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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), < 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
  1. Note that parameters cannot be compared across models. See main text for more information
  2. nac: non-academic group; aca: academic group; 2PDM: multigroup two-class performance decline mode; HYBRID: multigroup HYBRID model; MPDM: multigroup multiclass performance decline model. All parameter estimates are group-specific
  3. aSee Fig. 3. b Parameters are fixed