Table 7.
Dynamic Structural Equation Model (SEM) Results from a Bivariate Dual Change Score Model for Interval and Ordinal Scalings of Grade Point Averages (GPAs) and Weighted Center for Epidemiologic Studies-Depression (WCESD) Scale, including Alternative Misfits
| (a) Interval Scaling | (b) Ordinal* Scaling | |||
|---|---|---|---|---|
| Parameters | GPA | WCESD | GPA* | WCESD* |
| Fixed Effects | ||||
| Mean intercept, µ0 | 2.68 (202) | 1.48 (81) | =0 (=0) | =0 (=0) |
| Mean slope, µ1 | −0.66 (−.58) | 0.45 (.35) | 0.026 (1.00) | −0.052 (−2.34) |
| Constant change, α | =1 | =1 | =1 | =1 |
| Proportional change, β | 0.607 (2.57) | 0.140 (.22) | −0.109 (0.27) | −0.010 (−0.02) |
| Coupling, γ GPA → WCESD | 0.25 (−1.05) | 0.074 (−0.37) | ||
| Coupling, γ WCESD → GPA | 0.63 (−1.19) | 2.170 (−2.57) | ||
| Scaling coefficients, T | −1.8, −1.4, −0.7, −0.3, 0.01, 0.6, 1.1, 1.7 |
0.5, 1.4, 2.0, 2.7, 3.6 |
||
| Random Effects | ||||
| Intercept variance, σ02 | 0.40 (24) | 0.56 (15) | =1 (=0) | =1 (=0) |
| Slope variance, σ12 | 0.44 (1.2) | 0.05 (.38) | 4.58 (1.3) | 0.01 (0.71) |
| Cova. Slope & Level, σ01 | −0.31 (3.7) | −0.12 (.39) | −0.45 (−1.5) | −0.03 (−0.07) |
| Unique variance, ψ2 | 0.22 (35) | 0.49 (35) | 0.43 (14.7) | 0.81 (13.1) |
| Goodness-of-Fit | ||||
| “Dual Coupling” Misfit | 55.9 / 23 / 0.014 | 82.6 / 50 / 0.009 | ||
| “No GPA→ WCESD” | 56.7 / 24 / 0.014 | 82.0 / 51 / 0.009 | ||
| “No WCESD→ GPA” | 57.7 / 24 / 0.014 | 113. / 51 / 0.013 | ||
| “No Couplings” Misfit | 58.0 / 25 / 0.014 | 111. / 52 / 0.013 | ||
| “No Cross-Lags” Misfit | 83.0 / 27 / 0.017 | 191. / 54 / 0.019 | ||
| “No Slopes” Misfit | 168. / 32 / 0.024 | 1172. / 59 / 0.060 | ||
Notes: “Dual” model sample size is N=7,258 with 130 patterns of incomplete data; Ordinal ω4= .725; Not all model parameters are listed here; Obtain Technical Appendix (from authors) for Mplus input and output.