Table 3.
Simulation 3 Results
| Proportion correct K |
Average ARI |
|||||||
|---|---|---|---|---|---|---|---|---|
| Loadings (λ) | Factors (g) | Variables (v) | Correlation (ϕ) | Sample size (n) | Ward’s | K-means | Ward’s | K-means |
|
| ||||||||
| 0.7 | 2 | 4 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 4 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 4 | 0.5 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 4 | 0.5 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 6 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 6 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 2 | 6 | 0.5 | 500 | 0.98 | 1.00 | 0.9910 | 0.9933 |
| 0.7 | 2 | 6 | 0.5 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 4 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 4 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 4 | 0.5 | 500 | 0.98 | 0.99 | 0.9939 | 0.9938 |
| 0.7 | 4 | 4 | 0.5 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 6 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 6 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.7 | 4 | 6 | 0.5 | 500 | 0.92 | 0.97 | 0.9742 | 0.9711 |
| 0.7 | 4 | 6 | 0.5 | 1000 | 0.99 | 1.00 | 0.9988 | 0.9988 |
| 0.55 | 2 | 4 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 2 | 4 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 2 | 4 | 0.5 | 500 | 0.92 | 0.91 | 0.9443 | 0.9516 |
| 0.55 | 2 | 4 | 0.5 | 1000 | 0.98 | 0.99 | 0.9931 | 0.9927 |
| 0.55 | 2 | 6 | 0 | 500 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 2 | 6 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 2 | 6 | 0.5 | 500 | 0.92 | 0.91 | 0.9609 | 0.9721 |
| 0.55 | 2 | 6 | 0.5 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 4 | 4 | 0 | 500 | 0.99 | 0.99 | 0.9992 | 0.9992 |
| 0.55 | 4 | 4 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 4 | 4 | 0.5 | 500 | 0.64 | 0.59 | 0.8680 | 0.8552 |
| 0.55 | 4 | 4 | 0.5 | 1000 | 0.90 | 0.94 | 0.9668 | 0.9708 |
| 0.55 | 4 | 6 | 0 | 500 | 0.98 | 0.98 | 0.9977 | 0.9989 |
| 0.55 | 4 | 6 | 0 | 1000 | 1.00 | 1.00 | 1.0000 | 1.0000 |
| 0.55 | 4 | 6 | 0.5 | 500 | 0.53 | 0.59 | 0.8524 | 0.8498 |
| 0.55 | 4 | 6 | 0.5 | 1000 | 0.94 | 0.97 | 0.9841 | 0.9828 |
Note. The first five columns correspond to the cells of the experimental design: the strength of the factor loadings, the number of factors/communities, items per factor, correlation between factors, and sample size, respectively. The sixth and seventh columns indicate the proportion of problems in the cell for which Ward’s method and K-means led to the identification of the correct/true number of factors/communities. The eighth and eight ninth columns correspond to the cell average ARI values for the Ward’s and K-means implementations, respectively.