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Table 6 Model identification and model estimation for the post hoc modified measurement model in Fig. 3 (applying robust DWLS and ML using the statistical package LISREL)

From: Assessing adolescents’ perceived proficiency in critically evaluating nutrition information

Model Identification Unstandardized solution Completely standardized solution
DWLS ML DWLS ML
FP Observed variables Estimate (SE) Estimate (SE) Estimate Estimate
1 CNL1 factor loading .981 (.024) .976 (.024) .856 .852
  CNL2 factor loading 1.000*   1.000*   .872 .873
2 CNL3 factor loading .932 (.020) .930 (.020) .813 .812
3 CNL4 factor loading .932 (.023) .933 (.023) .813 .814
4 CNL5 factor loading .931 (.021) .931 (.021) .812 .813
5 CNL1 unique variance .267   .274   .267 .274
6 CNL2 unique variance .239   .238   .239 .238
7 CNL3 unique variance .339   .341   .339 .341
8 CNL4 unique variance .339   .337   .339 .337
9 CNL5 unique variance .340   .339   .340 .339
10 CNL1,CNL4 uniqueness relationship** − 0.061 (.021) − 0.059 (.021) −.061 −.059
11 CNL2,CNL5 uniqueness relationship** − 0.066 (.018) −0.067 (.018) −.066 −.067
  Latent variable   
12 CNL-Eval variance*** .761 .024 .762 .024 1.000 1.000
  1. Note. CNL1 - CNL5 are the observed variables, CNL-Eval is the latent variable. FP = Free parameter (counting the number of free parameters to be estimated with reference to the unstandardized soultion), DWLS = Diagonally Weighted Least Squares estimation, ML = Maximum Likelihood estimation, SE = Standard Error, Factor loading = the proportion of the total variance that an item shares with the other items ie., is common to the items (a variance component accounted for by the latent variable in the model), Unique variance = the proportion of the total variance that is unique to an item (a variance component not accounted for by the latent variable model in the model i.e., the unmodelled variance component). Additional correlation was specified between the error covariances of CNL1 and CNL4 and CNL2 and CNL5
  2. #) Lisrel reports unique variance components as 1-R2 for both the standardized and the unstandardized solutions, where R2 is the squared standardized factor loading when the item only load on one factor
  3. *) Factor loading constrained to 1 owing to item being used as reference or marker variable to resolve the origin and unit of measurement problem
  4. **) The relationship refers to the covariance (in the unstandardized solution) and the correlation (in the standardized solution) between the uniquene variance components of the repective observed variables. These relationships are data-driven re-specifications of M1
  5. ***) The variance of the latent variable is the “covariance with itself” in the unstandardized solution and the “correlation with itself” in the standardized solution. The latter is always 1