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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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