stata做因子分析的结果解释 Factor Analysis--Stata Annotated Output

tomhanks

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收藏 2012-01-12

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Stata Annotated Output
Factor AnalysisThis page shows an example factor analysis with footnotes explaining the output. We will do an iterated principal axes (ipf option) with SMC as initial communalities retaining three factors (factor(3) option) followed by varimax and promax rotations.
These data were collected on 1428 college students (complete data on 1365 observations) and are responses to items on a survey.  We will use item13 through item24 in our analysis.
use http://www.ats.ucla.edu/stat/stata/output/m255, clearfactor item13-item24, ipf factor(3)(obs=1365)          (iterated principal factors; 3 factors retained)  Factor    Eigenvaluea Differenceb Proportionc Cumulatived------------------------------------------------------------------    1       5.85150       5.04464    0.8336       0.8336    2       0.80687       0.44540    0.1149       0.9485    3       0.36146       0.23001    0.0515       1.0000    4       0.13146       0.07619    0.0187       1.0187    5       0.05527       0.02362    0.0079       1.0266    6       0.03164       0.02946    0.0045       1.0311    7       0.00218       0.00658    0.0003       1.0314    8    -0.00440       0.01466    -0.0006       1.0308    9    -0.01906       0.02688    -0.0027       1.0281 10    -0.04594       0.01440    -0.0065       1.0215 11    -0.06035       0.03050    -0.0086       1.0129 12    -0.09084             .    -0.0129       1.0000a. Eigenvalue: An eigenvalue is the variance of the factor. In the initial factor solution, the first factor will account for the most variance, the second will account for the next highest amount of variance, and so on. Some of the eigenvalues are negative because the matrix is not of full rank, that is, although there are 12 variables the dimensionality of the factor space is much less。 There are at most seven factors possible. b. Difference: Gives the differences between the current and following eigenvalue.
c. Proportion: Gives the proportion of variance accounted for by the factor.
d. Cumulative: Gives the cumulative proportion of variance accounted for by this factor plus all of the previous ones.

            Factor Loadingse Variable |    1       2       3 Uniquenessf-------------+-------------------------------------------    item13 | 0.71339 -0.39873 0.09231 0.32356    item14 | 0.70320 -0.33908 0.09782 0.38097    item15 | 0.72122 -0.24499 0.10575 0.40864    item16 | 0.64779 -0.18905 0.11144 0.53220    item17 | 0.78307 -0.07337 0.06670 0.37698    item18 | 0.73947 0.34478 0.11291 0.32157    item19 | 0.61655 0.41588 0.15515 0.42284    item20 | 0.55009 0.23916 0.09318 0.63152    item21 | 0.73173 0.11683 0.00067 0.45093    item22 | 0.61281 0.26089 -0.02282 0.55588    item23 | 0.81937 -0.02620 -0.34543 0.20863    item24 | 0.69515 0.01825 -0.38727 0.36646e. Factor Loadings: The factor loadings for this orthogonal solution represent both how the variables are weighted for each factor but also the correlation between the variables and the factor.
e. Uniqueness: Gives the proportion of the common variance of the variable not associated with the factors. Uniqueness is equal to 1 - communality.

rotate, varimax horstFactor analysis/correlation                      Number of obs =    1365 Method: iterated principal factors          Retained factors =       3 Rotation: orthogonal varimax (Horst on)       Number of params =    33 --------------------------------------------------------------------------       Factor  |    Variance Difference       Proportion Cumulative -------------+------------------------------------------------------------       Factor1  |    2.94943    0.29428          0.4202    0.4202       Factor2  |    2.65516    1.23992          0.3782    0.7984       Factor3  |    1.41524          .          0.2016    1.0000 -------------------------------------------------------------------------- LR test: independent vs. saturated:  chi2(66) = 8683.10 Prob>chi2 = 0.0000Rotated factor loadings (pattern matrix) and unique variancesg -----------------------------------------------------------       Variable |  Factor1 Factor2 Factor3 | Uniquenessh    -------------+------------------------------+--------------       item13 | 0.7714 0.1740 0.2260 |    0.3236          item14 | 0.7256 0.2130 0.2171 |    0.3810          item15 | 0.6756 0.2950 0.2187 |    0.4086          item16 | 0.5908 0.2926 0.1820 |    0.5322          item17 | 0.5867 0.4461 0.2825 |    0.3770          item18 | 0.2865 0.7386 0.2255 |    0.3216          item19 | 0.1702 0.7281 0.1343 |    0.4228          item20 | 0.2278 0.5396 0.1594 |    0.6315          item21 | 0.4020 0.5333 0.3210 |    0.4509          item22 | 0.2178 0.5584 0.2913 |    0.5559          item23 | 0.4488 0.3769 0.6692 |    0.2086          item24 | 0.3235 0.3205 0.6528 |    0.3665    -----------------------------------------------------------Factor rotation matrix -----------------------------------------                | Factor1  Factor2  Factor3    -------------+---------------------------       Factor1 |  0.6584 0.6121 0.4381       Factor2 | -0.6840 0.7294 0.0088       Factor3 |  0.3141 0.3055  -0.8989    -----------------------------------------

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tomhanks

2012-1-12 11:12:34

g. Rotated Factor Loadings: The factor loadings for the varimax orthogonal rotation represent both how the variables are weighted for each factor but also the correlation between the variables and the factor. A varimax rotation attempts to maximize the squared loadings of the columns.
h. Uniqueness: Same values as in e. above because it is still a three factor solution.

The blanks option displays only factor loading greater than a specific value (say 0.3).
rotate, varimax horst blanks(.3)

Factor analysis/correlation                      Number of obs =    1365
Method: iterated principal factors          Retained factors =       3
Rotation: orthogonal varimax (Horst on)       Number of params =    33

--------------------------------------------------------------------------
      Factor  |    Variance Difference       Proportion Cumulative
-------------+------------------------------------------------------------
      Factor1  |    2.94943    0.29428          0.4202    0.4202
      Factor2  |    2.65516    1.23992          0.3782    0.7984
      Factor3  |    1.41524          .          0.2016    1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated:  chi2(66) = 8683.10 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

-----------------------------------------------------------
      Variable |  Factor1 Factor2 Factor3 | Uniqueness
-------------+------------------------------+--------------
      item13 | 0.7714                   |    0.3236
      item14 | 0.7256                   |    0.3810
      item15 | 0.6756                   |    0.4086
      item16 | 0.5908                   |    0.5322
      item17 | 0.5867 0.4461          |    0.3770
      item18 |          0.7386          |    0.3216
      item19 |          0.7281          |    0.4228
      item20 |          0.5396          |    0.6315
      item21 | 0.4020 0.5333 0.3210 |    0.4509
      item22 |          0.5584          |    0.5559
      item23 | 0.4488 0.3769 0.6692 |    0.2086
      item24 | 0.3235 0.3205 0.6528 |    0.3665
-----------------------------------------------------------
(blanks represent abs(loading)<.3)

Factor rotation matrix

-----------------------------------------
               | Factor1  Factor2  Factor3
-------------+---------------------------
      Factor1 |  0.6584 0.6121 0.4381
      Factor2 | -0.6840 0.7294 0.0088
      Factor3 |  0.3141 0.3055  -0.8989
-----------------------------------------

rotate, promax horst blanks(.3)

Factor analysis/correlation                      Number of obs =    1365
Method: iterated principal factors          Retained factors =       3
Rotation: oblique promax (Horst on)          Number of params =    33

--------------------------------------------------------------------------
      Factor  |    Variance Proportion Rotated factors are correlated
-------------+------------------------------------------------------------
      Factor1  |    4.86265    0.6927
      Factor2  |    4.52052    0.6440
      Factor3  |    4.30842    0.6138
--------------------------------------------------------------------------
LR test: independent vs. saturated:  chi2(66) = 8683.10 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variancesi

-----------------------------------------------------------
      Variable |  Factor1 Factor2 Factor3 | Uniquenessj
-------------+------------------------------+--------------
      item13 | 0.8518                   |    0.3236
      item14 | 0.7855                   |    0.3810
      item15 | 0.6969                   |    0.4086
      item16 | 0.6044                   |    0.5322
      item17 | 0.5087                   |    0.3770
      item18 |          0.7626          |    0.3216
      item19 |          0.8200          |    0.4228
      item20 |          0.5541          |    0.6315
      item21 |          0.4298          |    0.4509
      item22 |          0.5265          |    0.5559
      item23 |                      0.7187 |    0.2086
      item24 |                      0.7502 |    0.3665
-----------------------------------------------------------
(blanks represent abs(loading)<.3)

Factor rotation matrix

-----------------------------------------
               | Factor1  Factor2  Factor3
-------------+---------------------------
      Factor1 |  0.8977 0.8593 0.8479
      Factor2 | -0.4157 0.4864 0.0071
      Factor3 |  0.1462 0.1581  -0.5301
-----------------------------------------
i. Rotated Factor Loadings: The factor loadings for the promax oblique rotation represent how the each of the variables are weighted for each factor. Note: these are not correlations between variables and factors. The promax rotation allows the factors to be correlated in an attempt to better approximate simple structure.
i. Uniqueness: Same values as in e. and h. above because it is still a three factor solution.
The estat common command is a postestimation command that displays the correlation among the factors of an oblique rotation.
estat common

Correlation matrix of the promax(3) rotated common factors

--------------------------------------------
      Factors |  Factor1 Factor2 Factor3
-------------+------------------------------
      Factor1 |       1
      Factor2 | .5923       1
      Factor3 | .6807    .6482       1
--------------------------------------------
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pavel1991

2015-2-15 15:39:16

好复杂呀

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小野说好啊

2020-12-17 18:46:04

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