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. Author manuscript; available in PMC: 2012 Apr 1.
Published in final edited form as: Alzheimer Dis Assoc Disord. 2011 Apr-Jun;25(2):128–137. doi: 10.1097/WAD.0b013e3181ffa76d

Table 4.

Evaluation of Invariance Across Groups: Standardized Factor Loadings

Test Model 1
Configural Invariance		 Model 2
Metric Invariance		 Model 3
Strong (Scalar)Factorial Invariance		 Model 4
Strict Invariance
Fix variances=1 and means=0;
free intercepts
factor loadings,
and residual variances		 Fix factor loadings, variances=1,
and means=0; free intercepts
and residual variances		 Fix intercepts, factor loadings, and
variances;
fix means=0 in reference
group; free residual variances		 Fix intercepts, factor loadings,
variances, and residual variances;
fix means=0 in reference group
Norm
N=2409		 MCI
N=2037		 Dem
N=1564		 Norm
N=2409		 MCI
N=2037		 Dem
N=1564		 Norm
N=2409		 MCI
N=2037		 Dem
N=1564		 Norm
N=2409		 MCI
N=2037		 Dem
N=1564
Memory
LM Immediate Recall 0.92 0.98 1.04 0.999 0.98 0.92 0.92 0.90 0.85 0.90 0.90 0.90
LM Delayed Recall 0.94 0.84 0.63 0.85 0.81 0.83 0.93 0.88 0.89 0.89 0.89 0.89
Attention
Digits Forward 0.65 0.59 0.66 0.65 0.64 0.61 0.64 0.63 0.60 0.62 0.62 0.62
Digits Fwd Length 0.59 0.56 0.63 0.61 0.58 0.57 0.60 0.58 0.57 0.58 0.58 0.58
Digits Backward 0.88 0.91 0.89 0.89 0.89 0.90 0.90 0.89 0.91 0.90 0.90 0.90
Digits Bkwd Length 0.83 0.86 0.85 0.85 0.84 0.85 0.85 0.85 0.86 0.86 0.86 0.86
Executive
Trails A 0.78 0.78 0.85 0.80 0.80 0.81 0.78 0.78 0.78 0.78 0.78 0.78
Trails B 0.86 0.86 0.80 0.86 0.84 0.84 0.86 0.84 0.84 0.85 0.85 0.85
WAIS (Digit Symbol) 0.79 0.82 0.90 0.82 0.83 0.86 0.83 0.84 0.87 0.84 0.84 0.84
Language
Animals 0.74 0.83 0.90 0.78 0.82 0.89 0.76 0.80 0.86 0.79 0.79 0.79
Vegetables 0.58 0.69 0.79 0.64 0.69 0.75 0.68 0.73 0.79 0.72 0.72 0.72
Boston Naming 0.63 0.64 0.67 0.66 0.63 0.64 0.64 0.61 0.63 0.62 0.62 0.62
Fit Statistics
CFI 0.985 0.975 0.967 0.957
TLI 0.978 0.969 0.963 0.958
RMSEA 0.047 0.055 0.060 0.064
SRMR 0.029 0.065 0.072 0.071
†BIC, p-value, df −460.77, −, df=138 −254.30, p<.0001, df=162 −70.33, p<.0001, df=178 112.90, p<.0001, df=202
†S-B χ2 p-value, df df = 138 p <.0001, df = 162 p <.0001, df = 178 p <.0001, df = 202
†

Nested models tested using BIC33 and Satorra-Bentler Scaled χ2 test.32 Model 1 was used as the starting point as the least constrained model. Each model was found to be statistically significantly different from the prior model based on both measures

CFI=Comparative fit index, better fit >0.90; range 0.0 -1.0 34

TLI= Tucker-Lewis index: better fit > 0.90; range 0.0 -1.0 36

RMSEA= Root mean square error of approximation: better fit <0.05 39

SRMR = Standardized root mean square residual: better fit <0.0539

BIC = Bayesian Information Criterion: better fit<0.0 33

S-B=Satorra-Bentler Scaled χ2 test. 32