Table 3.
Likelihood ratio-based tests for number of classes
| 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 | ||||||||||