Factor Analysis

[amera amery]

Hi,
I have a survey of 92 questions, grouped into 5 main topics. I applied factor analysis and determine 5 factors. The results I am getting for cumulative variance is very good, however the loading for questions in each factor is not as expectation, for example I am expecting the first 5 question to be in one factor. but the loading says different things. The uniqueness for the last 15 question( last group of question-red color) is vey high which means these questions are not covered by the model. Results as below:

. rotate

Factor analysis/correlation                      Number of obs    =        107
    Method: maximum likelihood                   Retained factors =          5
    Rotation: orthogonal varimax (Kaiser off)    Number of params =        390
                                                 Schwarz's BIC    =    6662.08
    Log likelihood =  -2419.84                   (Akaike's) AIC   =    5619.68

    --------------------------------------------------------------------------
         Factor  |     Variance   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      9.76978      3.99666            0.3438       0.3438
        Factor2  |      5.77312      0.72991            0.2032       0.5470
        Factor3  |      5.04321      0.62778            0.1775       0.7245
        Factor4  |      4.41544      1.00390            0.1554       0.8799
        Factor5  |      3.41153            .            0.1201       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated: chi2(3160)= 5991.86 Prob>chi2 = 0.0000
    LR test:   5 factors vs. saturated: chi2(2770)= 3445.07 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

    ----------------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3   Factor4   Factor5 
    -------------+--------------------------------------------------
     encodeing12 |  -0.0933   -0.2025    0.7176    0.0954   -0.0035 
     encodeing13 |  -0.0060    0.0348    0.6730    0.0628   -0.0350 
     encodeing14 |  -0.2131   -0.0385    0.6665    0.1257   -0.1781 
     encodeing15 |  -0.1644   -0.1365    0.7539   -0.0583   -0.0574 
     encodeing16 |  -0.1210   -0.0632    0.7266    0.1039    0.0141 
     encodeing17 |  -0.1758   -0.3353    0.6521    0.0968    0.0621 
     encodeing18 |  -0.1480   -0.0096    0.7198    0.0769   -0.0376 
     encodeing19 |  -0.0433   -0.0126    0.6249    0.0949   -0.0739 
     encodeing20 |   0.0297   -0.0140    0.0281   -0.7945   -0.1221 
     encodeing21 |   0.1817   -0.0366    0.0609    0.7061    0.1150 
     encodeing22 |   0.2049   -0.1139   -0.0053   -0.6944   -0.1016 
     encodeing23 |   0.0412   -0.0193    0.1738    0.7179    0.1783 
     encodeing24 |   0.0198   -0.0954   -0.1089   -0.6883   -0.0292 
     encodeing25 |   0.0673    0.0067    0.1591    0.7478    0.1597 
     encodeing26 |   0.0276    0.4931   -0.0794    0.0198    0.1129 
     encodeing27 |   0.7345    0.0422   -0.2093   -0.2005   -0.0407 
     encodeing28 |   0.3384    0.5893   -0.1641   -0.0453   -0.1942 
     encodeing29 |   0.6874   -0.0409   -0.2290    0.0457    0.1772 
     encodeing30 |  -0.0795    0.0479   -0.0152    0.1677    0.8016 
     encodeing31 |   0.7249    0.2455   -0.0511    0.0353   -0.1157 
     encodeing32 |   0.5734    0.3136   -0.0815   -0.0961   -0.1156 
     encodeing33 |   0.2444    0.7825   -0.0986    0.1070    0.0586 
     encodeing34 |   0.7946    0.0901   -0.1248    0.0311    0.0515 
     encodeing35 |   0.3595    0.7682   -0.1376    0.0611   -0.0371 
     encodeing36 |   0.7243    0.0355    0.0206   -0.0759    0.2035 
     encodeing37 |   0.1281    0.0431    0.0237    0.0702    0.7182 
     encodeing38 |   0.7104    0.2707   -0.0639    0.0011    0.0806 
     encodeing39 |   0.5694    0.5148    0.1337    0.0782    0.0226 
     encodeing40 |   0.3474    0.7560   -0.0110   -0.0628   -0.0175 
     encodeing41 |   0.8014    0.2557   -0.1367    0.0336   -0.2327 
     encodeing42 |   0.4425    0.6586   -0.2039   -0.0276   -0.0595 
     encodeing43 |   0.7487    0.0703    0.0217    0.0663    0.2633 
     encodeing44 |   0.0204   -0.0701   -0.0976    0.1184    0.8814 
     encodeing45 |   0.8228    0.1766    0.0565   -0.0251   -0.0043 
     encodeing46 |   0.5410    0.4289   -0.0317   -0.0022    0.0575 
     encodeing47 |   0.1849    0.8610   -0.0721    0.0367    0.0424 
     encodeing48 |   0.7296    0.1653   -0.1379    0.0115   -0.1239 
     encodeing49 |   0.4605    0.6015    0.0221   -0.0184    0.0123 
     encodeing50 |   0.7759    0.0855   -0.0240   -0.0277    0.0702 
     encodeing51 |   0.0111    0.0218   -0.0771    0.2192    0.7068 
     encodeing52 |   0.7309    0.3467   -0.0704    0.0629   -0.0539 
     encodeing53 |   0.6506    0.3757   -0.1006    0.0315   -0.0423 
     encodeing55 |   0.0615   -0.3325   -0.0857    0.0439   -0.1348 
     encodeing56 |  -0.1050   -0.0652   -0.0817    0.0533    0.1155 
     encodeing57 |  -0.0596   -0.1929   -0.1452    0.0668    0.1267 
     encodeing58 |   0.0081   -0.1263   -0.1560    0.1220   -0.0887 
     encodeing59 |  -0.1684   -0.0496   -0.1086    0.2456   -0.0305 
     encodeing60 |  -0.1445   -0.1584   -0.0315   -0.0169   -0.1545 
     encodeing61 |  -0.2128   -0.1675   -0.1999    0.2662    0.1324 
     encodeing62 |  -0.0970   -0.1510    0.0655    0.0133    0.0314 
     encodeing63 |  -0.0798    0.0276    0.1638    0.3008   -0.0075 
     encodeing64 |   0.0241    0.0371   -0.0123    0.3091    0.0805 
     encodeing65 |  -0.0862   -0.0971   -0.1231   -0.0212    0.0879 
     encodeing66 |   0.0142   -0.1229   -0.1073   -0.0330   -0.1951 
     encodeing67 |  -0.0125    0.0174    0.0721    0.4038    0.0140 
     encodeing68 |   0.2272   -0.1879   -0.1279    0.0673   -0.0675 
     encodeing69 |  -0.0217   -0.0251    0.0973    0.1196   -0.0671 
     encodeing70 |  -0.1718    0.0344    0.1047    0.2735   -0.0600 
     encodeing71 |  -0.0811    0.0439    0.0830    0.2436    0.0784 
     encodeing72 |  -0.1058    0.0983    0.0148    0.0503    0.1055 
     encodeing73 |   0.0941    0.0488   -0.0371   -0.0983   -0.0688 
     encodeing74 |   0.0908    0.0539    0.0537   -0.0080    0.1881 
     encodeing75 |   0.0224   -0.0082   -0.2226   -0.0494    0.0207 
     encodeing76 |   0.0228   -0.1094    0.0138    0.0212    0.0122 
     encodeing77 |   0.0565    0.0049   -0.2808   -0.3047   -0.1632 
     encodeing78 |  -0.0620   -0.0437   -0.0242   -0.0906   -0.0087 
     encodeing79 |  -0.0147    0.0658   -0.3803    0.0084   -0.1257 
     encodeing80 |   0.0543   -0.1547   -0.1792    0.1212    0.0023 
     encodeing81 |  -0.1151    0.0126   -0.1887    0.1657   -0.0796 
     encodeing82 |   0.1014   -0.0599    0.0642    0.0208    0.0358 
     encodeing83 |   0.1059   -0.1553   -0.1794   -0.0557   -0.1282 
     encodeing84 |  -0.0267    0.0558   -0.1108    0.1628   -0.1582 
     encodeing85 |   0.1482    0.1727    0.1949    0.0727    0.0377 
     encodeing86 |   0.1873   -0.0787   -0.1296    0.0834   -0.1218 
     encodeing87 |   0.3671    0.0060   -0.0290    0.0598   -0.0889 
     encodeing88 |  -0.0561    0.0642    0.0121    0.1115   -0.0932 
     encodeing89 |   0.0136    0.0755   -0.0269    0.3223   -0.1165 
     encodeing90 |  -0.0509    0.3005    0.0851    0.0935    0.1193 
     encodeing91 |  -0.0264    0.1701   -0.2679    0.0205   -0.2584 
     encodeing92 |  -0.1803    0.0515   -0.2301   -0.0452   -0.2613 
    ----------------------------------------------------------------

    ----------------------------
        Variable |   Uniqueness 
    -------------+--------------
     encodeing12 |      0.4262  
     encodeing13 |      0.5407  
     encodeing14 |      0.4613  
     encodeing15 |      0.3793  
     encodeing16 |      0.4424  
     encodeing17 |      0.4183  
     encodeing18 |      0.4525  
     encodeing19 |      0.5931  
     encodeing20 |      0.3520  
     encodeing21 |      0.4502  
     encodeing22 |      0.4525  
     encodeing23 |      0.4206  
     encodeing24 |      0.5041  
     encodeing25 |      0.3854  
     encodeing26 |      0.7366  
     encodeing27 |      0.3732  
     encodeing28 |      0.4716  
     encodeing29 |      0.4399  
     encodeing30 |      0.3204  
     encodeing31 |      0.3969  
     encodeing32 |      0.5436  
     encodeing33 |      0.3034  
     encodeing34 |      0.3413  
     encodeing35 |      0.2566  
     encodeing36 |      0.4265  
     encodeing37 |      0.4604  
     encodeing38 |      0.4115  
     encodeing39 |      0.3863  
     encodeing40 |      0.3034  
     encodeing41 |      0.2185  
     encodeing42 |      0.3246  
     encodeing43 |      0.3603  
     encodeing44 |      0.1942  
     encodeing45 |      0.2880  
     encodeing46 |      0.5191  
     encodeing47 |      0.2161  
     encodeing48 |      0.4059  
     encodeing49 |      0.4252  
     encodeing50 |      0.3844  
     encodeing51 |      0.4459  
     encodeing52 |      0.3338  
     encodeing53 |      0.4227  
     encodeing55 |      0.8582  
     encodeing56 |      0.9619  
     encodeing57 |      0.9176  
     encodeing58 |      0.9369  
     encodeing59 |      0.8962  
     encodeing60 |      0.9289  
     encodeing61 |      0.7983  
     encodeing62 |      0.9623  
     encodeing63 |      0.8755  
     encodeing64 |      0.8959  
     encodeing65 |      0.9598  
     encodeing66 |      0.9340  
     encodeing67 |      0.8311  
     encodeing68 |      0.8876  
     encodeing69 |      0.9706  
     encodeing70 |      0.8799  
     encodeing71 |      0.9191  
     encodeing72 |      0.9653  
     encodeing73 |      0.9730  
     encodeing74 |      0.9505  
     encodeing75 |      0.9470  
     encodeing76 |      0.9867  
     encodeing77 |      0.7985  
     encodeing78 |      0.9854  
     encodeing79 |      0.8350  
     encodeing80 |      0.9263  
     encodeing81 |      0.9172  
     encodeing82 |      0.9803  
     encodeing83 |      0.9129  
     encodeing84 |      0.9324  
     encodeing85 |      0.9035  
     encodeing86 |      0.9201  
     encodeing87 |      0.8529  
     encodeing88 |      0.9715  
     encodeing89 |      0.8760  
     encodeing90 |      0.8769  
     encodeing91 |      0.8314  
     encodeing92 |      0.8416  
    ----------------------------

I can not get the factors as expectation. Any recommendation will be appreciated.

[George Ford]

what format are the question answers?

[amera amery]

they are categorical answers vary from 1 to 5. Actually, I changed to CFA instead of EFA. and I have some general questions:
1- can I use the factor scores in regression analysis?
2- I am getting small negative values of factor scores. what does negative means? does it mean these participants answered negatively to that factor?

[Dirk Enzmann]

[deleted]

[Dirk Enzmann]

[deleted -- I don't know why the post appeared twice]

[Dirk Enzmann]

[Now the post has been deleted completely -- frustrating!]

[Dirk Enzmann]

Several comments:

• You should ask yourself whether the number of cases per item is sufficient in your case. A ratio of 1:1 is extremely low, rules of thumbs recommend a ratio of about 10:1 -- but it depends on whether your data are "well behaved", i.e. no cross-loadings, high communalities and several high item loadings (> 50) per factor. Additionally, in psychometrics it is rare to have measurement instruments with more than 30 items.
• In EFA you should carefully decide which criterion to use to determine the number of factors -- I would recommend parallel analysis.
• In EFA, again, you should have very good reasons to assume uncorrelated factors (you are using varimax rotation) -- otherwise you should rotate the solution obliquely and examine the correlation matrix of factors using the post-estimation command -estat common-.
• Especially with many items you should give the variables names that allow you to immediately identify the sub-scale or suspected factor to which the items belong, and you should use the post-estimation command -sortl- (from SSC) that enables you to quickly see whether the factor loadings fit to the pattern expected.

The following two introductory articles can give you a basic understanding of these issues:

• Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10(7), 1--7. [and the references therein]
• Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding Statistics, 2(1), 13--43.