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Table 2 Parameter estimates of performance decline and proficiency
From: Performance decline in low-stakes educational assessments: different mixture modeling approaches
nac | aca | Group comparisons | |
|---|---|---|---|
Est. (SE) | Est. (SE) | Wald’s χ 2 (df) | |
Distribution of latent classes | |||
Proportion of no-decline class (π I) | |||
2PDM | 0.81 (0.01) | 0.91 (0.01) | 106.80 (1), p < 0.001 |
HYBRID | 0.62 (0.01) | 0.82 (0.01) | 226.86 (1), p < 0.001 |
MPDM | 0.48 (0.03) | 0.68 (0.03) | 41.60 (1), p < 0.001 |
Shape parameter (ω) | |||
2PDM | |||
HYBRID | 4.78 (0.15) | 7.33 (0.27) | 72.27 (1), p < 0.001 |
MPDM | 6.47 (0.26) | 10.25 (0.47) | 70.52 (1), p < 0.001 |
Magnitude of PD | |||
2PDM | –a | –a | –a |
HYBRID: response threshold (\(\tilde{\upbeta }\)) | 3.76 (0.18) | 3.48 (0.31) | 0.65 (1), p = 0.42 |
MPDM: decrement (κ) | 0.80 (0.04) | 0.91 (0.07) | 2.85 (1), p = 0.09 |
Proficiency distribution | |||
No-decline class: mean (μ I ) | |||
2PDM | − 1.02 (0.03) | 0b | 1637.64 (1), p < 0.001 |
HYBRID | − 1.01 (0.03) | 0b | 1385.61 (1), p < 0.001 |
MPDM | − 1.01 (0.03) | 0b | 1321.48 (1), p < 0.001 |
No-decline class: standard deviation (σ) | |||
2PDM | 0.82 (0.02) | 1b | 133.48 (1), p < 0.001 |
HYBRID | 0.82 (0.02) | 1b | 124.16 (1), p < 0.001 |
MPDM | 0.82 (0.02) | 1b | 127.80 (1), p < 0.001 |
Decline classes | |||
2PDM: mean (\(\upmu_{{i_{0} }}\)) | − 0.95 (0.04) | 0.02 (0.08) | 167.28 (1), p < 0.001 |
HYBRID: slope (ρ) | − 0.01 (0.004) | − 0.05 (0.01) | 17.29 (1), p < 0.001 |
MPDM: slope (ρ) | − 0.01 (0.004) | − 0.03 (0.01) | 5.66 (1), p = 0.02 |