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Table 5 Results of structural equation models for longitudinal competence measurement ignoring clustered structure (N = 7276)

From: The achievement gap in reading competence: the effect of measurement non-invariance across school types

  Model 3a   Model 3b   Model 4a   Model 4b  
M SD 95% PPI M SD 95% PPI M SD 95% PPI M SD 95% PPI
School Type Covariates
 Grade 5
  HS     0.627 0.014 (0.600, 0.653)     0.614 0.015 (0.587, 0.644)
  MS     − 0.129 0.014 (− 0.156, − 0.101)     − 0.117 0.015 (− 0.145, − 0.089)
  CS     − 0.098 0.013 (− 0.124, − 0.073)     − 0.094 0.014 (− 0.119, − 0.066)
  AT     − 0.138 0.014 (− 0.165, − 0.109)     − 0.140 0.015 (− 0.170, − 0.112)
  LS     − 0.404 0.012 (− 0.427, − 0.380)     − 0.403 0.013 (− 0.428, − 0.378)
 Grade 7
  HS     0.609 0.012 (0.584, 0.633)     0.615 0.013 (0.589, 0.640)
  MS     − 0.156 0.012 (− 0.180, − 0.131)     − 0.158 0.013 (− 0.184, − 0.133)
  CS     − 0.053 0.012 (− 0.076, − 0.030)     − 0.054 0.012 (− 0.078, − 0.031)
  AT     − 0.111 0.013 (− 0.136, − 0.086)     − 0.113 0.013 (− 0.138, − 0.088)
  LS     − 0.406 0.012 (− 0.428, − 0.382)     − 0.406 0.012 (− 0.429, − 0.382)
 Grade 9             
  HS     0.631 0.014 (0.604, 0.658)     0.628 0.014 (0.599, 0.656)
  MS     − 0.162 0.014 (− v0.188, − 0.135)     − 0.155 0.014 (− 0.184, − 0.128)
  CS     − 0.043 0.013 (− 0.068, − 0.018)     − 0.041 0.013 (− 0.066, − 0.015)
  AT     − 0.148 0.014 (− 0.174, − 0.120)     − 0.155 0.014 (− 0.183, − 0.127)
  LS     − 0.398 0.013 (− 0.425, − 0.372)     − 0.396 0.013 (− 0.421, − 0.370)
Variance components of the random effects
 Grade 5 0.542 0.072 (0.401, 0.689) 0.391 0.050 (0.291, 0.490) 0.490 0.069 (0.368, 0.666) 0.337 0.046 (0.255, 0.438)
 Grade 7 0.126 0.015 (0.103, 0.157) 0.094 0.012 (0.074, 0.119) 0.123 0.013 (0.101, 0.152) 0.098 0.014 (0.078, 0.133)
 Grade 9 0.307 0.045 (0.216, 0.390) 0.221 0.028 (0.174, 0.282) 0.255 0.035 (0.202, 0.340) 0.204 0.029 (0.154, 0.266)
Correlations and Covariances between latent factors Correlation Covariance Correlation Covariance Correlation Covariance Correlation Covariance
 Grade 5 with Grade 7 0.754 0.188 0.753 0.194 0.743 0.178 0.751 0.192
 Grade 5 with Grade 9 0.771 0.281 0.767 0.304 0.766 0.242 0.766 0.275
 Grade 7 with Grade 9 0.810 0.168 0.808 0.155 0.807 0.134 0.809 0.142
PPP 0.005    0.003    0.117    0.045   
  1. Standardized results are presented for fixed effects. M  posterior mean, SD posterior standard deviation, PPI posterior probability interval (2.5 and 97.5 percentile of the posterior distribution). School type covariates: HS high schools, MS middle secondary schools, CS comprehensive schools, AT schools offering all school tracks except high school, LS lower secondary schools, PPP posterior predictive p value. In Models 3a and 3b, no school-type specific item discrimination or item difficulty estimates were accounted for. In Models 4a and 4b, school-type specific item discrimination and item difficulty estimates were taken into account for items exhibiting DIF
  2. Correlations and covariances were reported based on sample statistics