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Supplemental TextAdditional Details on MethodRecruitment and Survey ProcedureHere we provide additional details regarding the description of the recruitment and survey procedure given in the manuscript text. 2,267 students from six high school × cohort groups were recruited during the fall semester of their senior year (2012-2013 academic year for cohort 1 and 2013-2014 for cohort 2). These represented five district high schools in Pennsylvania and Massachusetts, as one high school participated in both cohorts. Each student’s family received a letter from their school principal describing the study along with an opt-out parent consent form. Students whose parents did not sign and return the opt-out form completed assent forms prior to data collection. The sample size reflects the maximum number of students that it was possible to recruit within the allotted time provided by the schools.All students and schools consented to baseline data collection. 94% (N=2,135) of students (hereafter called the original sample) from five high school × cohort groups additionally agreed to have their college outcomes tracked for six years and had available outcome data. 90% of those who did not consent to outcome tracking were from a single high school × cohort group. See Table S1.Students were surveyed once between November and April of their senior year of high school on school computers. Students at different schools completed the survey at different times due to differences in class schedules and in the timing of study approval by school administrators, as well as due to logistical constraints of staff who had to oversee data collection in two states. The survey contained a wide range of social, educational, and personality psychology scales, of which we examine three (see Baseline Measures section). Demographic and academic performance data, including report card grades, statewide standardized test scores, and SAT scores, were obtained from administrative records provided by students’ high schools.ParticipantsSamples. Participants came from one of four high schools and two cohorts. The first cohort graduated from one of four high schools in spring 2013 and could be tracked for six years (12 college semesters). The second cohort, representing one of the schools in the first cohort, graduated in spring 2014 and could be tracked for five years (10 college semesters). The primary analytic sample (hereafter called the analytic sample) had non-missing data for all covariates used in regression analyses: belonging certainty, growth mindset, grit, gender, historically marginalized ethnicity, free and reduced lunch status, grade 10/11 math and reading state standardized test scores, and grade 12 GPA. It consisted of 1850 participants (87% of the original sample). Representation from each high school × cohort group in the analytic full sample ranged in size from 128 students to 567 students. Comparison of original and analytic full samples. Descriptive statistics for the original sample (N=2,135) and analytic sample (N=1,850) on student psychological, demographic, and academic factors measured in high school are shown in Table S2. In general descriptive statistics are similar for the two samples, suggesting data is missing at random.Baseline characteristics of the analytic sample. The sample was highly diverse and included large numbers of both underrepresented racial-minority students and first-generation college students. In the analytic sample (N=1,850), 48% were male. 43% were from a historically marginalized racial-ethnic group (Black, Latino/a, or other Non-White or Asian). 56% were on free and reduced lunch status during high school, a higher proportion than the statewide average at the time of the study (38.3% for Pennsylvania and 43.6% in Massachusetts in 2013-2014). Generation status was available for 74% of the analytic sample (N=1,367; it was unavailable for one high school × cohort group); of these, 62% self-reported being first-generation—they did not have a parent who completed college. Students’ scores on statewide standardized tests administered in Grade 10 or 11 were slightly above average for their respective states in standard deviation units (Math: M=0.25, SD=1.00; Reading: M=0.08, SD=0.91). The average Grade 12 GPA was 2.8 on a 4-point scale (SD=0.81); it was 0.08 (SD=0.97) in standard deviation units computed using the mean and standard deviation of the original 2135-person sample. 63% of the primary sample (N=1,159) had SAT scores. Among these students, the average SAT Critical Reading score in national percentile units was 38.5 (SD=25.5). The average SAT Math percentile score was 44.5 (SD=26.8). These baseline characteristics were similar in the original sample (see Table S2).Number and levels of colleges attended. Individuals in the analytic sample (N=1,850) enrolled in one or more of 313 different 2- or 4-year colleges (82% 4-year colleges) at some point during the six years (12 college semesters) after high school. They first enrolled in one of 238 different colleges (84% 4-year colleges). Individuals in the original sample (N=2,135) enrolled in 339 different colleges (82% 4-year colleges) in the six years after high school and first enrolled in one of 256 colleges (82% 4-year colleges).Participant flow through the college pipeline in the analytic sample. As indicated in the manuscript text, the focal outcomes were enrollment, on-track progress, and on-time graduation. In the analytic sample (N=1,850), 20% never enrolled in college during the study period, 15% enrolled after semester 1, and 65% enrolled in semester 1. 38% of the sample (47% of those who ever enrolled) achieved on-track progress at 2- or 4-year college by remaining consecutively full-time enrolled for their first four semesters of college. 24% of the sample (30% of those who ever enrolled) earned an Associate’s or Bachelor’s degree within 100% time of starting college. These raw outcome attainment rates were similar in the original sample (N=2,135). Baseline High School Measures Psychological factors. Here we provide the full scales for the three psychological factors we used in regression analyses.Belonging Certainty. Belonging uncertainty was measured with three negatively valenced items (“Sometimes I worry that I will not belong in college.”; “I am anxious that I will not fit in at college.”; “When I face difficulties in high school, I wonder if I will really fit in when I get to college.”), and one positively valenced item (“I feel confident that I will belong in college.”) (Yeager, Walton et al., 2016; see also Walton & Cohen, 2007). Students self-reported the extent to which the statements were true for them: 1(Not at all true) to 5(Completely true). This is a broader measure of belonging uncertainty than assessments focused on belonging at a specific institution that have been used in past research (e.g., Walton & Cohen, 2007). The three negatively valenced items were reverse scored before being averaged with the other item, so the construct would be positively valenced like the two other psychological factors. Cronbach’s alpha for the scale was 0.79. The average belonging certainty score in the analytic sample was 3.77 (SD=0.96). Growth Mindset. Growth mindset of intelligence was measured with three items (“You have a certain amount of intelligence, and you really can't do much to change it.”; “Your intelligence is something about you that you can't change very much.”; “You can learn new things, but you can't really change your basic intelligence.”) (Dweck, 2000). These items were negatively valenced as this has been shown to produce greater variation in scores. Students reported the extent to which they agreed with each statement: 1(Strongly agree) to 6(Strongly disagree). Before analysis, the items were reverse-scored so that higher levels would reflect the underlying positively valenced construct of growth mindset versus fixed mindset. Cronbach’s alpha for the scale was 0.79. The average growth mindset score in the analytic sample was 4.29 (SD=1.20).Grit. Grit was measured with four positively valenced items (“I finish whatever I begin.”; “I work very hard. I keep working when others stop to take a break.”; “I stay interested in my goals, even if they take a long time (months or years) to complete.”; “I am diligent. I never give up.”) (Duckworth & Quinn, 2009). Students self-reported the extent to which the statements were like them: 1(Not at like me) to 5(Very much like me). Higher scores indicate higher levels of grit. Cronbach’s alpha for the scale was 0.77. The average grit score in the analytic sample was 3.81 (SD=0.73).Demographic and academic factors. Here we provide more detail on some of the demographic and academic measures than was possible to provide in the manuscript text.Race-Ethnicity. Participants had one of five ethnicities: Asian, Black, Latino/a, White, and Other Non-White. To preserve as much data as possible, especially for analyses involving interactions, we condensed this into a single dichotomous variable, defined as 0 if the student was a member of an ethnic group that did not face pervasive negative intellectual stereotypes (White or Asian) and 1 if the student was a member of an ethnic group that did (Black, Latino/a, and other Non-White), following past research (Yeager, Walton, et al., 2016). We refer to the latter group as having a historically marginalized ethnicity.Grade 10/11 State Standardized Test Scores. We used statewide standardized test scores as a measure of academic preparation because only 63% of our sample had SAT scores and analyses sought to track students’ postsecondary experiences whether or not they had taken the SAT. Partner high schools provided continuous standardized test scores that students completed as part of statewide assessments in Grade 10 (cohort 1) or Grade 11 (cohort 2). Scores were from the Massachusetts Comprehensive Assessment System (Massachusetts schools), the Pennsylvania System of School Assessment (cohort 1 Pennsylvania schools), or the Pennsylvania Keystone Exams (cohort 2 Pennsylvania schools). We used scores from the Reading/English Language Arts and Math sections. We constructed variables in standardized units using the statewide mean and standard deviation for a given subject test, separately for each state and cohort. Grade 12 GPA. All schools provided students’ GPA in the last year of high school, grade 12. The schools used different metrics for GPA: a 4-point scale, a 5-point scale, and a 100-point scale. The final variable for regression analyses was a standardized variable that standardized each participant’s raw GPA using the mean and standard deviation for the 2,135-person sample within each student’s high school cohort group. We also converted each school’s GPA to a 4-point scale, for purposes of descriptive statistics.Pairwise correlations among baseline factors. Pearson’s pairwise correlations among the nine high school student factors used in regression analyses are shown in Table S3 for the analytic sample. Belonging certainty was positively correlated with both growth mindset, rP=.184, p<.001, and grit, rP=.271, p<.001. Growth mindset was weakly positively correlated with grit, rP=.105, p<.001. These correlations were similar for the original sample (N=2,135).Student College Outcome DataStudents’ college outcome data was obtained from the National Student Clearinghouse (NSC; ). The raw data contained a row for each term in which a student was enrolled in college, including the start date, end date, college name, college level, and enrollment intensity (e.g., full-time, half-time) for that term, among other information. STATA code was developed to generate additional variables from the raw NSC data, namely those pertaining to enrollment, persistence, and graduation outcomes. Term enrollment data was obtained from the NSC on November 20, 2019. Thus students could be tracked for up to six years after their high school graduation in spring 2013 or 2014. Below we define key terms which we used to construct college outcomes from NSC data.Semester. Since the colleges in the dataset had varying calendar systems, we defined a uniform system for clocking enrollment in and progress through college. We defined spring terms as those that began during the months of January through April; summer terms as those that began during the months of May through July; and fall terms as those that began during the months of August through December. We excluded summer terms from analysis, because we were primarily interested in enrollment and persistence during the 9-month academic year, and enrollment during the summer does not necessarily signal on-track progress to earning a degree (similarly, a failure to enroll during the summer would not necessarily indicate a student was off track). For simplicity, we henceforth refer to fall and spring terms as fall and spring semesters. We started the clock in the fall semester after each cohort’s spring high school graduation and called it semester 1. The following spring semester was designated semester 2. We were able to track students for up to 12 of such college semesters.Term length. Within the months designated for each fall and spring semester, we summed the total number of weeks students completed at a given college level (2- or 4-year), using a student’s NSC-reported enrollment begin and end date for each term at that level. If the student completed only one term during a given semester, the term length was the difference between the enrollment end date and the enrollment begin date for that term, in weeks. If the student completed more than one term during a given semester, the term length was the sum total weeks of all terms completed within the semester. If a term that began in a given semester had an end date after the semester, we defined weeks enrolled as the difference between the enrollment begin date and the last date of the period we defined for each semester (12/31 for fall semesters and 4/30 for spring semesters). We defined two term lengths. A 1-week-minimum term refers to a term of at least 1 week (the time between the enrollment begin and end dates was at least 1 week) that started during the months we designated as fall or spring. 99.9% of all terms in the NSC dataset met this criteria (M=14.41 weeks, SD=2.99, Min=1.00, Max=21.71). A 12-week-minimum term refers to a term of at least 12 weeks in length that started during the months we designated as fall or spring. We chose 12 weeks to adequately capture meaningful attendance at colleges with varying term start and end dates. 88.2% of all terms fit this definition (M=15.34 weeks, SD=0.91, Min=12, Max=21.71). Enrollment intensity. The NSC provided eight different enrollment intensities for a given term: A=Absent, W=Withdrawn, D=Deceased, G=Graduate, L=less than half-time enrolled, H=half-time enrolled, Q=Three-quarter-time enrolled, F=full-time enrolled. We condensed these into two. Any intensity reflected an enrollment intensity that was full-time, part-time (quarter, half-time, or three-quarter time), or missing (7.6% of all colleges in the dataset did not report enrollment intensity to NSC). That is, whenever enrollment intensity was not explicitly defined as absent, withdrawn, deceased, or a graduate term by NSC, we made the conservative assumption that it referred to enrollment rather than non-enrollment. Full-time intensity counted only terms in which a student's enrollment intensity was full-time during the given term. Enrollment. For analyses of enrollment outcomes, we focused on whether students enrolled in college at least one semester for at least 12 weeks at any intensity. We focused on any intensity terms so that students could still be counted as enrolling even if they did not enroll full-time. We then examined three different timeframes for enrollment: ever enrollment (enrolling in college any semester from semester 1 to 12); immediate enrollment (enrolling in college in semester 1); delayed enrollment (enrolling in college after semester 1).Progress. In assessing progress through college, we focused on on-track progress, which we defined as completing four consecutive semesters at full-time status. For a semester to count as on-track progress, a student had to be enrolled in a 2- or 4-year college for at least 12 weeks during the months we designated for that semester (spring semesters: Jan-April; fall semesters: August-December). We started the clock for on-track progress in the first semester in which a student enrolled full-time for at least 12 weeks and allowed this clock to start in any semester from semester 1 to semester 9 (as the last semester of data collection was semester 12). Thus on-track progress could include consecutive full-time enrollment from semesters 1 to 4, 2 to 5, 3 to 6, 4 to 7, 5 to 8, 6 to 9, 7 to 10, 8 to 11, or 9 to 12, as long as these four semesters represented a student’s first four semesters of full-time, 12-week-minimum-term enrollment in college. In the analyses featured in the manuscript text, we allowed on-track progress to occur at 2- or 4-year college for all students, even if students first enrolled in 4-year college. In supplemental analyses, we also assessed predictors of on-track progress at 4-year college only.We called this progress “on track” because it was associated with being on track to earn a degree on time at either 2- or 4-year college. Students in the analytic sample who achieved on-track progress at 2- or 4-year college had far higher rates of graduating on time (53% vs. 9%) and graduating at all (79% vs. 22%) than students who did not achieve such progress. Graduation. We defined graduation as earning an Associate’s or Bachelor’s degree from a 2- or 4-year college. Although it is common to examine 150% time (6-year) or 200% time (8-year) degree attainment for 4-year college, our assessment window allowed us to assess only on-time graduation. In addition, we expected that rates of on-time graduation might be more affected than rates of eventual graduation by channel strength, as an outcome with a shorter deadline should be much harder to achieve in weak channels than in strong channels relative to an outcome that can be completed over a longer or indefinite time period. We defined graduating in 100% of normal time as meeting one of three criteria: 1) earning an Associate’s degree from a 2-year college within two years of the first semester of enrolling in 2-year college 2) earning an Associate’s degree from a 4-year college within four years of the first semester of enrolling in 4-year college or 3) earning a Bachelor’s degree from a 4-year college within four years of the first semester of enrolling in 4-year college. We conservatively defined the start of time for clocking on-time graduation as the first semester of enrolling in the designated college level at any intensity other than absent or withdrawn for at least one week. In supplemental analyses, we also assessed predictors of on-time Bachelor’s degree attainment only.Colleges attended. In analyses of 2- and 4-year college post-enrollment outcomes, featured in the manuscript text, we used the first 2- or 4-year college in which a student enrolled to define a student’s channel strength. In supplemental analyses of 4-year college outcomes, we used the first 4-year college in which a student enrolled. A college was counted as a student’s first college if it appeared in the NSC dataset, had a NSC college level of 2- or 4-year, and was the first college in which a student enrolled with an intensity that was not absent or withdrawn. A college was counted as a student’s first 4-year college if it appeared in the NSC dataset, had an NSC college level of 4-year, and was the first 4-year college in which a student enrolled with an intensity that was not absent or withdrawn. Students could have a first 4-year college even if they first or subsequently enrolled in a 1-year or 2-year college. Any colleges in which a student may have enrolled from January to June of their grade-12 year or earlier were not counted.Operationalizing Channel StrengthFor each post-enrollment outcome (on-track progress and on-time graduation), we defined students as being in stronger or weaker institutional channels to that outcome according to the strength of characteristics postsecondary institutions had for supporting persistence in and degree attainment in college. As explained in the manuscript text, we did not have data on differences in the strength of specific institutional channels to enrollment. For simplicity, we operationalized the strength of channels to post-enrollment outcomes using well-known ways of categorizing colleges (which were also easy to operationalize into dichotomous indicators). We created a bipolar strong versus weak channel threshold by distinguishing 4-year colleges from 2-year colleges, using the college level reported by the NSC for a student’s first college. As we theorized channel strength is also a continuum, we used ordinal selectivity ratings of 4-year colleges provided by Barron’s Profiles of American Colleges (Barron’s Guide) to also distinguish relatively stronger-channel from relatively weaker-channel colleges (see below). First enrolling in a 2-year college or not enrolling in college were always classified as being in a weaker channel, for all thresholds. The manuscript text focused on two of these channel-strength thresholds, first enrolling in a 4-year college or first enrolling in a Barron’s Top 5 college. Supplemental tables also provide results for two intermediate thresholds, when a stronger channel is defined as first enrolling in a Barron’s Top 7 college or a Barron’s Top 6 college.To validate our classifications of channel strength and to understand how study colleges related to colleges in national samples, we integrated students’ NSC college data with various institutional indicators from the Integrated Postsecondary Education Data System (IPEDS), for the years 2011 (two years before cohort 1 graduated high school) to 2017 (the last year of available data in IPEDS at the time of our analysis), and from the most recent three years of Barron’s Guide (2016 to 2018; the editions to which we had access). Selectivity Ratings in Barron’s GuideA database was constructed for colleges listed in Barron’s Guide for the years 2016 (online), 2017 (print), and 2018 (online). Barron’s Guide ranks all accredited four-year colleges that grant Bachelor’s degrees and admit first-time college students according to their degree of admissions competitiveness (see table below). Barron’s Guide cautions that these rankings may not reflect an institution’s academic standards or quality of education provided to enrolled students. RankingBarron’s Guide CategoryCutoff Used for Distinguishing Stronger from Weaker ChannelsNot Rated9NoncompetitiveCutoff for Any Barron’s Guide8Less Competitive7CompetitiveCutoff for Barron’s Top 76Competitive+Cutoff for Barron’s Top 65Very CompetitiveCutoff for Barron’s Top 54Very Competitive +3Highly Competitive2Highly Competitive +1Most CompetitiveThe final Barron’s Guide ranking for a student’s first college was an average of the college’s ranking for each of the three years from 2016 to 2018, rounded to the nearest whole number. A ranking of Very Competitive was the minimum ranking to be a stronger channel when the stronger-channel criterion was Barron’s Top 5 (top 5 ordinal categories). Table S4 shows the criteria Barron’s Guide uses to categorize colleges in the top seven Barron’s categories. Comparing Study Colleges to an IPEDS National Sample Defining a national comparison sample. To understand how institutional characteristics of study colleges compared to national averages, we accumulated data for all colleges in IPEDS for the years 2011 to 2017, a total of 8,718 colleges, and removed colleges meeting one or more of the following criteria during one of the seven years: their level was 1-year, they were inactive in the current year, they had an admissions rate of 0%, they were online only, and/or they were a private for-profit university. This left 3,644 colleges in the national 2- or 4-year college sample.Barron’s Guide Membership. Table S5 shows the percentage of colleges in the national 2- or 4-year college sample and in the study sample who were listed in Barron’s Guide during 2016 to 2018 and met the criteria for different Barron’s Guide thresholds (Top 7 to Top 4). In the analytic sample, 76% of students’ first colleges had a Barron’s Guide rating; 62% of first colleges were in Barron’s Top 7; 26% of first colleges were in Barron’s Top 5.IPEDS Institutional Indicators. We also obtained and computed various institutional indicators from IPEDS to further understand how representative study colleges were of colleges nationally (a detailed description of these indicators is available upon request).In general, study colleges (i.e., the first college in which a student enrolled) in the analytic sample were comparable but somewhat higher performing than the national sample across various indicators. The average (from 2011 to 2017) admissions rate in study colleges was 71.2%, relative to 80.9% nationally. The average full-time enrollment rate in study colleges was 79.4%, relative to 68.8% nationally. The average full-time retention rate in study colleges was 75.9%, relative to 68.9% nationally. The average 100%-time graduation rate in study colleges was 41.6%, relative to 29.6% nationally. The average total net assets in study colleges was $549.5 million, relative to $267.9 million nationally. The average endowment size in study colleges was $348.4 million, relative to $184.6 million nationally. See Table S6.Validating the Channel Strength Thresholds Using National SamplesCorrelations among institutional indicators theorized to create strong channels. Barron’s Guide ratings are primarily intended to reflect higher levels of admissions competitiveness. However, we theorize that selectivity alone is insufficient for creating a strong channel to on-track progress and on-time degree attainment. To confirm that indicators of selectivity, such as admissions rates and SAT scores (at 4-year colleges), were associated with other kinds of post-enrollment institutional indicators theorized to be associated with stronger channels (e.g., financial resources, full-time enrollment rates, and graduation rates), we computed Pearson’s pairwise correlations among percentile scores for various institutional indicators in the national sample of 2- and 4-year colleges. As expected, all indicators were highly correlated, consistent with the idea that institutions that are higher on one kind of structural characteristic (or, in the case of admissions rates, lower) that helps institutions to establish and maintain strong channels to persistence also tend to be higher on others (correlation table available upon request).4-year college versus 2-year college. To confirm our assumption that 4-year colleges provided stronger channels to on-track progress and degree attainment than 2-year colleges, we compared 4-year colleges in the national sample of 2- and 4-year colleges to 2-year colleges in that sample on a range of institutional indicators, including admissions rate, full-time enrollment and retention rates, graduation rates, and financial resources, by regressing each indicator on a dichotomous contrast distinguishing 4-year (=1) from 2-year colleges (=0). For each indicator, 4-year colleges had a significantly higher mean, on average, than 2-year colleges (regression table available upon request).Higher versus lower Barron’s ratings. To confirm our assumption that colleges in higher Barron’s categories provided stronger channels to progress and graduation than colleges in lower Barron’s categories, we conducted similar correlational and regression analyses among all 4-year colleges in the national sample with a Barron’s Guide rating. As expected, being in a higher (more selective) Barron’s category was associated with higher progress and completion rates (higher rates of full-time enrollment, retention, and graduation), higher total resources (total net assets, endowment), higher resource allocation per student (higher amounts spent on instruction and student services per undergraduate), and a higher capacity to provide financial aid (higher average amount of aid awarded per undergraduate) [regression table available upon request]. Regression Samples The manuscript text reports regression analyses and figures for the full sample of students who agreed to college tracking. In the supplement, we report results for two additional samples to understand the extent to which results in the full sample were sensitive to enrollment decisions. The supplement provides regression tables for all three samples as well as figures comparing the magnitude and direction of regression coefficients for these samples (Figs. S1 to S3). We define these samples below.Analytic full sample. The full sample included all students who agreed to have their college outcomes tracked for six years, whether or not they ever enrolled in college (N=2,135 total; N=1,850 with non-missing baseline data). Ever enrolled in college sample. This sample included only those students who ever enrolled in a 2- or 4-year college (N=1,687 total; N=1,496 with non-missing baseline data). As in the full sample, on-track progress was coded 1 if students completed four consecutive full-time, 12-week-minimum semesters at either 2- or 4-year college; on-time graduation was coded 1 if students earned an Associate’s or Bachelor’s degree in 100% time of starting a 2- or 4-year college. Ever enrolled in 4-year college sample. This sample included only those students who ever enrolled in a 4-year college (N=1,251 total; N=1,143 with non-missing baseline data). Students were included in this sample even if they also enrolled in 1-year or 2-year college as long as they also enrolled in a 4-year college. Unlike in the full or ever-enrolled samples, college outcomes could only be attained at 4-year college. On-track progress was only coded 1 if students completed four consecutive full-time, 12-week-minimum semesters at 4-year college. On-time graduation was only coded 1 if students earned a Bachelor’s degree within 4 years from a 4-year college.Approach for Handling Missing Data: Multiple ImputationIn addition to complete-data analyses for each sample, we also used multiple imputation (mi) commands in STATA to conduct analyses with all students with college outcome data, whether or not they had available data for all baseline predictors. We conducted multiple imputation separately for each outcome. We first declared the data to be mi data and then registered as regular variables the outcome, high school × cohort ID, channel strength (for on-track progress and on-time graduation outcomes), gender, and free and reduced lunch status to indicate these variables had complete data and did not need to be imputed. We registered as imputed variables belonging certainty, growth mindset, grit, ethnicity, grade 10/11 math and reading state standardized test scores, and grade 12 GPA, to indicate that these variables did have missing values. Using STATA’s mi impute chained command, we then imputed values for all variables registered as imputed using the method of chained equations in the 2,135-person sample. We used logistic regression to impute values for the dichotomous historically marginalized ethnicity variable and linear regression to impute values for all other imputed variables. The imputation model also included the relevant outcome, gender, free and reduced lunch status, and a set of dichotomous dummy variables for high school × cohort group. For each imputation analysis, 15 imputations were conducted with the same random number seed to facilitate replicability. This procedure yielded 15 imputed values for each variable for each student who was missing data for that variable; values for students not missing data for that variable remained unchanged. We then standardized all predictors and, for post-enrollment analyses, created interaction terms between channel strength and each of the three psychological predictors. We then used the same logistic regression model and associated specifications as in each complete-data analysis in conjunction with the mi estimate command. Organization of Supplemental ResultsIn the supplement we report more detailed results than was possible to report in the manuscript text. We begin by reporting the logistic-regression results (see Tables S7 to S12) obtained using multiple imputation in the original full sample who agreed to college tracking (N=2,135). For post-enrollment outcomes, we focus on the 4-year college and Barron’s Top 5 channel-strength thresholds, the thresholds used when reporting results for the complete-data full sample in the manuscript text.Next we provide the effects of psychological factors on enrollment obtained from complete-data analyses for two additional samples: students who ever enrolled in college (N=1,496); and students who ever-enrolled in 4-year college (N=1,143). We exclude the outcomes of ever enrollment and delayed enrollment as these were not relevant for all three samples. Finally, for analyses involving interactions between channel strength and psychological factors, we provide results for additional channel-strength thresholds that could be created using Barron’s Guide ratings for all three samples. Approach for Reporting Supplemental ResultsFor all analyses, we report the raw log-odds coefficient of each psychological factor and the associated z-value, p-value, and odds ratio (obtained by exponentiating the log-odds coefficient). As in the manuscript text, regression coefficients for psychological factors represent the variance between each psychological factor and the log-odds of attaining the outcome that is not shared with the other two psychological factors (or with demographic and academic factors). We also report 95% confidence intervals for the odds ratio (obtained by exponentiating the 95% confidence limits for the log-odds coefficient) and probabilities of outcome attainment for individuals with low (-1 SD) and high (+1 SD) levels of each psychological factor, when all other predictors in the model are set to the relevant sample average. We sometimes report a subset of these when seeking to summarize results from several similar analyses.For each analysis involving an interaction between channel strength and psychological factors, we first report or summarize interactions between channel strength and each psychological factor (the coefficient for the relevant interaction term when the weaker channel is defined as 0 rather than 1), then the simple association of each psychological factor in weaker channels (the coefficient for each psychological factor when the weaker channel is defined as 0 rather than 1), and last the simple association of each psychological factor in stronger channels (the coefficient for each psychological factor when the stronger channel is defined as 0 rather than 1).Multiple-Imputation Results in the Full Sample (N=2,135)Outcomes Pursued Before Postsecondary Institutional Entry Ever enrolled within 6 years after high school. Among all students who agreed to college tracking, multiple-imputation analyses showed that higher belonging certainty predicted higher log-odds of ever enrolling in college, b=0.13, z=2.68, p=.008, OR=1.14, 95% CI [1.04, 1.26], PLow=80.0% vs PHigh=83.9%. Higher growth mindset also predicted higher odds of ever enrolling in college, b=0.12, z=2.60, p=.010, OR=1.13, 95% CI [1.03, 1.23], PLow=80.3% vs PHigh=83.7%. Grit was non-predictive, z=0.42, p=.67, OR=1.02. See column 2 of Table S7.Immediate enrollment (in semester 1). Among all students who agreed to college tracking, multiple-imputation analyses showed that higher belonging certainty predicted higher log-odds of enrolling in college immediately, b=0.14, z=3.09, p=.002, OR=1.15, 95% CI [1.05, 1.26], PLow=61.9% vs PHigh=68.4%. Growth mindset did not predict immediate enrollment, z=-0.66, p=.51, OR=0.99. Grit was also nonpredictive of this outcome, z=0.27, p=.79, OR=1.01. See column 4 of Table S7.Delayed enrollment (after semester 1). Among students who did not enroll in college by semester 1, multiple-imputation analyses showed that higher belonging certainty did not predict delayed enrollment in college, z=0.68, p=.50, OR=1.04. Higher growth mindset did predict higher log-odds of delayed enrollment, b=0.26, z=3.83, p<.001, OR=1.29, 95% CI [1.13, 1.47], PLow=39.3% vs PHigh=51.9%. Grit did not predict delayed enrollment, z=0.25, p=.81, OR=1.02. See column 6 of Table S7.Summary. As in the complete-data sample, multiple-imputation analyses showed that mindset factors, especially belonging certainty, were predictive of enrollment outcomes, which we hypothesized were typically pursued in weak channels, whereas grit was not.Outcomes Pursued After Postsecondary Institutional Entry, Accounting for Institutional ChannelBelow we report multiple-imputation results for the incomplete-data full sample (N=2,135) when accounting for channel strength × psychology interactions (see Table 8 for analyses of these outcomes that exclude interactions with channel strength) and channel strength is defined as first enrolling in a 4-year college or Barron’s Top 5 college, as in the manuscript text. Regression results are displayed in Tables S9 and S10 for on-track progress and in Tables S11 and S12 for on-time graduation.Interaction between channel strength and psychological factors for on-track progress. Belonging Certainty. Multiple-imputation analyses indicated that there was no interaction between channel strength and belonging certainty for on-track progress at 2- or 4-year college for the 4-year-college threshold, z=-0.19, p=.85, OR=0.99, but there was for the Barron’s Top 5 threshold, b=-0.39, z=-2.40, p=.016, OR=0.68, 95% CI [0.50, 0.93]. Belonging certainty did not predict higher on-track progress in 4-year-college-threshold weaker channels (e.g., 2-year colleges), z=0.19, p=.85, OR=1.01, but did in Barron’s Top 5-threshold weaker channels (e.g., 2-year colleges and lower-rated or unrated 4-year colleges), b=0.17, z=2.05, p=.041, OR=1.18, 95% CI [1.01, 1.39], PLow=22.8% vs PHigh=29.3%. Belonging certainty was non-predictive of on-track progress in 4-year-college-threshold stronger channels, z=0.01, p=.99, OR=1.00, and directionally negative in Barron’s Top 5-threshold stronger channels, z=-1.36, p=.18, OR=0.80.Growth Mindset. There was a significant interaction between channel strength and growth mindset for on-track progress for both the 4-year-college, b=-0.26, z=-3.06, p=.002, OR=0.77, 95% CI [0.65, 0.91], and Barron’s Top 5 thresholds, b=-0.29, z=-2.90, p=.004, OR=0.75, 95% CI [0.62, 0.91]. Growth mindset positively predicted on-track progress in weaker channels for each threshold, in both 4-year-college-threshold weaker channels, b=0.25, z=5.80, p<.001, OR=1.29, 95% CI [1.18, 1.40], PLow=5.4% vs PHigh=8.6%, and Barron’s Top 5-threshold weaker channels, b=0.14, z=2.39, p=.017, OR=1.15, 95% CI [1.03, 1.29], PLow=23.3% vs PHigh=28.7%. Growth mindset did not predict on-track progress in 4-year-college-threshold stronger channels, z=-0.22, p=.82, OR=0.99, and was negatively predictive in Barron’s Top 5-threshold stronger channels, b=-0.15, z=-2.48, p=.013, OR=0.86, 95% CI [0.77, 0.97], PLow=54.4% vs PHigh=47.0%. Grit. There was no significant interaction between channel strength and grit for on-track progress for either threshold, |z|s≤0.98, ps≥0.33. However, unlike in the complete-data sample, higher grit was also predictive of higher odds of on-track progress in 4-year-college-threshold weaker channels, b=0.25, z=1.94, p=.052, OR=1.28, 95% CI [1.00, 1.64], PLow=5.4% vs PHigh=8.5%, though the standard error associated with this coefficient was much larger than for growth mindset (0.13 vs. 0.04). Grit was non-predictive in Barron’s Top 5-threshold weaker channels, z=1.58, p=.11, OR=1.09. Grit had a directionally positive but non-significant association with on-track progress in 4-year-college-threshold stronger channels, z=1.22, p=.22, OR=1.08, and a marginal positive association in Barron’s Top 5-threshold stronger channels, z=1.74, p=.083, OR=1.18.Summary. As in complete-data analyses, the association between mindset factors and on-track progress in multiple-imputation analyses differed by channel; this association was positive in weaker channels and zero or negative in stronger channels. This pattern was evident for both thresholds for growth mindset but only for the Barron’s Top 5 threshold for belonging certainty. The association between grit and on-track progress did not differ by channel. While grit’s simple slope did reach significance in 4-year-college-threshold weaker channels, this pattern was not observed in the other threshold. Overall, the magnitude of the association between grit and on-track progress was not consistently more positive in stronger channels than in weaker channels.Interaction between channel strength and psychological factors for on-time graduation. Belonging Certainty. Multiple-imputation analyses indicated that there was no interaction between channel strength and belonging certainty for on-time graduation for the 4-year-college threshold, z=0.17, p=.87, OR=1.04, but there was for the Barron’s Top 5-threshold, b=-0.33, z=-2.74, p=.006, OR=0.72, 95% CI [0.57, 0.91]. Belonging certainty did not predict higher on-time graduation from 2- or 4-year college in 4-year-college-threshold weaker channels, z=0.16, p=.88, OR=1.03. It was a marginal positive predictor of on-time graduation in Barron’s Top 5-threshold weaker channels, b=0.20, z=1.87, p=.062, OR=1.22, 95% CI [0.99, 1.51], PLow=11.5% vs PHigh=16.3%. Belonging certainty did not predict on-time graduation in 4-year-college-threshold stronger channels, z=0.95, p=.34, OR=1.07, and had a directionally negative association in Barron’s Top 5-threshold stronger channels, z=-1.35, p=.18, OR=0.88.Growth Mindset. There was a marginally significant interaction between channel strength and growth mindset for the 4-year-college threshold, b=-0.19, z=-1.88, p=.061, OR=0.83, 95% CI [0.68, 1.01], but no interaction for the Barron’s Top 5 threshold, z=-0.47, p=.64, OR=0.96. Growth mindset had a marginally significant positive association with on-time graduation in 4-year-college-threshold weaker channels, b=0.12, z=1.75, p=.081, OR=1.13, 95% CI [0.98, 1.30], PLow=6.2% vs PHigh=7.8%, and no association in Barron’s Top 5-threshold weaker channels, z=0.37, p=.71, OR=1.01. Growth mindset had a directionally negative association with on-time graduation in 4-year-college-threshold stronger channels, z=-1.27, p=.21, OR=0.94, and no association in Barron’s Top 5-threshold stronger channels, z=-0.39, p=.70, OR=0.97.Grit. There was no interaction between channel strength and grit for the 4-year-college-threshold, z=-0.58, p=.56, OR=0.91, and a marginally significant interaction for the Barron’s Top 5 threshold, b=0.18, z=1.71, p=.088, OR=1.20, 95% CI [0.97, 1.48]. Grit had no association with on-time graduation in weaker channels, |z|s1.02, ps.31, or in 4-year-college-threshold stronger channels, z=1.03, p=.30, OR=1.04. It had a significant positive association when students were in Barron’s Top 5-threshold stronger channels, b=0.18, z=3.44, p=.001, OR=1.20, 95% CI [1.08, 1.34], PLow=21.8% vs PHigh=28.7%. Summary. As in complete-data analyses, the association between belonging certainty and on-time graduation from 2- or 4-year college in multiple-imputation analyses differed by channel for the Barron’s Top 5 threshold; this association was marginally positive in weaker channels defined by this threshold and directionally negative in stronger channels. Growth mindset showed the same pattern of results but for the 4-year-college threshold. The interaction between grit and channel strength on on-time graduation was marginally significant for the Barron’s Top 5 threshold; the association between grit and on-time graduation was positive and significant in stronger channels defined by this threshold and zero in weaker channels, the opposite of the pattern displayed by belonging certainty.Main-Effects Results in Different Ever-Enrolled Samples for Enrollment OutcomesEnrolled in College Immediately (in Semester 1). Ever enrolled in college sample (N=1,496). Among students with complete data who ever enrolled in college, higher belonging certainty predicted higher log-odds of enrolling in college in semester 1, b=0.13, z=2.98, p=.003, OR=1.14, 95% CI [1.05, 1.24], PLow=80.1% vs PHigh=83.9%. Growth mindset negatively predicted immediate enrollment, b=-0.18, z=-3.26, p=.001, OR=0.83, 95% CI [0.75, 0.93], PLow=84.6% vs PHigh=79.3%. Grit was nonpredictive of this outcome, z=-0.31, p=.76, OR=0.98. See column 1 of Table S13 (see column 2 for the corresponding multiple-imputation analysis).Ever enrolled in 4-year college sample (N=1,143). Among students with complete data who ever enrolled in 4-year college, higher belonging certainty predicted higher log-odds of enrolling in 4-year college in semester 1, b=0.18, z=5.00, p<.001, OR=1.20, 95% CI [1.12, 1.29], PLow=70.7% vs PHigh=77.6%. Growth mindset did not predict immediate enrollment in 4-year college, z=-1.46, p=.15, OR=0.95. Grit was also nonpredictive of this outcome, z=0.32, p=.75, OR=1.02. See column 1 of Table S18 (see column 2 for the corresponding multiple-imputation analysis).Summary. As in the full sample results reported in the manuscript text, for all students who agreed to college tracking, belonging certainty positively predicted immediate enrollment in both college-going samples. Growth mindset negatively predicted immediate enrollment in 2- or 4-year college among students who ever enrolled in college. Grit did not predict immediate enrollment in any sample. For main-effects results concerning on-track progress and on-time graduation for these samples, see columns 3 and 5 in Tables S13 and S18. Interactions Between Channel Strength and Psychological Factors on Post-Enrollment Outcomes, by Sample, for Multiple Channel-Strength ThresholdsBelow we summarize results from analyses of the interaction between channel strength and psychological factors on post-enrollment outcomes using six different channel-strength thresholds: 4-year college, any Barron’s rating, Barron’s Top 7, Top 6, Top 5, and Top 4, rather than only the two thresholds reported in the manuscript text. For brevity, the tables feature four of these thresholds. As noted earlier, regression tables show coefficients from both complete-data and multiple-imputation versions of each analysis. We present summaries of results for the full sample and two additional samples (defined according to students’ ever enrollment decisions).On-Track Progress, Accounting for Institutional Channel Analytic full sample. Regression models predicting on-track progress at 2- or 4-year college in different-strength channels among all students who agreed to college tracking are shown in Tables S9 to S10. In this sample (N=2,135 total; N=1,850 with non-missing baseline data), the association between belonging certainty and on-track progress at 2- or 4-year college differed by channel in thresholds equal to or more selective than Barron’s Top 6. This association was positive in weaker channels and zero or negative in stronger channels. The association between growth mindset and on-track progress differed by channel in all thresholds. Growth mindset had a positive association with on-track progress when students were in weaker channels defined by any of the thresholds; its magnitude was largest for the 4-year college threshold. Growth mindset had no association with on-track progress in stronger channels and a negative association in the most selective stronger channels.The association between grit and on-track progress did not consistently differ by channel, as it tended to be a positive predictor in both channels. The interaction term was only significant for the Barron’s Top 6 threshold. Yet its simple slope in each channel showed the opposite pattern of the mindset factors. With two exceptions (multiple-imputation analyses using the 4-year-college and any-Barron’s-Guide thresholds), grit did not predict on on-track progress at 2- or 4-year college in weaker channels. Grit had a stronger, positive association with on-track progress in stronger channels, particularly for Barron’s Top 7 and Barron’s Top 6 stronger channels. Ever enrolled in college sample. Regression models predicting on-track progress at 2- or 4-year college as a function of different-strength channels among students who ever enrolled in college are shown in Tables S14 to S15.In the ever-enrolled sample (N=1,687 total; N=1,496 with non-missing baseline data), the association between mindset factors and on-track progress at 2- or 4-year college among students differed by channel, as in the full sample. The interaction term was significant for two thresholds for belonging certainty (Barron’s Top 6 and Top 5) and for five thresholds for growth mindset (all except Barron’s Top 6). This interaction reflected a tendency for mindset factors to have positive associations with on-track progress in weaker channels and zero or negative associations in stronger channels. Belonging certainty had a significant positive association with on-track progress when students were in weaker college channels defined by the three more selective thresholds (Barron’s Top 6, Top 5, and Top 4). Growth mindset had a significant positive association with on on-track progress when students were in weaker college channels defined by the three less selective thresholds (4-year college, membership in Barron’s Guide, and Barron’s Top 7). Neither mindset factor predicted on-track progress in stronger channels and had a significant negative association with on-track progress in one or more of the stronger channels defined by the most selective thresholds (Barron’s Top 6 and higher).Grit showed a different pattern. It was a directionally positive predictor in both channels. The positive association of grit with on-track progress in weaker channels was inconsistent in magnitude and never significant for any threshold. It was more consistently higher in magnitude and significant in stronger channels, especially those that were equal to or more selective than Barron’s Top 7. However, the interaction between grit and channel strength was not consistently significant; it was only significant for the Barron’s Top 6 threshold.Ever enrolled in 4-year college sample. Regression models predicting on-track progress at 4-year college in different-strength channels among students who ever enrolled in 4-year college are shown in Table S19. Thresholds less selective than Barron’s Top 7 were not relevant for this analysis.In the 4-year college sample (N=1,251 total; N=1,143 with non-missing baseline data), mindset factors did not differ by channel. In weaker 4-year college channels, there were no positive associations between mindset factors and on-track progress, as was found in the less restrictive (full and ever enrolled) samples. In stronger 4-year college channels, similar to the other samples, the association between mindset factors and on-track progress was non-significant, and in one case (growth mindset in Barron’s Top 5 stronger channels), negative.In this sample, grit interacted with channel strength in expected ways. Grit had a significant negative association with on-track progress in two weaker 4-year college channels (4-year colleges with lower ratings than Barron’s Top 7 and 6) and no association in the others (4-year colleges with lower ratings than Barron’s Top 5 and Top 4). Grit had a positive association with on-track progress in stronger 4-year college channels, which was significant for three of four thresholds (all except Barron’s Top 4). In addition, unlike in less restrictive enrollment samples, the interactions between grit and channel strength were significant for two (Barron’s Top 7 and Top 6) of the four thresholds.On-Time Graduation, Accounting for Institutional Channel Analytic full sample. Regression models predicting on-time graduation from 2- or 4-year college (earning an Associate’s or Bachelor’s degree in 100% time) in different-strength channels among all students who agreed to college tracking are shown in Tables S11 to S12.In this sample (N=2,135 total; N=1,850 with non-missing baseline data), the association between belonging certainty and on-time graduation significantly differed by channel for the three thresholds equal to or more selective than Barron’s Top 6; this association was positive and marginally significant in weaker channels defined by these thresholds and zero or negative in stronger channels. The association between growth mindset and on-time graduation did not consistently differ by channel; the interaction term was only significant for the 4-year college threshold. There was no significant positive association between growth mindset and on-time graduation in weaker channels and no association or a negative association in stronger channels. The simple slopes for grit showed the opposite pattern of belonging certainty. The association between grit and on-time graduation was zero in weaker channels and consistently positive in stronger channels. This positive association was significant for four thresholds and marginally significant for the other two. However, the interaction between grit and channel strength was marginally significant in one case (Barron’s Top 5) and otherwise non-significant.Ever enrolled in college sample. Regression models predicting on-time graduation from 2- or 4-year college as a function of different-strength channels among students who ever enrolled in college are shown in Tables S16 to S17.In the ever-enrolled sample (N=1,687 total; N=1,496 with non-missing baseline data), the association between belonging certainty and on-time graduation significantly differed by channel for thresholds equal to or more selective than Barron’s Top 6. This reflected a positive association between belonging certainty and on-time graduation in weaker channels defined by these thresholds and a zero or negative association in stronger channels. This positive association in weaker channels was significant in the ever-enrolled sample, whereas it had been marginally significant in the full sample that included never-enrolled students. As in the full sample, the association between growth mindset and on-time graduation did not significantly differ by channel. Growth mindset did not have a positive association with on-time graduation when students were in weaker college channels defined by any threshold. In fact in some cases it had a negative association in either weaker or stronger channels.As in the full sample, the simple slopes for grit showed the opposite pattern of belonging certainty. The association between grit and on-time graduation was zero in weaker channels and positive and significant in stronger channels for all thresholds. Its magnitude was largest for the most selective stronger channels (Barron’s Top 6 and above). However, the interaction between grit and channel strength was either marginally significant or non-significant.Ever enrolled in 4-year college sample. Regression models predicting on-time Bachelor’s degree attainment as a function of different-strength channels among students who ever enrolled in 4-year college are shown in Table S20. In the 4-year college sample (N=1,251 total; N=1,143 with non-missing baseline data), belonging certainty and grit interacted with channel strength in expected ways. The association between belonging certainty and on-time Bachelor’s degree attainment significantly differed by channel for thresholds equal to or more selective than Barron’s Top 6. It was positive and significant in weaker channels defined by these thresholds and non-significant or negative (Barron’s Top 4) in stronger channels. In this sample and for this outcome, growth mindset did not differ by channel, except for the Barron’s Top 5 threshold. However, its association with on-time Bachelor’s degree attainment was negative and significant in all weaker 4-year college channels and non-significant in all stronger 4-year college channels. Grit showed the opposite pattern of belonging certainty. It had no association with on-time Bachelor’s degree attainment in all weaker 4-year college channels. Grit had a significant, positive association with on-time Bachelor’s degree attainment in three stronger 4-year college channels (Barron’s Top 6 and higher); it was marginally significant for the Barron’s Top 7 threshold. However, the interactions between grit and channel strength were non-significant or marginally significant. ................
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