Within-college human capital and racial ethnic differences in academic performance

Table 2. Effects of Selected Independent Variables on the Intercept and Slope Parameters of a Linear Growth-Curve Model Predicting Student Grade Point Average across the College Career

			Intercept Parameter				Slope Parameter
Time Invariant Independent Variables			Coefficient		Robust SE		Coefficient		Robust SE
Race/Ethnicity (ref: White)
Black			-.28	**	.05		.04	*	.02
Latino			-.12	**	.04		.02		.01
Asian			.02		.04		-.03		.02
Bi-Multiracial			-.13	*	.05		.04		.02
Female			.11	**	.03		.00		.01
Mother's Education			-.03		.02		.01		.01
Father's Education			.02		.02		.00		.01
US Citizen			-.01		.05		.02		.02
SAT-Mathematics			.00	**	.00		.00		.00
Good Student Identity (High School)			.00		.02		.01		.01
Self-Perceived HS Ability			.06	**	.02		.00		.01
HS Confidence: Mathematics			-.08	**	.02		.01		.01
HS Confidence: English			.02		.02		.00		.01
Time Management (Year One)			.13	**	.02		-.01		.01
Major Field (ref: Natural Sciences)
Social Sciences			.09	**	.03		-.01		.01
Humanities			.07		.05		.00		.02
Intercept			.84	**	.28		.35	**	.11
			First Year GPA				Second Year GPA			Fourth Year GPA
Time Varying Independent Variables			Coefficient		Robust SE		Coefficient		Robust SE	Coefficient		Robust SE
Self-Assessed Academic Skills			.00		.00		-.01	*	.00	-.01	*	.00
Academic Self Confidence			.01		.02		.01		.02	.00		.02
Work Hard Attributions			.10	**	.04		.06		.04	-.01		.05
Active Learning Behaviors			-.03	**	.01		-.01		.01
Good Student Identity			.04	*	.02		.03	*	.02	.02		.02
Global Self Esteem			.00		.01		.01		.01	.00		.01
Hours Spent Studying			.00		.00		.00		.00	.00		.00
Self-Assessed Ability			.05	*	.02		.06	**	.02	.02		.02
Self-Assessed Smartness			.05	*	.02		.02		.02	-.05	*	.02
	Residual Variances
	Coefficient		Robust SE				RMSEA (Root Mean Square Error of Approximation)
First Year GPA	.10	**	.01									.043
Second Year GPA	.09	**	.01
Third Year GPA	.08	**	.01				SRMR (Standardized Root Mean Square Residual)
Fourth Year GPA	.07	**	.01									.036
Intercept	.11	**	.01
Slope	.01	**	.00
Note: Weighted estimates; N = 1,255
* p < .05, ** p < .01

Table 3. Fixed Effects Estimates of the Effects of Race/Ethnicity and Time Varying Characteristics on Student Grade Point Average across the College Career

	Coefficient		Robust SE
Race/Ethnicity
Black x Year	.06	**	.02
Latino x Year	.02		.01
Asian x Year	-.04	**	.02
Bi-Multiracial x Year	.02		.02
Year	.08	**	.01
Major Field
Social Sciences	.02		.04
Humanities	.04		.05
Undeclared	.03		.04
Self-Assessed Academic Skills	.01	*	.00
Academic Self Confidence	.01		.01
Work Hard Attributions	.05	*	.02
Good Student Identity	.02		.01
Global Self Esteem	.01		.01
Hours Spent Studying	.00		.00
Self-Assessed Ability	.02		.02
Self-Assessed Smartness	-.01		.02
Constant	2.65	**	.12
Note: Weighted estimates; N = 3,137 observations/1,119 subjects
* p < .05, ** p < .01

Table 4. Unadjusted and Adjusted Black-White Achievement Gap by Year in College

College Year	Unadjusted Gap	Adjusted Gap^a	Difference	% of Gross Gap
1	.422	.282	.140	33
2	.391	.245	.146	37
3	.375	.205	.170	45
4	.179	.165	.014	8
^aAs predicted using the growth curve model

1 For the actual placement of respondents in racial ethnic categories we used US Census type questions that measure first whether or not the respondent is Hispanic and then elicit a racial category. Virtually all of our “Hispanic” respondents also reported their race as white, so we classify this group as Latino. Other groups are placed on the basis of the race question, which includes bi- and multi-racial options. If data were missing on the census questions, we used the admission form race item when possible. The race category frequencies differ slightly here from previous publications with the CLL data as we previously did not make the missing data adjustment (XXXXX 2005).

2 Elsewhere we also provide detailed comparisons between Duke and other elite universities in the United States and other major research universities in the United States (XXXXX 2005). In short, our study is not designed to be representative of the population of U.S. colleges and universities. Rather it is fairly representative of highly selective institutions of higher education in the United States. Again, some evidence suggests the achievement gap is largest in these types of institutions (Bowen and Bok 1998).

3 Although the MAR assumption is difficult, if not impossible, to test, we did attempt to explore its feasibility by examining missing value patterns on covariates, based on subjects’ values on the same covariates at different waves. For example, to explore whether academic self-confidence was feasibly missing at random in the sophomore year, we looked at missing values on academic self-confidence in the freshman and senior years to see if there was any association between scores at other waves and the probability of being missing at the wave in question. Although this technique does not provide formal evidence to support the MAR assumption, it does give us confidence that this assumption is feasible in our data and that the use of FIML is justified.

4 We ran the Hausman test on unweighted data despite the fact that the models we present are weighted, as Stata does not allow probability weights for random effects models. Consequently, we ran both a fixed effects model and a corresponding random effects model without weights for the purposes of the test. The assumption that one of the estimators has minimal asymptotic variance is violated in the case of probability weighted observations as well. In addition to the weighting issue, the random effects model we include in the comparison for the Hausman test differs from the model we present in other regards. We cannot include the time-varying covariates in the random effects model for the Hausman test in order for it to match the fixed effects model. Finally, to run the Hausman test, we ran our random effects model in the same statistical software as our fixed effects model, but the model we present in the paper was run using the SEM framework (as weighting is allowed). Therefore, while the Hausman test run on unweighted data favors the FE model, we still present both the fixed effects model and the latent growth curve model. We believe that the latent growth curve model answers important questions not answered by the fixed effects model and tests indicate acceptable model fit.

5 ICE in Stata (Royston 2005) performs multiple imputation via chained equations (van Buuren et al. 1999). The first step of the procedure is to impute values 10 times for all variables with missing values using an iterative multivariable regression technique, after which missing values are filled in by taking observations at random from the conditional distribution of missing observations. The imputation model is repeated for each variable in the analytic model with missing data. The imputation models use the appropriate family and link function, based on the distribution of the variable and 5 imputed data sets are generated. The fixed effects model was run on all 5 imputed datasets and the results combined across models (Rubin 1987).