Rによるやさしい統計学 第16章 : 因子分析
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The document discusses using factor analysis to analyze a dataset with 5 variables and 200 observations. It performs factor analysis with 2 factors using varimax rotation and promax rotation. It also examines the unrotated factor solution. The analysis finds that 2 factors explain 54.3% of the total variance in the variables.
![1
> eigen( )
$values
[1] 2.5573782 1.0656034 0.5058941 0.4461472 0.4249772
$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.4040025 0.57915506 -0.3526733 -0.30988872 0.53004894
[2,] -0.4791362 0.36314955 -0.1046695 0.07323541 -0.78881668
[3,] -0.4380493 -0.48395278 0.2494573 -0.71311577 -0.05603054
[4,] -0.4064807 -0.54402387 -0.6062633 0.39786745 0.11383232
[5,] -0.5000967 0.05029462 0.6594556 0.48142803 0.28411115
@holidayworking () R 16 2006 6 26 8 / 18](https://image.slidesharecdn.com/factoranalysis-100626195523-phpapp02/85/R-16-8-320.jpg)
![> <- promax(loadings( ), m=4)
> print( )
$loadings
Loadings:
Factor1 Factor2
0.801 -0.156
0.749
0.815
0.692
0.461 0.348
Factor1 Factor2
SS loadings 1.419 1.291
Proportion Var 0.284 0.258
Cumulative Var 0.284 0.542
$rotmat
[,1] [,2]
[1,] 0.6062459 0.5303245
[2,] -1.0284319 1.0695617
@holidayworking () R 16 2006 6 26 15 / 18](https://image.slidesharecdn.com/factoranalysis-100626195523-phpapp02/85/R-16-15-320.jpg)
![rotmat
> <- solve(t( $rotmat)%*%
$rotmat)
>
[,1] [,2]
[1,] 1.0000000 0.5462117
[2,] 0.5462117 1.0000000
1 2 0.5462117
@holidayworking () R 16 2006 6 26 16 / 18](https://image.slidesharecdn.com/factoranalysis-100626195523-phpapp02/85/R-16-16-320.jpg)
Rによるやさしい統計学 第16章 : 因子分析
- 1. R 16 @holidayworking 2006 6 26 @holidayworking () R 16 2006 6 26 1 / 18
- 2. 1 2 3 R @holidayworking () R 16 2006 6 26 2 / 18
- 3. ) Twitter: @holidayworking : : : T-SQUARE F1 : Java, PL/SQL: Python, Ruby: @holidayworking () R 16 2006 6 26 3 / 18
- 4. i i i i : 5 @holidayworking () R 16 2006 6 26 4 / 18
- 5. R R factanal factanal(x, factors, rotation = "varimax") x factors rotation (varimax) (promax) @holidayworking () R 16 2006 6 26 5 / 18
- 6. 5 1 60.00 64.00 55.00 55.00 55.00 2 41.00 44.00 46.00 55.00 44.00 3 55.00 63.00 62.00 58.00 70.00 4 60.00 45.00 44.00 53.00 49.00 5 58.00 56.00 61.00 67.00 58.00 ( ) 195 64.00 47.00 52.00 42.00 48.00 196 39.00 36.00 35.00 38.00 36.00 197 42.00 43.00 43.00 57.00 39.00 198 64.00 58.00 47.00 33.00 56.00 199 49.00 47.00 46.00 49.00 54.00 200 51.00 51.00 49.00 50.00 46.00 @holidayworking () R 16 2006 6 26 6 / 18
- 7. > <- cor( ) > 1.0000000 0.5500166 0.1953799 0.1630274 0.4275140 0.5500166 1.0000000 0.3317530 0.2944938 0.5178159 0.1953799 0.3317530 1.0000000 0.5301135 0.4575891 0.1630274 0.2944938 0.5301135 1.0000000 0.3876493 0.4275140 0.5178159 0.4575891 0.3876493 1.0000000 0.55 0.53 4 0.39 0.52 ⇒ @holidayworking () R 16 2006 6 26 7 / 18
- 8. 1 > eigen( ) $values [1] 2.5573782 1.0656034 0.5058941 0.4461472 0.4249772 $vectors [,1] [,2] [,3] [,4] [,5] [1,] -0.4040025 0.57915506 -0.3526733 -0.30988872 0.53004894 [2,] -0.4791362 0.36314955 -0.1046695 0.07323541 -0.78881668 [3,] -0.4380493 -0.48395278 0.2494573 -0.71311577 -0.05603054 [4,] -0.4064807 -0.54402387 -0.6062633 0.39786745 0.11383232 [5,] -0.5000967 0.05029462 0.6594556 0.48142803 0.28411115 @holidayworking () R 16 2006 6 26 8 / 18
- 9. > <- factanal( , factors=2) > print( , cutoff=0) Call: factanal(x = , factors = 2) Uniquenesses Loadings Uniquenesses: SS loadings 0.471 0.395 0.379 0.548 0.491 Proportion Var Loadings: Cumulative Var Factor1 Factor2 0.722 0.084 0.730 0.268 0.177 0.768 0.156 0.654 0.537 0.470 Factor1 Factor2 SS loadings 1.399 1.317 Proportion Var 0.280 0.263 Cumulative Var 0.280 0.543 Test of the hypothesis that 2 factors are sufficient. The chi square statistic is 0.08 on 1 degree of freedom. @holidayworking () The p-value is 0.782 R 16 2006 6 26 9 / 18
- 10. 1 > <- 1 - $uniquenesses > 0.5288198 0.6049597 0.6213085 0.4523362 0.5087881 @holidayworking () R 16 2006 6 26 10 / 18
- 11. 1 2 0.722 0.084 0.529 0.730 0.268 0.605 0.537 0.470 0.509 0.177 0.768 0.621 0.156 0.654 0.452 0.722 1.317 1 ⇒ 2 ⇒ @holidayworking () R 16 2006 6 26 11 / 18
- 12. @holidayworking () R 16 2006 6 26 12 / 18
- 13. > <- factanal( , factors=2,rotation="promax") > print( , cutoff=0) Call: factanal(x = , factors = 2, rotation = "promax") Uniquenesses: 0.471 0.395 0.379 0.548 0.491 Loadings: Factor1 Factor2 0.801 -0.156 0.749 0.050 -0.051 0.815 -0.038 0.692 0.461 0.348 Factor1 Factor2 SS loadings 1.419 1.291 Proportion Var 0.284 0.258 Cumulative Var 0.284 0.542 Test of the hypothesis that 2 factors are sufficient. The chi square statistic is 0.08 on 1 degree of freedom. @holidayworking () The p-value is 0.782 R 16 2006 6 26 13 / 18
- 14. > <- factanal( , factors=2,rotation="none") > print( , cutoff=0) Call: factanal(x = , factors = 2, rotation = "none") Uniquenesses: 0.471 0.395 0.379 0.548 0.491 Loadings: Factor1 Factor2 0.583 -0.435 0.714 -0.307 0.657 0.436 0.563 0.368 0.713 -0.028 Factor1 Factor2 SS loadings 2.106 0.611 Proportion Var 0.421 0.122 Cumulative Var 0.421 0.543 Test of the hypothesis that 2 factors are sufficient. The chi square statistic is 0.08 on 1 degree of freedom. @holidayworking () The p-value is 0.782 R 16 2006 6 26 14 / 18
- 15. > <- promax(loadings( ), m=4) > print( ) $loadings Loadings: Factor1 Factor2 0.801 -0.156 0.749 0.815 0.692 0.461 0.348 Factor1 Factor2 SS loadings 1.419 1.291 Proportion Var 0.284 0.258 Cumulative Var 0.284 0.542 $rotmat [,1] [,2] [1,] 0.6062459 0.5303245 [2,] -1.0284319 1.0695617 @holidayworking () R 16 2006 6 26 15 / 18
- 16. rotmat > <- solve(t( $rotmat)%*% $rotmat) > [,1] [,2] [1,] 1.0000000 0.5462117 [2,] 0.5462117 1.0000000 1 2 0.5462117 @holidayworking () R 16 2006 6 26 16 / 18
- 17. R factanal @holidayworking () R 16 2006 6 26 17 / 18
- 18. @holidayworking () R 16 2006 6 26 18 / 18