A Hierarchical Linear Modeling Approach to Higher Education Instructional Costs


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1 A Hierarchical Linear Modeling Approach to Higher Education Instructional Costs Qin Zhang and Allison Walters University of Delaware NEAIR 37 th Annual Conference November 15, 2010
2 Cost Factors Middaugh, Graham, Shahid & Carroll ( 2003) utilized OLS regression to identify cost factors associated with direct instructional expenditures, based on the three cycles of Delaware Study data ( , , and ): Level of the department s teaching activity, measured by total undergraduate and graduate credit hours taught Faculty workload such as average undergraduate and graduate student credit hours per faculty Department size, measured in terms of total number of tenured/tenuretrack faculty
3 Cost Factors Proportion of tenured/tenuretrack faculty Personnel expenditure as percent of total instructional expenditure Relative emphasis of departmental teaching on undergraduate versus graduate instruction, measured by highest degree offered and proportion of bachelor s degrees awarded in a department Institution mission based on Carnegie classification
4 Cost Factors The Delaware Study data follow a classical hierarchical data structure in which disciplines can be considered the level 1 units and institutions the level 2 units. The proportion of the total variance in costs tied to the institution level ranges from 19% to 24% during the three data collection cycles ( , , and ).
5 Research Objective To incorporate level 2/institutional level variables and utilize HLM techniques to explore how they contribute to the explanation of instructional costs. Level 1: academic disciplines Level 2: higher education institutions To examine whether multilevel modeling will provide substantially different estimations for level 1 cost factors from those based on OLS regression.
6 Data Source Data collected during the academic year for the Delaware Study of Instructional Costs and Productivity Self reported information by participating institutions on teaching loads by faculty category, academic and fiscal year student credit hour production and direct expenses for instruction by academic discipline.
7 Data Source N= 4405 disciplines nested within 174 institutions Number of disciplines reported by each institution ranges from 4 to 63 Dependent variable: log transformed direct instructional cost per student credit hour taught
8 Measures Level 1/Discipline level variables: o SUGALL: average undergraduate student credit hours per faculty (fall data) o SGRALL: average graduate student credit hours per faculty (fall data) o PCFTEA1: tenured/tenuretrack faculty as percent of total faculty o PCGSCH: academic year graduate student credit hours as percent of total student credit hours
9 Measures o PCTPER: personnel expenditure as percent of total instructional expenditure o SCHAYG: academic year graduate student credit hours o SCHAYU: academic year undergraduate student credit hours o SUGTT: average undergrad student credit hours per tenured/tenuretrack faculty (fall data) o PHD: Doctor s as highest degree offered (1: yes; 0: no)
10 Measures o MASTERS: Master s as highest degree offered (1: yes; 0: no) o UGGRMIX: the number of bachelor s degree as proportion of total degrees awarded (1: 0 to less than 75%; 0: 75% to 100%) o Discipline groupings: disciplines are grouped into 24 broad categories based on fourdigit CIP wherever possible, or twodigit CIP as appropriate. Then these categories are transformed into dummy variable for the analysis, for example, BUSN, ENG, COMPSC, NURS, ARTS, CHEM, PHYS, ECON, GEOL, BIO, COMM, and MATH.
11 Measures o Interaction terms between discipline grouping variables and highest degrees offered (PHD and MASTERS) and UGGRMIX, for example, NURSMIX, ENGPHD, ENGMASTER, and GEOLPHD.
12 Measures Level 2/Institution level variable: o ccr: Carnegie Classification research (1: yes; 0: no) o ccd: Carnegie Classification doctoral (1: yes; 0: no) o ccm: Carnegie Classification comprehensive (1: yes; 0: no) o public: 1: yes; 0: no
13 OLS regression Various HLM models Analyses
14 Results: OLS Regression See Table 1: detailed information on parameter estimates for final OLS regression model Adjusted R square=0.69 Consistent with the previous study where a separate regression equation was fitted for each of discipline groupings.
15 Results: HLM Models Oneway ANOVA with random effects Level 1: Y ij = β 0j + r ij Level 2: β 0j = γ 00 + u 0j Combined: Y ij = γ 00 + u 0j + r ij IntraClass Correlation (ICC)=0.235 About 24 percent of the variance in instructional cost is between institutions and there is substantial evidence of nesting of disciplines within schools.
16 Results: HLM Models Random Coefficients Regression to estimate the variability in the regression coefficients, including the level 1 intercept and level 1 slopes, across the level 2 units The variances of the intercept and the slopes for SUGALL, PCFTEA1, SGRALL, PCGSCH, PCTPER, SCHAYG, SCHAYU, SUGTT, busn, arts, nurs, bio, and nursmix, are highly significant
17 Results: HLM Models Means and slopes as outcomes model Incorporate level2 variables to explain the variability in the level 1 intercept and slopes o Level 1: Y ij = β 0j + β 1j (SUGALL) ij + β 2j (SGRALL) ij + β 3j (PCFTEA1) ij + β 4j (PCGSCH) ij + β 5j (PCTPER) ij + β 6j (SCHAYG) ij + β 7j (SCHAYU) ij + β 8j (SUGTT) ij + β 9j (MASTERS) ij + β 10j (PHD) ij + β 11j (UGGRMIX) ij + β 12j (BUSN) ij + β 13j (ENG) ij + β 14j (COMPSC) ij + β 15j (NURS) ij + β 16j (ARTS) ij + β 17j (CHEM) ij + β 18j (PHYS) ij + β 19j (ECON) ij + β 20j (GEOL) ij + β 21j (BIO) ij + β 22j (COMM) ij + β 23j (MATH) ij + β 24j (NURSMIX) ij + β 25j (ENGPHD) ij + β 26j (ENGMASTER) ij + β 27j (GEOLPHD) ij + r ij
18 Results: HLM Models o Level 2: β 0j = γ 00 + γ 01 (ccr) j + γ 02 (ccd) j + γ 03 (ccm) j + γ 04 (public) j + u 0j β 3j = γ 30 + γ 31 (ccd) j + γ 32 (public) j + u 3j β 12j = γ γ 121 (ccr) j + γ 122 (ccd) j + γ 123 (public) j + u 12j β 16j = γ γ 161 (ccr) j + γ 162 (public) j + u 16j
19 Results: HLM Models o Combined Multilevel Equation: Y ij = β 0j + γ 01 (ccr) j + γ 02 (ccd) j + γ 03 (ccm) j + γ 04 (public) j + β 1j (SUGALL) ij + β 2j (SGRALL) ij + γ 30 (PCFTEA1) ij + γ 31 (ccd) j (PCFTEA1) ij + γ 32 (public) j (PCFTEA1) ij + β 4j (PCGSCH) ij + β 5j (PCTPER) ij + β 6j (SCHAYG) ij + β 7j (SCHAYU) ij + β 8j (SUGTT) ij + β 9j (MASTERS) ij + β 10j (PHD) ij + β 11j (UGGRMIX) ij + γ 120 (BUSN) ij + γ 121 (ccr) j (BUSN) ij + γ 122 (ccd) j (BUSN) ij + γ 123 (public) j (BUSN) ij + β 13j (ENG) ij + β 14j (COMPSC) ij + β 15j (NURS) ij + γ 160 (ARTS) ij + γ 161 (ccr) j (ARTS) ij + γ 162 (public) j (ARTS) ij + β 17j (CHEM) ij + β 18j (PHYS) ij + β 19j (ECON) ij + β 20j (GEOL) ij + β 21j (BIO) ij + β 22j (COMM) ij + β 23j (MATH) ij + β 24j (NURSMIX) ij + β 25j (ENGPHD) ij + β 26j (ENGMASTER) ij + β 27j (GEOLPHD) ij + u 0j + u 3j (PCFTEA1) ij + u 12j (BUSN) ij + u 16j (ARTS) ij + r ij
20 Comparing Models: OLS vs. HLM See Table 1: detailed information on parameter estimates for the final HLM model. Also the results for an OLS regression model mimicking the HLM model. See Table 2 for random component estimates: significant residual variation in both intercepts and slopes.
21 Limitation and Future Directions Selfselected participating institutions and not a random sample Convergence problem New Level 2 variables
22 Questions? Qin Zhang Allison Walters
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