>(0.0414)</td><td>(0.0405)</td><td>(0.0643)</td><td>(0.0698)</td><td>(0.0682)</td></tr><tr><td><italic>N</italic></td><td>1280</td><td>1280</td><td>1280</td><td>656</td><td>656</td><td>656</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.224</td><td>0.217</td><td>0.233</td><td>0.246</td><td>0.159</td><td>0.220</td></tr></tbody></table> </ephtml> </p> <p>Note: Also included in models are variables in the full model, that is, column 6 in Table 4. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < .1.</p> <p>To examine the peer effect beyond means, we added to our empirical models several variables describing the mix of roommates in each room. Table 6 reports estimates allowing peer effects to depend on this mix in terms of their CEE scores.[<reflink idref="bib8" id="ref79">8</reflink>] In the first specification, we counted the number of roommates whose CEE scores were in the bottom or top 25% of the overall sample. Results in the first column suggested that each additional roommate in the bottom 25% would decrease own fall semester GPA by about a 0.06 standard deviation, while each additional roommate in the top 25% would increase own fall semester by about a 0.10 standard deviation. These effects are quite large when considering that this specification also controlled for roommates' average CEE scores, suggesting that peer effects may operate beyond just means, that is, the mean-preserving transformation of roommates' academic ability may create additional effects. When spring semester GPAs were used as the dependent variables, these effects became smaller. Finally, when cumulative GPAs were used as the dependent variables, results showed an effect of –0.05 standard deviation although not statistically significant for each additional roommates in the bottom 25%, while the effect of having one additional roommate in the top 25% was about 0.08 standard deviation, which is significant at the.05 level.</p> <p>Table 6. Peer effects based on composition of roommates' CEE scores, reduced sample.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Fall semester</td><td>Spring semester</td><td>Cumulative</td></tr></thead><tbody><tr><td>Std CEE</td><td>0.124***</td><td>0.125***</td><td>0.119***</td><td>0.120***</td><td>0.132***</td><td>0.132***</td></tr><tr><td>(0.0217)</td><td>(0.0217)</td><td>(0.0209)</td><td>(0.0209)</td><td>(0.0207)</td><td>(0.0208)</td></tr><tr><td>Std CEE squared</td><td>−0.00242</td><td>−0.00175</td><td>0.00946</td><td>0.00976</td><td>0.00453</td><td>0.00503</td></tr><tr><td>(0.0115)</td><td>(0.0114)</td><td>(0.0101)</td><td>(0.0100)</td><td>(0.0112)</td><td>(0.0111)</td></tr><tr><td>Roommates' avg. CEE</td><td>−0.0596</td><td>−0.0520</td><td>−0.0139</td><td>−0.00713</td><td>−0.0368</td><td>−0.0288</td></tr><tr><td>(0.0610)</td><td>(0.0602)</td><td>(0.0633)</td><td>(0.0630)</td><td>(0.0614)</td><td>(0.0609)</td></tr><tr><td># RM in bottom 25%</td><td>−0.0645+</td><td /><td>−0.0320</td><td /><td>−0.0504</td><td /></tr><tr><td>(0.0388)</td><td /><td>(0.0361)</td><td /><td>(0.0370)</td><td /></tr><tr><td># RM in top 25%</td><td>0.0950*</td><td /><td>0.0665</td><td /><td>0.0846*</td><td /></tr><tr><td>(0.0378)</td><td /><td>(0.0407)</td><td /><td>(0.0385)</td><td /></tr><tr><td>1 RM in Bottom 25%</td><td /><td>−0.0492</td><td /><td>−0.0450</td><td /><td>−0.0503</td></tr><tr><td /><td>(0.0494)</td><td /><td>(0.0480)</td><td /><td>(0.0474)</td></tr><tr><td>>1 RM in bottom 25%</td><td /><td>−0.148+</td><td /><td>−0.0689</td><td /><td>−0.113</td></tr><tr><td /><td>(0.0813)</td><td /><td>(0.0794)</td><td /><td>(0.0794)</td></tr><tr><td>1 RM in Top 25%</td><td /><td>0.0349</td><td /><td>0.0384</td><td /><td>0.0383</td></tr><tr><td /><td>(0.0542)</td><td /><td>(0.0541)</td><td /><td>(0.0530)</td></tr><tr><td>>1 RM in Top 25%</td><td /><td>0.216**</td><td /><td>0.136</td><td /><td>0.184*</td></tr><tr><td /><td>(0.0775)</td><td /><td>(0.0855)</td><td /><td>(0.0793)</td></tr><tr><td><italic>N</italic></td><td>1936</td><td>1936</td><td>1936</td><td>1936</td><td>1936</td><td>1936</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.345</td><td>0.346</td><td>0.355</td><td>0.355</td><td>0.387</td><td>0.388</td></tr></tbody></table> </ephtml> </p> <p>Note: Also included in models are variables in the full model, that is, column 6 in Table 4. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < .1.</p> <p>In the second specification, we further relaxed the assumption of a linear relationship between the number of roommates in the bottom or top 25% and own GPAs by inserting dummy variables indicating different mixes of roommates' CEE scores. Compared with no roommate in the bottom 25%, having one roommate in the bottom 25% had a small and insignificant negative effect on own fall semester GPA; however, this negative effect was much larger at a 0.15 standard deviation when more than one roommate was in the bottom 25%. Only the estimate for more than one roommate in the bottom 25% is significant at the 0.1 level. The positive externality of roommates in the top 25% exhibited a similar pattern. Having one roommate in the top 25% did not seem to create positive externalities to own fall semester GPA, while this effect was much larger at 0.22 standard deviation and statistically significant when more than one roommate in the top 25% was present. When spring semester and first-year cumulative GPAs were used as dependent variables, the estimates appeared to be smaller and in most cases not statistically significant, except that having more than one roommate in the top 25% continued to have a large effect on one's first-year cumulative GPA.</p> <p>Finally, we repeated the estimates in Table 6 separately for female and male students. Results in the first column of Table 7 suggest that for female students, having each additional roommate in the bottom 25% had a small and insignificant negative effect on own GPA, while each additional roommate in the top 25% increased own GPA by 0.08 standard deviation. The non-linear specifications further indicated that having just one roommate in the bottom or top 25% did not seem to decrease or increase own GPA significantly; however, having more than one roommate in the top quartile resulted in rather large and statistically significant changes in own GPA for female students. For instance, having more than one roommate in the top quartile led to a more than 0.2 standard deviation improvement. Having more than one roommate in the bottom quartile had negative but statistically insignificant effects on own GPA. This result is probably due to the fact that students' CEE scores were positively skewed in our sample, so that students in the bottom quartile were not that different from their peers. Table 8 reports estimates for male students. None of the peer effects estimates was statistically significant.</p> <p>Table 7. Peer effects based on composition of roommates' CEE scores, female students.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Fall semester</td><td>Spring semester</td><td>Cumulative</td></tr></thead><tbody><tr><td>Std CEE</td><td>.0779**</td><td>.0785**</td><td>.109***</td><td>.109***</td><td>.103***</td><td>.103***</td></tr><tr><td>(0.0240)</td><td>(0.0239)</td><td>(0.0232)</td><td>(0.0232)</td><td>(0.0230)</td><td>(0.0229)</td></tr><tr><td>Std CEE squared</td><td>0.00910</td><td>0.0103</td><td>.0207*</td><td>.0215*</td><td>.0168+</td><td>.0179*</td></tr><tr><td>(0.00841)</td><td>(0.00824)</td><td>(0.00892)</td><td>(0.00888)</td><td>(0.00871)</td><td>(0.00861)</td></tr><tr><td>Roommates' avg. CEE</td><td>−0.0316</td><td>−0.0344</td><td>−0.00306</td><td>−0.0132</td><td>−0.0165</td><td>−0.0239</td></tr><tr><td>(0.0697)</td><td>(0.0704)</td><td>(0.0734)</td><td>(0.0741)</td><td>(0.0698)</td><td>(0.0706)</td></tr><tr><td># RM in Bottom 25%</td><td>−0.0350</td><td /><td>−0.00699</td><td /><td>−0.0208</td><td /></tr><tr><td>(0.0446)</td><td /><td>(0.0400)</td><td /><td>(0.0412)</td><td /></tr><tr><td># RM in top 25%</td><td>.0839*</td><td /><td>0.0808+</td><td /><td>.0876*</td><td /></tr><tr><td>(0.0426)</td><td /><td>(0.0471)</td><td /><td>(0.0437)</td><td /></tr><tr><td>1 RM in bottom 25%</td><td /><td>−0.00423</td><td /><td>−0.00220</td><td /><td>−0.00228</td></tr><tr><td /><td>(0.0544)</td><td /><td>(0.0535)</td><td /><td>(0.0524)</td></tr><tr><td>>1 RM in bottom 25%</td><td /><td>−0.104</td><td /><td>−0.0444</td><td /><td>−0.0763</td></tr><tr><td /><td>(0.0932)</td><td /><td>(0.0906)</td><td /><td>(0.0901)</td></tr><tr><td>1 RM in top 25%</td><td /><td>0.0180</td><td /><td>0.0418</td><td /><td>0.0322</td></tr><tr><td /><td>(0.0585)</td><td /><td>(0.0630)</td><td /><td>(0.0592)</td></tr><tr><td>>1 RM in Top 25%</td><td /><td>0.204*</td><td /><td>0.194+</td><td /><td>0.212*</td></tr><tr><td /><td>(0.0880)</td><td /><td>(0.0996)</td><td /><td>(0.0913)</td></tr><tr><td><italic>N</italic></td><td>1280</td><td>1280</td><td>1280</td><td>1280</td><td>1280</td><td>1280</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.199</td><td>0.202</td><td>0.206</td><td>0.208</td><td>0.213</td><td>0.215</td></tr></tbody></table> </ephtml> </p> <p>Note: Also included in models are variables in the full model, that is, column 6 in Table 4. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < .05. **<emph>p</emph> < .01. ***<emph>p</emph> < .001. +<emph>p</emph> < 0.1.</p> <p>Table 8. Peer effects based on composition of roommates' CEE scores, male students.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Fall semester</td><td>Spring semester</td><td>Cumulative</td></tr></thead><tbody><tr><td>Std CEE</td><td>.211***</td><td>.210***</td><td>.123**</td><td>.120**</td><td>.177***</td><td>.174***</td></tr><tr><td>(0.0414)</td><td>(0.0420)</td><td>(0.0427)</td><td>(0.0428)</td><td>(0.0412)</td><td>(0.0417)</td></tr><tr><td>Std CEE squared</td><td>−0.0162</td><td>−0.0165</td><td>−0.0109</td><td>−0.0116</td><td>−0.0142</td><td>−0.0148</td></tr><tr><td>(0.0222)</td><td>(0.0221)</td><td>(0.0189)</td><td>(0.0190)</td><td>(0.0215)</td><td>(0.0215)</td></tr><tr><td>Roommates' avg. CEE</td><td>−0.0351</td><td>−0.0344</td><td>0.0339</td><td>0.0562</td><td>0.00195</td><td>0.0160</td></tr><tr><td>(0.127)</td><td>(0.125)</td><td>(0.123)</td><td>(0.124)</td><td>(0.126)</td><td>(0.127)</td></tr><tr><td># RM in bottom 25%</td><td>−0.0713</td><td /><td>−0.0506</td><td /><td>−0.0663</td><td /></tr><tr><td>(0.0719)</td><td /><td>(0.0734)</td><td /><td>(0.0725)</td><td /></tr><tr><td># RM in top 25%</td><td>0.0580</td><td /><td>0.00101</td><td /><td>0.0283</td><td /></tr><tr><td>(0.0815)</td><td /><td>(0.0773)</td><td /><td>(0.0786)</td><td /></tr><tr><td>1 RM in bottom 25%</td><td /><td>−0.106</td><td /><td>−0.132</td><td /><td>−0.131</td></tr><tr><td /><td>(0.102)</td><td /><td>(0.0998)</td><td /><td>(0.0989)</td></tr><tr><td>>1 RM in bottom 25%</td><td /><td>−0.150</td><td /><td>−0.0735</td><td /><td>−0.119</td></tr><tr><td /><td>(0.146)</td><td /><td>(0.153)</td><td /><td>(0.149)</td></tr><tr><td>1 RM in top 25%</td><td /><td>0.0298</td><td /><td>−0.0125</td><td /><td>0.00565</td></tr><tr><td /><td>(0.119)</td><td /><td>(0.106)</td><td /><td>(0.113)</td></tr><tr><td>>1 RM in Top 25%</td><td /><td>0.141</td><td /><td>−0.0534</td><td /><td>0.0355</td></tr><tr><td /><td>(0.167)</td><td /><td>(0.160)</td><td /><td>(0.160)</td></tr><tr><td><italic>N</italic></td><td>656</td><td>656</td><td>656</td><td>656</td><td>656</td><td>656</td></tr><tr><td><italic>R</italic><sup>2</sup></td><td>0.246</td><td>0.247</td><td>0.160</td><td>0.162</td><td>0.221</td><td>0.222</td></tr></tbody></table> </ephtml> </p> <p>Note: Also included in models are variables in the full model, that is, column 6 in Table 4. Standard errors are clustered at the room level. Standard errors in parentheses. *<emph>p</emph> < 0.05. **<emph>p</emph> < 0.01. ***<emph>p</emph> < 0.001. +<emph>p</emph> < 0.1.</p> <p>The difference in peer effects by gender could be due to a couple of reasons. Firstly, male students in our sample underperform in CEE than female students. For example, only about 10% of male students live with two or more high achievers, while this proportion is 16% for female students. Combining with a smaller sample for male students, it is not surprising that we fail to detect any significant peer effects from the top 25% roommates for male students as we did for female students. The second possibility is that male students are less influenced by their peers than their female counterparts, at least in China. An earlier study by Han and Li ([<reflink idref="bib13" id="ref80">13</reflink>]) had evidenced similar gender difference in Chinese students' academic performance and decision to join the Chinese Communist Party.</p> <p>As a robustness check, we re-estimated peer effects in Tables 4–8 by including those students who were from the same high schools, which increased our final sample size from 1936 to 2348. This set of analyses, however, yielded similar results as reported in this paper. These results are available upon request. Since it is important in principle to eliminate potential self-selection into rooms, we chose to exclude these students from our final sample.</p> <hd id="AN0120040857-8">7. Concluding remarks</hd> <p>It is important to note some limitations of this study. Studies on peer effects almost always focused on single institutions because they provided detailed administrative data that are critical in estimating peer effects. Our study is not an exception in that regard. Although our analysis provides some evidence for peer effects in college housing units at a single institution, these effects could be stronger or weaker in other colleges in China. For example, the college in our study is moderate in college selectivity, with the vast majority of students in this college having test scores around 70–80th percentile. Students in colleges that are less or more selective may experience quite different peer influences. In addition, being in a regional college means many students still have strong family ties while in college, which is very different from students in national colleges where students spend more time hence exert stronger influences on each other. In other words, our results may not be extended to all colleges in China, although we feel that the college in this study represents a large group of colleges with moderate selectivity.</p> <p>With these limitations in mind, we summarize our main findings and provide some policy implications. In this study, we used housing assignment data from a Chinese college to investigate peer effects on college grades. One of the strengths of this study is the rich administrative data we collected on roommate assignment in this particular college, which allowed us to test several scenarios of non-random housing assignment. We argued, based on extensive interviews with the Director of Residence Life of this college and after rigorous tests using available data, that housing assignment is random, conditional on several known variables, which renders great confidence in our estimates of peer effects. In addition, the quadruple room setting provided a unique setting for the investigation of roommate mix.</p> <p>Study results provided some evidence for peer effects in college housing units. First, peer effects through means occurred during both fall and spring semesters of the first year in college, suggesting peer effects at the very beginning of students' college life. In particular, a one standard deviation increase in roommates' average college entrance exam scores improved individual GPAs by a 0.08 standard deviation, which was about 60% as strong as that of own CEE scores. Although the estimated effects in this study were not large in absolute terms, they were quite large when compared with the effect of own CEE scores on college GPAs. The relative magnitude of peer effects reported in this study is much larger than in studies based on US data (e.g. Sacerdote [<reflink idref="bib28" id="ref81">28</reflink>]) and Italy (Brunello, De Paola, and Scoppa [<reflink idref="bib4" id="ref82">4</reflink>]), but is similar to results from China (e.g. Han and Li [<reflink idref="bib13" id="ref83">13</reflink>]) and South Africa (Garlick [<reflink idref="bib12" id="ref84">12</reflink>]). Although we were not able to identify reasons for these differences based on our data, future research should examine cross-country variations in the relationship between admission tests and academic performance in college. Further, whether peer effects persist into later years was not clear, as students go through the initial transitional period in college and interpersonal relationships (and hence peer effects) quickly extend beyond the boundaries of their dorm rooms. We are currently examining data on students' academic performance and major choices in subsequent years.</p> <p>Second, this study also investigated the ways in which peer heterogeneity affects academic outcomes in a quadruple room setting. Several previous studies used small-size residence rooms (e.g. double-occupancy rooms) and were not able to examine the effect of roommate composition on academic outcomes. Our results suggested that students are also influenced by the mix of roommates, suggesting that mean-preserving transformations of roommates' academic ability would have effects on students' academic performance. In fact, once roommate composition was considered in models, roommate means were never statistically significant. These results are consistent with Lyle ([<reflink idref="bib20" id="ref85">20</reflink>]), who found strong peer heterogeneity effects in large-size groups of around 30. The effect of peer composition appeared to be more pronounced for female than for male students, which echoes Han and Li ([<reflink idref="bib13" id="ref86">13</reflink>]) who found that female students were more likely to be influenced by their peers than their male counterparts.</p> <p>Finally, having more than one roommate in the bottom or top quartile had large and significant peer effects, especially for female students. Sacerdote ([<reflink idref="bib27" id="ref87">27</reflink>]) found that in doubles and triples, having a roommate in the top quartile of admission scores raised own freshmen year GPA by 0.06 point. Our results suggested that having one roommate in the top quartile in quadruples did not raise the student's GPA; instead, the positive effects of having more than one roommate in the top quartiles suggested some sort of tipping point for peer effects. That is, a minor proportion (e.g. 1 in 4) of roommates in the bottom or top quartile did not exert significant externality to other roommates; however, when the proportion reached half (e.g. 2 in 4) or higher, peer effects more than doubled. These findings extend the shining light model proposed and tested in the literature (e.g. Hoxby and Weingarth [<reflink idref="bib15" id="ref88">15</reflink>]). In other words, one single excellent student in a relative large residence room may not benefit everyone. It takes two shining lights to brighten the room in the context of quadruple residence rooms. Future research could look at whether this tipping point phenomenon holds when the size of peer groups increases, that is, are a larger number of excellent students needed to exert positive peer influences in a larger peer group?</p> <p>Results of this study have some policy implications for college housing assignments. The traditional model of peer effects shown in Equation (<reflink idref="bib5" id="ref89">5</reflink>) assumes that peer effects operate through means. Under this model, the externality of each student to other students is fixed and does not depend on his or her roommates or room sizes. As such, any rearrangement of students would not improve the collective academic performance of all students, that is, a zero sum game. However, when peer effects operate through the composition of students, students may be reallocated to improve both individual and overall academic performance. One straightforward implication of our results is not to put two or more low-performing students in the same room. In contrast, we may wish to assign high-performing students in pairs into the same room to create positive externality for other roommates. This may be controversial, however, because it potentially raises a fairness concern.</p> <hd id="AN0120040857-9">Disclosure statement</hd> <p>No potential conflict of interest was reported by the authors.</p> <ref id="AN0120040857-10"> <title> Notes </title> <blist> <bibl id="bib1" idref="ref13" type="bt">1</bibl> <bibtext> Though the students are not assigned based on revealed living habits, they are assigned to their registration type, time, and available building upon their registration. We control all these conditions to avoid possible hidden similarities between students sharing similar registration pattern. In addition, our data collection and field work suggested that in some cases our random assignment process is not entirely clear-cut. For example, friends may compromise the random assignment process by registering—intentionally or unintentionally—at approximately the same time. We remedy this by deleting possible self-selected roommates which are identified through detailed students' background information and registration process information.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref24" type="bt">2</bibl> <bibtext> Studies have also examined peer effects of roommates on social outcomes including drinking, smoking, and joining fraternity (Eisenberg, Golberstein, and Whitlock [10]; Sacerdote [27]; Wilson [32]).</bibtext> </blist> <blist> <bibl id="bib3" idref="ref56" type="bt">3</bibl> <bibtext> We use a students' College Entrance Exam score as a measurement of academic ability. The College Entrance Exam is a standard test for high school seniors before they enter college. A detailed description is provided in the data session.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref27" type="bt">4</bibl> <bibtext> In China's higher education system, over 2100 colleges and universities are broadly grouped into four tiers based on academic reputation and admission selectivity. The first tier, located at the top of the higher education hierarchy, consists of approximately 120 key national colleges and universities. These institutions attract top students nationally. The next tier consists of well-known regional colleges and universities, who also attract students from other provinces. The third tier becomes more regional focused. And the last group consists of a large number of sub-baccalaureate institutions.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref3" type="bt">5</bibl> <bibtext> High school students select between Science and Humanity tracks in their 11th grade. 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  Label: Title
  Group: Ti
  Data: It Takes Two Shining Lights to Brighten the Room: Peer Effects with Random Roommate Assignments
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Liang%22">Zhang, Liang</searchLink><br /><searchLink fieldCode="AR" term="%22Pu%2C+Shi%22">Pu, Shi</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Education+Economics%22"><i>Education Economics</i></searchLink>. 2017 25(1):3-21.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
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  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 19
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2017
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Higher+Education%22">Higher Education</searchLink><br /><searchLink fieldCode="EL" term="%22Postsecondary+Education%22">Postsecondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22College+Housing%22">College Housing</searchLink><br /><searchLink fieldCode="DE" term="%22Grades+%28Scholastic%29%22">Grades (Scholastic)</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+Point+Average%22">Grade Point Average</searchLink><br /><searchLink fieldCode="DE" term="%22College+Freshmen%22">College Freshmen</searchLink><br /><searchLink fieldCode="DE" term="%22Interpersonal+Relationship%22">Interpersonal Relationship</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Analysis%22">Statistical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Gender+Differences%22">Gender Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Asians%22">Asians</searchLink><br /><searchLink fieldCode="DE" term="%22Correlation%22">Correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Academic+Achievement%22">Academic Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Peer+Influence%22">Peer Influence</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22China%22">China</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/09645292.2016.1203867
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0964-5292
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We used housing assignment data from a college in China to investigate peer effects on college grades. Study results provided some evidence for peer effects in college housing units. First, peer effects through means occurred during both fall and spring semester of the first year in college, with estimated effect much larger than that in previous studies. Second, students are also influenced by the mix of roommates. Finally, having more than one roommate in the top quartile has large and significant effects for female students; however, this positive effect is not statistically significant for male students.
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  Label: Abstractor
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  Data: As Provided
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  Data: 33
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2016
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  Label: Accession Number
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  Data: EJ1122235
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        Value: 10.1080/09645292.2016.1203867
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
        StartPage: 3
    Subjects:
      – SubjectFull: College Housing
        Type: general
      – SubjectFull: Grades (Scholastic)
        Type: general
      – SubjectFull: Grade Point Average
        Type: general
      – SubjectFull: College Freshmen
        Type: general
      – SubjectFull: Interpersonal Relationship
        Type: general
      – SubjectFull: Statistical Analysis
        Type: general
      – SubjectFull: Gender Differences
        Type: general
      – SubjectFull: Asians
        Type: general
      – SubjectFull: Correlation
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      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Academic Achievement
        Type: general
      – SubjectFull: Peer Influence
        Type: general
      – SubjectFull: China
        Type: general
    Titles:
      – TitleFull: It Takes Two Shining Lights to Brighten the Room: Peer Effects with Random Roommate Assignments
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            NameFull: Zhang, Liang
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            NameFull: Pu, Shi
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            – TitleFull: Education Economics
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