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Table 3 Likelihood ratio-based tests for number of classes

From: Revisiting the hypothesis of syndromic frailty: a cross-sectional study of the structural validity of the frailty phenotype

      Bootstrap      
k-class    Differences   1000 draws Observed Coefficients S.E Coverage Power
Models Entropy BIC in BIC LL p = 0,05 −2*(LL [H1]-LL [H0]) Bias Bias   
A: Latent classes: no factor loadings and no factor variance
1. classes differ on intercepts [LCA-ev models]
 4 classes*** N.A.** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 3 classes | 2 classes 0,681 65,379 −187 −32,611,7 17,5 231,4* 0,22% 1,58% 95,1% 99,9%
 2 classes | 1 class 0,670 65,566 − 952 − 32,727,4 16,7 988,8* 0,18% 1,63% 95,0% 100,0%
 1 class N/A 66,518 N.A. −33,221,8 N/A N.A. 0,10% 1,58% 94,9% 99,1%
 ***Search process stopped. One class with case count equal to 14 only.
2. classes differ on intercepts and residual errors [LCA-uv models]
 5 classes*** 0,557 65,251 N.A. −32,444,4 N.A. N.A. 1,16% 17,2% 93,5% 96,7%
 4 classes |3 classes 0,628 65,264 −62 −32,476,5 28,2 135,8* 0,55% 3,70% 94,3% 99,2%
 3 classes | 2 classes 0,601 65,326 −156 −32,544,4 27,7 245,6* 0,39% 1,56% 94,4% 96,6%
 2 classes | 1 class 0,696 65,482 − 1036 −32,667,2 31,5 1109,2* 0,15% 1,40% 95,1% 95,2%
 1 class N.A. 66,518 N.A. −33,221,8 N.A. N.A. 0,10% 1,58% 94,9% 99,1%
 ***S.E. bias greater than 10%
B: Factor mixture model - Classes do not differ on residual errors and factor variance
1. Strict measurement invariance [SiMI-ev models]
 3 classes*** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 2 classes | 1 class 0,219 65,359 10 −32,612,7 6,7 12,8* 2,98% 3,07% 94,9% 97,1%
 1 class N/A 65,349 N.A. −32,619,1 N.A. N.A. 0,89% 1,30% 95,1% 99,8%
 ***Search process stopped. One class with case count equal to one.
2. Weak measurement invariance [WMI-ev models]
 4 classes**** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 3 classes! 1 classes 0,657 65,250 −99 −32,528,5 30,0 181,2* 1,08% 1,82% 94,9% 99,3%
 2 classes*** 0,743 65,281 N.A. −32,566,5 N.A. N.A. 0,32% 10,6% 94,6% 99,8%
 1 class N/A 65,349 N.A. −32,619,1 N/A N.A. 0,89% 1,30% 95,1% 99,8%
 **** Search process stopped. One class with count equal to 18 only.
 ***S.E. bias greater than 10%
3. No measurement invariance [NMI-ev models]
 3 classes*** | 2 classes 0,484 65,264 −29 −32,506,2 24,8 103,2 1,75% 9,98% 95,1% 99,1%
 2 classes | 1 class 0,709 65,293 −56 −32,557,8 26,0 122,6* 0,42% 1,82% 95,0% 96,6%
 1 class N.A. 65,349 N/A −32,619,1 N.A. N.A. 0,89% 1,30% 95,1% 99,8%
 *** 3 classes model not significant
C: Factor mixture model - Classes differ on residual errors and factor variance
1. Strong measurement invariance [SoMI-uv models]
 5 classes*** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 4 classes | 2 classes 0,585 65,232 −32 −32,482,7 30,9 136,0* 0,96% 7,45% 93,6% 94,6%
 3 classes*** 0,437 65,234 N.A. −32,506,1 N.A. N.A. 0,71% 13,0% 94,4% 99,3%
 2 classes | 1 class 0,420 65,264 −85 −32,550,7 18,1 136,8* 0,68% 2,03% 93,9% 92,9%
1 class N.A. 65,349 N.A. −32,619,1 N.A. N.A. 0,89% 1,30% 95,1% 99,8%
 ***S.E. bias greater than 10%          
 ****           
2. Week measurement invariance [WMI-uv models]
 4 classes | 3 classes*** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 3 classes | 2 classes 0,393 65,202 −55 −32,456,9 27,1 143,0* 1,10% 6,43% 94,6% 99,0%
 2 classes | 1 class 0,399 65,257 −92 −32,528,4 33,7 181,4* 0,88% 8,11% 94,6% 99,3%
 1 class N.A. 65,349 N/A −32,619,1 N.A. N.A. 0,89% 1,30% 95,1% 99,8%
 *** The loglikelihood ratio for the (k-1) = 3-class model could not be computed. None of the coefficients on the factor part and of its variance were statistically significant. This model degenerated into the LPA 4-class model with equal variances
3. No measurement invariance [NMI-uv models]
 4 classes** N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A.
 3 classes | 1 classes 0,408 65,211 − 138 −32,438,8 58,4 360,6* 3,04% 9,8% 92,9% 94,1%
 2 classes*** 0,375 65,250 N.A. −32,510,1 N.A. N.A. 1,64% 10,7% 93,3% 99,1%
 1 class N.A. 65,349 N.A. −32,619,1 N.A. N.A. 0,89% 1,30% 95,1% 99,8%
 ** Search for a reduced model degenerated into the LPA model with 4 classes with unequal variances.    
 ***S.E. bias greater than 10%          
Note: * Null hypothesis rejected at p ≤ 0,05         
**N.A.: Not Applicable or Non Available