Table 2.
Proportion of population models for which the best implementation and the R psych and SPSS implementations were among the best
| Best | Psychunity | PsychSMC | SPSS | |
|---|---|---|---|---|
| RMSE | ||||
| N = 180, pos. eigen. | .69 | .46 | .52 | .67 |
| N = 180, neg. eigen. | .50 | .10 | .00 | .60 |
| N = 450, pos. eigen. | .72 | .45 | .56 | .68 |
| N = 450, neg. eigen. | .78 | .00 | .00 | .78 |
| WMRMSE | .70 | .45 | .53 | .68 |
| Heywood cases | ||||
| N = 180, pos. eigen. | 1 | 1 | 1 | 1 |
| N = 180, neg. eigen. | 1 | 1 | .00 | 1 |
| N = 450, pos. eigen. | 1 | 1 | 1 | 1 |
| N = 450, neg. eigen. | 1 | 1 | .00 | 1 |
| WMHeywood | 1 | 1 | .98 | 1 |
| Ind.-to-Fac. Corres. | ||||
| N = 180, pos. eigen. | .93 | .70 | .93 | .91 |
| N = 180, neg. eigen. | 1 | .70 | .00 | 1 |
| N = 450, pos. eigen. | .92 | .72 | .86 | .90 |
| N = 450, neg. eigen. | .89 | .11 | .00 | .89 |
| WMInd.−to−Fac.Corres. | .93 | .70 | .88 | .91 |
| WMoverall | .88 | .72 | .80 | .86 |
| Settings | ||||
| PAF | ||||
| Communality method | SMC | unity | SMC | SMC |
| Criterion type | sum | sum | sum | max. ind. |
| Absolute eigenvalues | yes | no | no | yes |
| Convergence criterion | 10− 3 | 10− 3 | 10− 3 | 10− 3 |
| Promax rotation | ||||
| Varimax type | kaiser | svd | svd | kaiser |
| P type | norm | unnorm | unnorm | norm |
| k | 4 | 4 | 4 | 4 |
For positive eigenvalues, the proportion of the 108 population models for which the respective setting combination was among the best setting combinations is shown. For negative eigenvalues, the proportion of the population models including data sets that resulted in negative eigenvalues for which the respective setting combination was among the best setting combinations is shown. The top row contains the identifiers of the implementations, their settings are listed in the bottom part of the table. Boldface indicates that this implementation was most frequently among the best implementations for the respective data sets. Best = implementations with best results overall; Psychunity/PsychSMC = R psych implementation with unity/SMC as initial communality estimates; SPSS = SPSS implementation; RMSE = root mean square error; pos. eigen. = all-positive eigenvalues; neg. eigen. = some negative eigenvalues; WM = Weighted mean, where the weights are the number of datasets used in the respective regression analyses (those with negative eigenvalues made up only about 2% of all datasets and are thus weighted much less strongly; see Table best_implementations.xlsx in the online repository, https://osf.io/6prcz/); Ind.-to-Fac. Corres. = indicator-to-factor correspondences; PAF = principal axis factoring; P type = target matrix type; k = power in promax; MAC = maximum absolute correlation; SMC = squared multiple correlation; sum = deviance of the sum of all communalities; max. ind. = maximum absolute deviance of any communality; unnorm = unnormalized; norm = normalized; svd = singular value decomposition