Hello all,
I have conducted Principal Component Factor Analysis (PCFA without rotation) and Exploratory Factor Analysis (EFA) using both SPSS and Stata, but I am getting differing results for the Bartlett scores. I plan to share the code and data files from both platforms and would greatly appreciate any feedback or guidance on whether I might be making an error in the process.
Thank you in advance for your help.
Stata codes:
Stata shows the following outputs on the Results window:
. pca ind1 ind2 ind3 ind4 ind5
Principal components/correlation Number of obs = 251,401
Number of comp. = 5
Trace = 5
Rotation: (unrotated = principal) Rho = 1.0000
--------------------------------------------------------------------------
Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 4.32578 4.03587 0.8652 0.8652
Comp2 | .289908 .0526725 0.0580 0.9231
Comp3 | .237236 .141594 0.0474 0.9706
Comp4 | .0956419 .0442101 0.0191 0.9897
Comp5 | .0514318 . 0.0103 1.0000
--------------------------------------------------------------------------
Principal components (eigenvectors)
------------------------------------------------------------------------------
Variable | Comp1 Comp2 Comp3 Comp4 Comp5 | Unexplained
-------------+--------------------------------------------------+-------------
ind1 | 0.4646 -0.1185 -0.2180 -0.5552 0.6437 | 0
ind2 | 0.4420 -0.0073 -0.7487 0.4618 -0.1757 | 0
ind3 | 0.4402 -0.4946 0.5249 0.4971 0.1977 | 0
ind4 | 0.4658 -0.1719 0.1577 -0.4652 -0.7157 | 0
ind5 | 0.4220 0.8437 0.3027 0.1227 0.0590 | 0
------------------------------------------------------------------------------
. factor ind1 ind2 ind3 ind4 ind5, ipf factors(1)
(obs=251,401)
Factor analysis/correlation Number of obs = 251,401
Method: iterated principal factors Retained factors = 1
Rotation: (unrotated) Number of params = 5
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 4.16953 4.10169 1.0000 1.0000
Factor2 | 0.06785 0.05953 0.0163 1.0163
Factor3 | 0.00831 0.04568 0.0020 1.0183
Factor4 | -0.03736 0.00144 -0.0090 1.0093
Factor5 | -0.03881 . -0.0093 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(10) = 1.6e+06 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
ind1 | 0.9719 | 0.0554
ind2 | 0.8925 | 0.2034
ind3 | 0.8871 | 0.2130
ind4 | 0.9761 | 0.0472
ind5 | 0.8298 | 0.3114
---------------------------------------
. predict bartlett_stata, bartlett
Scoring coefficients (method = Bartlett)
------------------------
Variable | Factor1
-------------+----------
ind1 | 0.37276
ind2 | 0.09327
ind3 | 0.08850
ind4 | 0.43947
ind5 | 0.05663
------------------------
The data on indicators and the generated Barlett scores are below:
Below is the "same" excercise performed on SPSS. I am sharing the syntax, the results and the generated Barlett scores:
SPSS Syntax
Here is the output on the Results window:
Factor Analysis
And here is the generated Barlett scores by SPSS, you can compare it with the Stata generated scores right next to it.
I tried to be as clear as possible, please let me know if you need more information that would help to clarify the discrepency.
Thank you in advance,
Nick
I have conducted Principal Component Factor Analysis (PCFA without rotation) and Exploratory Factor Analysis (EFA) using both SPSS and Stata, but I am getting differing results for the Bartlett scores. I plan to share the code and data files from both platforms and would greatly appreciate any feedback or guidance on whether I might be making an error in the process.
Thank you in advance for your help.
Stata codes:
Code:
pca ind1 ind2 ind3 ind4 ind5 factor ind1 ind2 ind3 ind4 ind5, ipf factors(1) predict bartlett_stata, bartlett
. pca ind1 ind2 ind3 ind4 ind5
Principal components/correlation Number of obs = 251,401
Number of comp. = 5
Trace = 5
Rotation: (unrotated = principal) Rho = 1.0000
--------------------------------------------------------------------------
Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 4.32578 4.03587 0.8652 0.8652
Comp2 | .289908 .0526725 0.0580 0.9231
Comp3 | .237236 .141594 0.0474 0.9706
Comp4 | .0956419 .0442101 0.0191 0.9897
Comp5 | .0514318 . 0.0103 1.0000
--------------------------------------------------------------------------
Principal components (eigenvectors)
------------------------------------------------------------------------------
Variable | Comp1 Comp2 Comp3 Comp4 Comp5 | Unexplained
-------------+--------------------------------------------------+-------------
ind1 | 0.4646 -0.1185 -0.2180 -0.5552 0.6437 | 0
ind2 | 0.4420 -0.0073 -0.7487 0.4618 -0.1757 | 0
ind3 | 0.4402 -0.4946 0.5249 0.4971 0.1977 | 0
ind4 | 0.4658 -0.1719 0.1577 -0.4652 -0.7157 | 0
ind5 | 0.4220 0.8437 0.3027 0.1227 0.0590 | 0
------------------------------------------------------------------------------
. factor ind1 ind2 ind3 ind4 ind5, ipf factors(1)
(obs=251,401)
Factor analysis/correlation Number of obs = 251,401
Method: iterated principal factors Retained factors = 1
Rotation: (unrotated) Number of params = 5
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 4.16953 4.10169 1.0000 1.0000
Factor2 | 0.06785 0.05953 0.0163 1.0163
Factor3 | 0.00831 0.04568 0.0020 1.0183
Factor4 | -0.03736 0.00144 -0.0090 1.0093
Factor5 | -0.03881 . -0.0093 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(10) = 1.6e+06 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
ind1 | 0.9719 | 0.0554
ind2 | 0.8925 | 0.2034
ind3 | 0.8871 | 0.2130
ind4 | 0.9761 | 0.0472
ind5 | 0.8298 | 0.3114
---------------------------------------
. predict bartlett_stata, bartlett
Scoring coefficients (method = Bartlett)
------------------------
Variable | Factor1
-------------+----------
ind1 | 0.37276
ind2 | 0.09327
ind3 | 0.08850
ind4 | 0.43947
ind5 | 0.05663
------------------------
The data on indicators and the generated Barlett scores are below:
Code:
* Example generated by -dataex-. For more info, type help dataex clear input float(ind1 ind2 ind3 ind4 ind5 bartlett_stata) -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.0625 -.036781464 -1.1741071 -1.8214285 -.625 -.6910955 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08181819 -.06459768 -1.0636363 -2.040909 -.6636364 -.8296663 -.08482143 -.05161264 -1.232143 -2.1875 -.6339286 -.8594399 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SPSS Syntax
Code:
DATASET ACTIVATE DataSet1. FACTOR /VARIABLES ind1 ind2 ind3 ind4 ind5 /MISSING LISTWISE /ANALYSIS ind1 ind2 ind3 ind4 ind5 /PRINT INITIAL CORRELATION SIG DET KMO EXTRACTION /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /ROTATION NOROTATE /SAVE BART(ALL) /METHOD=CORRELATION.
Factor Analysis
Notes | ||
Output Created | 18-JUN-2025 12:36:55 | |
Comments | ||
Input | Active Dataset | DataSet1 |
Filter | <none> | |
Weight | <none> | |
Split File | <none> | |
N of Rows in Working Data File | 251401 | |
Missing Value Handling | Definition of Missing | MISSING=EXCLUDE: User-defined missing values are treated as missing. |
Cases Used | LISTWISE: Statistics are based on cases with no missing values for any variable used. | |
Syntax | FACTOR /VARIABLES ind1 ind2 ind3 ind4 ind5 /MISSING LISTWISE /ANALYSIS ind1 ind2 ind3 ind4 ind5 /PRINT INITIAL CORRELATION SIG DET KMO EXTRACTION /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /ROTATION NOROTATE /SAVE BART(ALL) /METHOD=CORRELATION. |
|
Resources | Processor Time | 00:00:00.22 |
Elapsed Time | 00:00:00.19 | |
Maximum Memory Required | 4576 (4.469K) bytes | |
Variables Created | FAC1_1 | Component score 1 |
Correlation Matrixa | ||||||
ind1 | ind2 | ind3 | ind4 | ind5 | ||
Correlation | ind1 | 1.000 | .897 | .855 | .935 | .799 |
ind2 | .897 | 1.000 | .770 | .849 | .756 | |
ind3 | .855 | .770 | 1.000 | .902 | .727 | |
ind4 | .935 | .849 | .902 | 1.000 | .812 | |
ind5 | .799 | .756 | .727 | .812 | 1.000 | |
Sig. (1-tailed) | ind1 | .000 | .000 | .000 | .000 | |
ind2 | .000 | .000 | .000 | .000 | ||
ind3 | .000 | .000 | .000 | .000 | ||
ind4 | .000 | .000 | .000 | .000 | ||
ind5 | .000 | .000 | .000 | .000 | ||
a. Determinant = .001 |
KMO and Bartlett's Test | ||
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. | .878 | |
Bartlett's Test of Sphericity | Approx. Chi-Square | 1640856.417 |
df | 10 | |
Sig. | .000 |
Communalities | ||
Initial | Extraction | |
ind1 | 1.000 | .934 |
ind2 | 1.000 | .845 |
ind3 | 1.000 | .838 |
ind4 | 1.000 | .938 |
ind5 | 1.000 | .770 |
Extraction Method: Principal Component Analysis. |
Total Variance Explained | ||||||
Component | Initial Eigenvalues | Extraction Sums of Squared Loadings | ||||
Total | % of Variance | Cumulative % | Total | % of Variance | Cumulative % | |
1 | 4.326 | 86.516 | 86.516 | 4.326 | 86.516 | 86.516 |
2 | .290 | 5.798 | 92.314 | |||
3 | .237 | 4.745 | 97.059 | |||
4 | .096 | 1.913 | 98.971 | |||
5 | .051 | 1.029 | 100.000 | |||
Extraction Method: Principal Component Analysis. |
Component Matrixa | |
Component | |
1 | |
ind1 | .966 |
ind2 | .919 |
ind3 | .915 |
ind4 | .969 |
ind5 | .878 |
Extraction Method: Principal Component Analysis.a | |
a. 1 components extracted. |
And here is the generated Barlett scores by SPSS, you can compare it with the Stata generated scores right next to it.
Code:
ind1 ind2 ind3 ind4 ind5 bartlett_stata bartlett_SPSS -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.062500000000000 -.036781500000000 -1.1741070 -1.8214290 -.625000000000000 -.691095500000000 -.67392 -.081818200000000 -.064597700000000 -1.0636360 -2.0409090 -.663636400000000 -.829666300000000 -.80200 -.081818200000000 -.064597700000000 -1.0636360 -2.0409090 -.663636400000000 -.829666300000000 -.80200 -.081818200000000 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I tried to be as clear as possible, please let me know if you need more information that would help to clarify the discrepency.
Thank you in advance,
Nick
Comment