| This study seeks to investigate how reliability influences the number of components extracted by different procedures under varying conditions of sample size (n), component loading (aij) and variable-to-component ratio (p:m). It compares four procedures, Kaiser rule, scree plot, Horn's parallel analysis procedure and modified Horn's parallel analysis procedure.;To investigate this issue, a Monte Carlo study was conducted. The underlying population correlation matrices were generated for each possible p, p:m and aij combination and the components upon which these population correlation matrices were based were independent of each other. The population correlation matrices were generated by specifying the component pattern matrix based on the combination of values for p:m and aij. The program was run four times to yield four different population correlation matrices, one correlation matrix for each combination of conditions. Ten samples were created for each combination of p:m, aij, rhoxx' and n. For each sample, the four extraction methods were compared for bias and RMSE.;Based on the results of this study, it has been shown that reliability has influence under certain conditions but not under other conditions. Modified Horn's parallel analysis procedure has the best overall performance, followed by Horn's parallel analysis procedure although the two procedures are quite close in performance. Both procedures display slight bias at low reliability values, with HPA overestimating, and MHPA underestimating the number of components. The scree plot is also highly accurate, in most cases, it is comparable to MHPA and HPA, and in some cases, it is even better. The Kaiser rule as expected is very poor in most situations. In all the situations, it is wrong; it overestimates the correct number of components. Overall, all the procedures perform worst at the reliability value of .60 and are best at the reliability value of 1.00. |
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