- From the menu, click on Analyze -> Dimension Reduction -> Factor…
- In the appearance window, move all variables to Variables… ->Continue
- Hit Descriptives… -> Check KMO and Barlett’s test of sphericity -> Continue
- Hit Extraction… -> check Scree plot -> choose Method: Principal components (if you are running PCA) or Method: Principal Axis Factoring (if you are running EFA) -> Continue
- Hit Rotation… -> choose rotation Method -> Varimax (if you want orthogonal rotation) or Direct Oblim (If you want oblim rotation) -> Continue
- Hit Scores… -> check Save as variables -> Continue
- Hit Continue and then hit Paste. The SPSS syntax is below:
FACTOR
/VARIABLES E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 A1 A2 A3 A4 A5 A6 A7 A8
A9 A10 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10
/MISSING LISTWISE
/ANALYSIS E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 A1 A2 A3 A4 A5 A6 A7 A8
A9 A10 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10
/PRINT INITIAL KMO EXTRACTION ROTATION
/FORMAT SORT BLANK(.35)
/PLOT EIGEN
/CRITERIA MINEIGEN(1) ITERATE(25)
/EXTRACTION PC
/CRITERIA ITERATE(25)
/ROTATION VARIMAX
/SAVE REG(ALL)
/METHOD=CORRELATION.
Output:
From the above table:
Communalities – This is the proportion of each variable’s variance that can be explained by the factors (e.g., the underlying latent continua). It is also noted as h2 and can be defined as the sum of squared factor loadings for the variables.
Initial – The initial values on the diagonal of the correlation matrix are 1 (for PCA)
Extraction – The values in this column indicate the proportion of each variable’s variance that can be explained by the retained factors.
From the above table:
Component – The initial number of components is the same as the number of variables used in the factor analysis.
Initial Eigenvalues – By definition, the initial value of the communality in a principal components analysis is 1.
Total – This column contains the eigenvalues. The first factor will always account for the most variance (and hence have the highest eigenvalue), and the next factor will account for as much of the left over variance as it can, and so on. Hence, each successive factor will account for less and less variance.
% of Variance – This column contains the percent of total variance accounted for by each factor (=Total/number of variables).
Cumulative % – This column contains the cumulative percentage of variance accounted for by the current and all preceding factors. For example, the second row shows a value of 100%. This means that the first two components together account for 100% of the total variance.
Extraction Sums of Squared Loadings – The number of rows in this panel of the table correspond to the number of factors retained. In this example, we ratined two components (using eigenvalue > 1 rule). The values in this panel of the table are calculated in the same way as the values in the left panel, except that here the values are based on the common variance. The values in this panel of the table will always be lower than the values in the left panel of the table, because they are based on the common variance, which is always smaller than the total variance.
Rotation Sums of Squared Loadings – The values in this panel of the table represent the distribution of the variance after the rotation. Varimax rotation tries to maximize the variance of each of the factors, so the total amount of variance accounted for is redistributed over the three extracted factors.
From the above table:
Component Matrix – This table contains component loadings, which are the correlations between the variable and the component. Because these are correlations, possible values range from -1 to +1.
Component – The columns under this heading are the principal components that have been extracted. As you can see by the footnote provided by SPSS (a.), two components were extracted (the two components that had an eigenvalue greater than 1).
Write up:
The PCA results from Bartlett’s Test of Sphericity indicate that variables are corelated ( (1225) = 376827.7 p <.001). Using a rule for extracting factors (eigenvalue greater than 1), eight factors were extracted explaining 16%, 9.23%, 7.49%, 7.1%, 5.52%, 3.16%, 2.66%, and 2.1% of variance in all 50 variables. After orthogonal rotation totaling, 53.3% of variance explained by eight factors. E4, E6, E7, E5, E2, E3, E8 E9, E10, E1, and A2 were loaded on Factor 1 (loadings were -.754, -.627, .747, .741, -.727, .658, -.631, .660, -.7, .695, and .351 respectively). The following were loaded on Factor 2;N8, N6, N7, N9, N1, N10, N3, N2, N5, N4 and C4 (loadings were .768, .762, .739, .729, .723, .661, .651, -.59, .575, -.401, and .352 respectively). The following were loaded on Factor 3; A4, A9, A6, A5, A8, A7, A2, A10, A3, and A1(loadings were .812, .754, .675, -.667, .653, -.617, .568, .468, -.45 and -.425). The following were loaded on Factor 4; C9, C5, C6, C1, C7, C2, C4, C8, C10, C3(loadings were .676, .671, -.652, .644, .605, -.603, -.599, -.531, .52, and .454 respectively). The following were loaded on Factor 5; O8, O1, O7, and O2(loadings were .764, .754, .547, -.426 respectively). The following were loaded on Factor 6; O6, O3, O10, O5 (loadings were -.785, .776, .702, and .573 respectively). The following were loaded on Factor 7; O2and O4 (loadings were .554 and .55 respectively). A1 was loaded on Factor 8 with a value of .489. Some items are cross-loaded.
Sources:
https://openpsychometrics.org/tests/IPIP-BFFM https://ipip.ori.org/new_ipip-50-item-scale.htm
Reference:
Goldberg, L. R. (1992). The development of markers for the Big-Five factor structure. Psychological Assessment, 4(1), 26–42. https://doi.org/10.1037/1040-3590.4.1.26