Table 5.
Alternative Latent Curve Results from Fitting Univariate Dual Change Score Model to Different Scalings of Grade Point Averages (GPAs) (Ordinal GPA*)
| Parameters & Fit | (a) Interval GPA Linear Change |
(b) Interval GPA AR(1) Change |
(c) Interval GPA Dual Change |
(d) Ordinal GPA* Linear Change |
(e) Ordinal GPA* AR(1) Change |
(f) Ordinal GPA* Dual Change |
|---|---|---|---|---|---|---|
| Fixed Effects | ||||||
| Mean intercept, µ0 | 2.65 (211) | 2.69 (201) | 2.68 (210) | =0 | =0 | =0 |
| Mean slope, µ1 | 0.09 (17.) | =0 | −1.79 (3.3) | 0.14 (14) | =0 | 0.07 (4.6) |
| Constant change, α | =1 | =0 | =1 | =1 | =0 | =1 |
| Proportion change, β | =0 | 0.037 (15) | 0.69 (3.4) | =0 | =0.69 (3.2) | 0.84 (3.3) |
| Scaling coefficients, T | =1 | =1 | =1 | −1.8, −;1.3 −.70, −.30 .06, .66 1.2, 1.8 |
−2.0, −;1.5 −.77, −.31 .07, .75 1.3, 2.0 |
−1.9, −;1.4 −.80, −.30 .03, .67 1.2, 1.9 |
| Variable Intercepts, µ | =0 | −0.07 (3.6) | =0 | =0 | 0.16 (15) | =0 |
| Random Effects | ||||||
| Intercept Variance, σ02 | 0.42 (25) | 0.42 (25) | 0.40 (25) | =1 | = 1 | =1 |
| Slope variance, σ12 | 0.02 (5.1) | =0 | 1.22 (2.1) | 0.04 (6.3) | =0 | 0.78 (1.81) |
| Common slope-level, σ01 | −0.05 (7) | =0 | −0.29 (4.1) | −0.11 (8.7) | =0 | −.88 (−3.6) |
| Unique variance, ψ2 | .22 (35) | .027 (38) | .22 (35) | 0.48 (18) | 0.70 (27) | 0.53 (18) |
| Residual Variance, σe2 | =0 | −0.03 (5.7) | =0 | =0 | −0.05 (2.9) | =0 |
| Goodness of Fit | ||||||
| Misfit index χ2 / df | 48./8 | 114./8 | 24./7 | 174./26 | 246./26 | 94./25 |
| Change in fit Δχ2 / Δdf | 350./3 | 284./3 | 24./1; 90./1 | 985./3 | 913./3 | 80/1; 152./1 |
| WLSM scaling factor κ | 1 | 1 | 1 | 0.723 | 0.739 | 0.651 |
| RMSEA ε | .027 | .044 | .019 | .029 | .034 | .020 |
Note: Weighted least squares mean (WLSM) estimator based on weighted least squares plus mean adjusted variances. Sample size N=6,896, 15 patterns of incomplete data; Level Only Baseline for the two scalings are GPA=398/11 with ε=0.071, and GPA
*
=1159/29, κ=0.871, ε=0.075. Obtain Technical Appendix (from authors) for Mplus input and output. AR = autoregression. Root Mean Square Error of Approximation = RMSEA.