因素分析主要目的是希望將資料的共變異數結構能夠用少數的"因素(factor)"來表達。
雖然因素分析中的因素負荷(factor loading)可由主成分分析中獲取,但和主成分分析的
目的與理論仍有相當程度的差異。此類方法一般區分為探索性因素分析(Exploratory Confirmatory FA, EFA)
與驗證性因素分析(Confirmatory FA, CFA),當你對於模式中欲萃取的因素個數以及變數間的影響參數未明時稱為探索性因素分析,
可應用於大部份的研究。驗證性因素分析則是指分析人員應用資料來分析已存在的模式(如其它學者所提出的模式假設),藉以驗證模式的正確性。此處所提供的方法主要為探索性因素分析
I ,欲使用驗證性因素分析,可連結至
結構方程模式(Structure Equation Modeling, SEM) 。
I:本方法使用資料的相關矩陣為分析基礎,以避變數免單位的差異過大影響分析結果。
本方法使用之R相關套件與參考文獻:
相關套件: stats、base、graphics、psych、GPArotation
參考文獻:(依套件名稱排序)
R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL:http://www.R-project.org/.
Revelle, W. (2013) psych: Procedures for Personality and Psychological Research, Northwestern University, Evanston, Illinois, USA. URL:http://CRAN.R-project.org/package=psych Version = 1.4.2.
Bernaards, Coen A. and Jennrich, Robert I. (2005) Gradient Projection Algorithms and Software for ArbitraryRotation Criteria in Factor Analysis, Educational and Psychological Measurement: 65, 676-696. URL:http://www.stat.ucla.edu/research/gpa
範例F-5:
數學家高斯曾說過”數學為科學之母”,數學的希臘語辭源為”學問的基礎”(取自維基百科),由此可見數學的重要性。某中學老師欲了解學生的數學能力,以Holzinger & Swineford (1939)之問卷對該校七、八年級學生進行智力測驗分析。問卷含五種構念I (空間、語言、速度、記憶及數學能力)並以24道試題呈現。隨機抽取145名七、八年級學生為施測對象協助完成測驗。資料包含性別、年齡(年)、年齡(月)、24道試題成績與年級,記錄如下表,資料說明於表後。
表:智力測驗分析表
編號
性別
年齡(年)
年齡(月)
t1
t2
t3
t4
t5
...
t23
t24
年級
1
1
13
0
23
19
13
4
46
...
11
17
7
2
2
11
10
33
22
12
17
43
...
31
32
7
3
1
12
6
34
24
14
22
36
...
21
18
7
:
:
:
:
:
:
:
:
:
:
:
:
:
145
1
13
5
26
24
16
27
51
...
31
29
8
性別:男性(1)、女性(2)
年級:七年級(7)、八年級(8)
註I:題1-4衡量空間概念、題5-9衡量語言、題10-13衡量速度、題14-19衡量記憶、題20-24衡量數學能力
Q1:
該中學教師認為由於年代的差異,此世代的學生可能因為學習環境的改變對於問卷中的構念可能有所影響,而有不同的解讀方式,希望針對問卷結果分析是否有新的構念或不同的解釋,該如何分析?
問題解析 欲將資料中24個試題進一步區分出不同的構念,須量測問卷中的試題特性及將具相似特性的試題歸納並產生新的構念群,且此構念群足以代表問卷中原有的試題,適合使用維度縮減的分析方法。
統計方法 綜合問題解析中的說明,所使用的統計方法須包含具有量測資料特性能力及維度縮減的方法。可採用分析方法:主成份分析(PCA)或探索性因素分析(EFA)。
因素分析 - 分析結果
分析方法: 因素分析
資料名稱: 範例F-5
變數名稱: t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18, t19, t20, t21, t22, t23, t24
因素選取方法: 主成份法(PCA)
轉軸方式: 不轉軸
計算時間: 0.402秒
樣本敘述統計量I :
變數名稱 Variable
樣本數 Count
平均數 Mean
中位數 Median
最小值 Minimum
最大值 Maximum
標準差 Std. dev.
t1 145 29.5793 30 11 51 6.9138 t2 145 24.8 25 9 37 4.445 t3 145 14.3034 14 6 23 2.8218 t4 145 15.9655 15 3 36 8.317 t5 145 44.8483 44 16 84 11.6579 t6 145 9.9517 9 1 19 3.3754 t7 145 18.8483 19 4 28 4.6493 t8 145 28.2 28 10 43 5.3575 t9 145 17.2828 16 2 41 7.9475 t10 145 90.1793 89 30 149 23.7822 t11 145 68.5931 67 19 118 16.6635 t12 145 109.7655 110 61 200 20.995 t13 145 191.7793 191 112 333 37.0354 t14 145 176.2759 177 130 198 10.8285 t15 145 89.3724 89 73 112 7.5424 t16 145 103.4 103 87 119 6.8011 t17 145 7.2069 7 0 26 4.5688 t18 145 9.4759 9 1 20 4.4738 t19 145 15.2414 16 4 20 3.5964 t20 145 30.3448 30 -18 87 19.7802 t21 145 14.4552 15 2 24 4.8319 t22 145 27.731 27 7 50 9.8243 t23 145 18.7517 19 1 40 9.3605 t24 145 25.8276 26 11 35 4.7131
I:樣本敘述統計量皆不包含遺失值
共變異數矩陣:
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t1 47.801 10.0125 7.2605 25.7979 26.408 7.9726 9.9357 12.0778 17.4253 17.1315 35.2512 44.6507 124.6565 9.7071 11.6161 19.7181 5.3376 11.4932 6.6439 49.2433 12.3803 28.1013 30.3254 8.9061 t2 10.0125 19.7583 2.3875 15.4167 14.2542 3.4208 3.2958 3.7139 6.8764 7.0153 11.175 15.675 40.8028 3.9375 4.5194 8.7403 0.2222 5.1514 1.7639 25.8819 6.3069 10.2375 14.1931 4.3125 t3 7.2605 2.3875 7.9628 8.5869 10.1575 2.48 3.4839 5.0431 5.8372 8.6188 11.6452 11.7244 40.6508 7.6379 3.9557 5.8917 1.6451 3.3199 1.5721 11.7627 4.5276 4.4433 7.6523 1.5874 t4 25.7979 15.4167 8.5869 69.1724 36.8975 9.2067 11.092 16.9167 22.9543 14.7632 25.1248 41.6585 114.7632 14.5235 12.874 16.3333 5.278 12.9887 5.3903 54.8036 16.5575 31.4212 33.3247 9.0982 t5 26.408 14.2542 10.1575 36.8975 135.9074 24.4648 35.4421 35.8431 66.7376 87.1038 66.5281 51.4503 148.2649 32.9935 19.2652 14.0125 11.3302 13.6908 8.2035 92.2332 17.9793 50.9242 47.3579 22.8348 t6 7.9726 3.4208 2.48 9.2067 24.4648 11.3935 11.2773 9.4125 19.1665 16.7657 20.2233 7.3567 39.3087 10.4648 6.3375 6.6167 4.2531 2.5092 3.0465 28.9195 4.293 12.9105 13.6615 6.8875 t7 9.9357 3.2958 3.4839 11.092 35.4421 11.2773 21.6157 15.7597 25.321 28.0691 19.2087 19.3114 61.2302 11.7366 5.5152 6.3458 5.3233 3.8227 4.0369 42.1638 7.0626 18.2922 17.7537 9.6403 t8 12.0778 3.7139 5.0431 16.9167 35.8431 9.4125 15.7597 28.7028 22.8528 37.7833 26.2139 32.6583 80.3708 14.0764 6.8625 10.8847 6.625 6.0708 5.0347 45.5972 9.3389 19.1167 24.7792 9.8125 t9 17.4253 6.8764 5.8372 22.9543 66.7376 19.1665 25.321 22.8528 63.1625 33.7684 38.0256 20.2126 79.9934 21.5048 12.7829 12.7542 10.3508 7.8437 7.9035 70.9782 10.4468 38.3891 36.8832 15.6463 t10 17.1315 7.0153 8.6188 14.7632 87.1038 16.7657 28.0691 37.7833 33.7684 565.5926 185.2957 293.1257 368.4357 40.4224 26.905 22.1569 32.7404 33.1363 17.012 76.153 46.1748 36.1875 56.8295 59.3367 t11 35.2512 11.175 11.6452 25.1248 66.5281 20.2233 19.2087 26.2139 38.0256 185.2957 277.6736 147.64 325.3124 58.4464 29.9651 35.6222 27.1889 24.688 17.3628 67.0649 31.9157 51.8967 39.1413 32.2905 t12 44.6507 15.675 11.7244 41.6585 51.4503 7.3567 19.3114 32.6583 20.2126 293.1257 147.64 440.7919 410.8229 29.6415 25.8865 18.3097 26.6739 32.161 8.1195 104.5953 36.1977 41.8532 69.4344 40.9385 t13 124.6565 40.8028 40.6508 114.7632 148.2649 39.3087 61.2302 80.3708 79.9934 368.4357 325.3124 410.8229 1371.6176 77.5821 38.5689 69.7833 32.2543 53.6335 33.6023 181.3752 77.1081 105.5652 132.9657 62.3089 t14 9.7071 3.9375 7.6379 14.5235 32.9935 10.4648 11.7366 14.0764 21.5048 40.4224 58.4464 29.6415 77.5821 117.2567 31.5979 28.1042 18.4078 9.09 8.5163 66.1889 9.5402 26.533 25.4231 15.0271 t15 11.6161 4.5194 3.9557 12.874 19.2652 6.3375 5.5152 6.8625 12.7829 26.905 29.9651 25.8865 38.5689 31.5979 56.8881 16.0653 11.9363 10.3424 4.972 39.2526 8.4613 18.1911 17.8153 5.7174 t16 19.7181 8.7403 5.8917 16.3333 14.0125 6.6167 6.3458 10.8847 12.7542 22.1569 35.6222 18.3097 69.7833 28.1042 16.0653 46.2556 10.5486 10.7875 6.2083 52.9931 11.6361 19.4556 22.5861 8.6597 t17 5.3376 0.2222 1.6451 5.278 11.3302 4.2531 5.3233 6.625 10.3508 32.7404 27.1889 26.6739 32.2543 18.4078 11.9363 10.5486 20.8736 9.0953 5.3803 25.1712 4.1691 13.2783 12.8295 7.3831 t18 11.4932 5.1514 3.3199 12.9887 13.6908 2.5092 3.8227 6.0708 7.8437 33.1363 24.688 32.161 53.6335 9.09 10.3424 10.7875 9.0953 20.015 5.7871 26.8278 7.65 14.5942 11.0287 8.5687 t19 6.6439 1.7639 1.5721 5.3903 8.2035 3.0465 4.0369 5.0347 7.9035 17.012 17.3628 8.1195 33.6023 8.5163 4.972 6.2083 5.3803 5.7871 12.9344 12.1037 5.7574 12.2529 10.0395 6.3336 t20 49.2433 25.8819 11.7627 54.8036 92.2332 28.9195 42.1638 45.5972 70.9782 76.153 67.0649 104.5953 181.3752 66.1889 39.2526 52.9931 25.1712 26.8278 12.1037 391.2553 38.8558 92.6837 95.3848 34.4071 t21 12.3803 6.3069 4.5276 16.5575 17.9793 4.293 7.0626 9.3389 10.4468 46.1748 31.9157 36.1977 77.1081 9.5402 8.4613 11.6361 4.1691 7.65 5.7574 38.8558 23.3469 17.7552 20.2318 10.204 t22 28.1013 10.2375 4.4433 31.4212 50.9242 12.9105 18.2922 19.1167 38.3891 36.1875 51.8967 41.8532 105.5652 26.533 18.1911 19.4556 13.2783 14.5942 12.2529 92.6837 17.7552 96.5174 46.7036 17.495 t23 30.3254 14.1931 7.6523 33.3247 47.3579 13.6615 17.7537 24.7792 36.8832 56.8295 39.1413 69.4344 132.9657 25.4231 17.8153 22.5861 12.8295 11.0287 10.0395 95.3848 20.2318 46.7036 87.6185 19.0194 t24 8.9061 4.3125 1.5874 9.0982 22.8348 6.8875 9.6403 9.8125 15.6463 59.3367 32.2905 40.9385 62.3089 15.0271 5.7174 8.6597 7.3831 8.5687 6.3336 34.4071 10.204 17.495 19.0194 22.2131
相關係數矩陣:
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t1 1 0.3258 0.3721 0.4486 0.3276 0.3416 0.3091 0.3261 0.3171 0.1042 0.306 0.3076 0.4868 0.1297 0.2228 0.4193 0.169 0.3716 0.2672 0.3601 0.3706 0.4137 0.4686 0.2733 t2 0.3258 1 0.1903 0.417 0.2751 0.228 0.1595 0.156 0.1947 0.0664 0.1509 0.168 0.2479 0.0818 0.1348 0.2891 0.0109 0.259 0.1103 0.2944 0.2936 0.2344 0.3411 0.2058 t3 0.3721 0.1903 1 0.3659 0.3088 0.2604 0.2655 0.3336 0.2603 0.1284 0.2477 0.1979 0.389 0.25 0.1859 0.307 0.1276 0.263 0.1549 0.2107 0.3321 0.1603 0.2897 0.1194 t4 0.4486 0.417 0.3659 1 0.3805 0.3279 0.2869 0.3797 0.3473 0.0746 0.1813 0.2386 0.3726 0.1613 0.2052 0.2888 0.1389 0.3491 0.1802 0.3331 0.412 0.3846 0.4281 0.2321 t5 0.3276 0.2751 0.3088 0.3805 1 0.6217 0.6539 0.5739 0.7203 0.3142 0.3425 0.2102 0.3434 0.2614 0.2191 0.1767 0.2127 0.2625 0.1957 0.4 0.3192 0.4446 0.434 0.4156 t6 0.3416 0.228 0.2604 0.3279 0.6217 1 0.7186 0.5205 0.7145 0.2089 0.3595 0.1038 0.3144 0.2863 0.2489 0.2882 0.2758 0.1662 0.251 0.4331 0.2632 0.3893 0.4324 0.4329 t7 0.3091 0.1595 0.2655 0.2869 0.6539 0.7186 1 0.6327 0.6853 0.2539 0.2479 0.1978 0.3556 0.2331 0.1573 0.2007 0.2506 0.1838 0.2414 0.4585 0.3144 0.4005 0.408 0.4399 t8 0.3261 0.156 0.3336 0.3797 0.5739 0.5205 0.6327 1 0.5367 0.2965 0.2936 0.2903 0.4051 0.2426 0.1698 0.2987 0.2707 0.2533 0.2613 0.4303 0.3608 0.3632 0.4941 0.3886 t9 0.3171 0.1947 0.2603 0.3473 0.7203 0.7145 0.6853 0.5367 1 0.1787 0.2871 0.1211 0.2718 0.2499 0.2132 0.236 0.2851 0.2206 0.2765 0.4515 0.272 0.4917 0.4958 0.4177 t10 0.1042 0.0664 0.1284 0.0746 0.3142 0.2089 0.2539 0.2965 0.1787 1 0.4676 0.5871 0.4183 0.157 0.15 0.137 0.3013 0.3114 0.1989 0.1619 0.4018 0.1549 0.2553 0.5294 t11 0.306 0.1509 0.2477 0.1813 0.3425 0.3595 0.2479 0.2936 0.2871 0.4676 1 0.422 0.5271 0.3239 0.2384 0.3143 0.3571 0.3312 0.2897 0.2035 0.3964 0.317 0.2509 0.4112 t12 0.3076 0.168 0.1979 0.2386 0.2102 0.1038 0.1978 0.2903 0.1211 0.5871 0.422 1 0.5283 0.1304 0.1635 0.1282 0.2781 0.3424 0.1075 0.2519 0.3568 0.2029 0.3533 0.4137 t13 0.4868 0.2479 0.389 0.3726 0.3434 0.3144 0.3556 0.4051 0.2718 0.4183 0.5271 0.5283 1 0.1935 0.1381 0.277 0.1906 0.3237 0.2523 0.2476 0.4309 0.2901 0.3836 0.357 t14 0.1297 0.0818 0.25 0.1613 0.2614 0.2863 0.2331 0.2426 0.2499 0.157 0.3239 0.1304 0.1935 1 0.3869 0.3816 0.3721 0.1876 0.2187 0.309 0.1823 0.2494 0.2508 0.2944 t15 0.2228 0.1348 0.1859 0.2052 0.2191 0.2489 0.1573 0.1698 0.2132 0.15 0.2384 0.1635 0.1381 0.3869 1 0.3132 0.3464 0.3065 0.1833 0.2631 0.2322 0.2455 0.2523 0.1608 t16 0.4193 0.2891 0.307 0.2888 0.1767 0.2882 0.2007 0.2987 0.236 0.137 0.3143 0.1282 0.277 0.3816 0.3132 1 0.3395 0.3545 0.2538 0.3939 0.3541 0.2912 0.3548 0.2702 t17 0.169 0.0109 0.1276 0.1389 0.2127 0.2758 0.2506 0.2707 0.2851 0.3013 0.3571 0.2781 0.1906 0.3721 0.3464 0.3395 1 0.445 0.3274 0.2785 0.1889 0.2958 0.3 0.3429 t18 0.3716 0.259 0.263 0.3491 0.2625 0.1662 0.1838 0.2533 0.2206 0.3114 0.3312 0.3424 0.3237 0.1876 0.3065 0.3545 0.445 1 0.3597 0.3032 0.3539 0.332 0.2634 0.4064 t19 0.2672 0.1103 0.1549 0.1802 0.1957 0.251 0.2414 0.2613 0.2765 0.1989 0.2897 0.1075 0.2523 0.2187 0.1833 0.2538 0.3274 0.3597 1 0.1701 0.3313 0.3468 0.2982 0.3737 t20 0.3601 0.2944 0.2107 0.3331 0.4 0.4331 0.4585 0.4303 0.4515 0.1619 0.2035 0.2519 0.2476 0.309 0.2631 0.3939 0.2785 0.3032 0.1701 1 0.4065 0.4769 0.5152 0.3691 t21 0.3706 0.2936 0.3321 0.412 0.3192 0.2632 0.3144 0.3608 0.272 0.4018 0.3964 0.3568 0.4309 0.1823 0.2322 0.3541 0.1889 0.3539 0.3313 0.4065 1 0.374 0.4473 0.4481 t22 0.4137 0.2344 0.1603 0.3846 0.4446 0.3893 0.4005 0.3632 0.4917 0.1549 0.317 0.2029 0.2901 0.2494 0.2455 0.2912 0.2958 0.332 0.3468 0.4769 0.374 1 0.5079 0.3778 t23 0.4686 0.3411 0.2897 0.4281 0.434 0.4324 0.408 0.4941 0.4958 0.2553 0.2509 0.3533 0.3836 0.2508 0.2523 0.3548 0.3 0.2634 0.2982 0.5152 0.4473 0.5079 1 0.4311 t24 0.2733 0.2058 0.1194 0.2321 0.4156 0.4329 0.4399 0.3886 0.4177 0.5294 0.4112 0.4137 0.357 0.2944 0.1608 0.2702 0.3429 0.4064 0.3737 0.3691 0.4481 0.3778 0.4311 1
特徵值及解釋變異比例表I :
編號 特徵值 eigenvalue 解釋變異比例 Proportion of var. 累積特徵值 Cumulative eigenvalue 累積解釋變異比例 Cumulative proportion of var. 1 8.2388 0.3433 8.2388 0.3433 2 2.0307 0.0846 10.2695 0.4279 3 1.6522 0.0688 11.9217 0.4967 4 1.5328 0.0639 13.4545 0.5606 5 1.0905 0.0454 14.545 0.606 6 0.9438 0.0393 15.4888 0.6454 7 0.8013 0.0334 16.2901 0.6788 8 0.7911 0.033 17.0812 0.7117 9 0.734 0.0306 17.8152 0.7423 10 0.6994 0.0291 18.5146 0.7714 11 0.6142 0.0256 19.1288 0.797 12 0.5844 0.0243 19.7132 0.8214 13 0.5236 0.0218 20.2368 0.8432 14 0.5045 0.021 20.7413 0.8642 15 0.4761 0.0198 21.2173 0.8841 16 0.4467 0.0186 21.6641 0.9027 17 0.3596 0.015 22.0236 0.9177 18 0.3496 0.0146 22.3732 0.9322 19 0.3409 0.0142 22.7142 0.9464 20 0.3332 0.0139 23.0474 0.9603 21 0.2899 0.0121 23.3372 0.9724 22 0.2658 0.0111 23.603 0.9835 23 0.2077 0.0087 23.8107 0.9921 24 0.1893 0.0079 24 1
I:選取因素個數,通常建議所選之因素其特徵值大於1
陡坡圖(scree plot)I :
I:選取因素個數,通常建議所選之因素其特徵值大於1
因素負荷(loadings)及解釋變異表(未轉軸):
變數 因素負荷 主成份1 主成份2 主成份3 主成份4 主成份5 t1 0.607 0.0496 0.4229 -0.1479 0.0168 t2 0.4048 -0.0199 0.4902 -0.2016 -0.1862 t3 0.4708 0.0282 0.3036 -0.1135 0.5655 t4 0.57 -0.0828 0.4625 -0.1912 -0.0094 t5 0.7009 -0.3863 -0.1977 -0.134 0.0872 t6 0.6851 -0.4569 -0.1999 0.0381 0.1096 t7 0.681 -0.4569 -0.2874 -0.0989 0.0657 t8 0.6882 -0.248 -0.1508 -0.1299 0.1246 t9 0.6939 -0.5061 -0.1934 0.026 -0.0186 t10 0.4818 0.4716 -0.49 -0.2247 -0.0103 t11 0.5836 0.3705 -0.2237 -0.0069 0.214 t12 0.4959 0.5246 -0.1744 -0.3453 0.0169 t13 0.6261 0.2968 0.0212 -0.3752 0.2526 t14 0.4484 0.0655 -0.0537 0.5352 0.3374 t15 0.4131 0.1301 0.1213 0.5017 0.1811 t16 0.534 0.142 0.3498 0.3454 0.1143 t17 0.4922 0.2473 -0.2181 0.5077 -0.0522 t18 0.5512 0.377 0.1433 0.1597 -0.1986 t19 0.4655 0.145 -0.0407 0.249 -0.3049 t20 0.6373 -0.1848 0.1339 0.116 -0.1879 t21 0.6328 0.24 0.1362 -0.1733 -0.1219 t22 0.6399 -0.1425 0.0968 0.1126 -0.3451 t23 0.7058 -0.0944 0.1477 -0.0613 -0.1932 t24 0.6604 0.162 -0.3269 -0.0299 -0.2907 解釋變異 8.2388 2.0307 1.6522 1.5328 1.0905 解釋變異比例 0.3433 0.0846 0.0688 0.0639 0.0454 累積解釋變異比例 0.3433 0.4279 0.4967 0.5606 0.606
變數共通性(communality)表:
變數 取1個因素 取2個因素 取3個因素 取4個因素 取5個因素 t1 0.3684 0.3709 0.5497 0.5716 0.5719 t2 0.1638 0.1642 0.4045 0.4451 0.4798 t3 0.2217 0.2225 0.3147 0.3276 0.6474 t4 0.3249 0.3318 0.5457 0.5822 0.5823 t5 0.4913 0.6405 0.6795 0.6975 0.7051 t6 0.4693 0.678 0.718 0.7195 0.7315 t7 0.4637 0.6725 0.7551 0.7649 0.7692 t8 0.4736 0.5351 0.5579 0.5748 0.5903 t9 0.4815 0.7376 0.775 0.7757 0.776 t10 0.2321 0.4545 0.6946 0.7451 0.7452 t11 0.3406 0.4778 0.5279 0.5279 0.5737 t12 0.2459 0.5211 0.5516 0.6708 0.6711 t13 0.392 0.4801 0.4805 0.6213 0.6851 t14 0.201 0.2053 0.2082 0.4947 0.6085 t15 0.1707 0.1876 0.2023 0.454 0.4868 t16 0.2852 0.3054 0.4277 0.547 0.5601 t17 0.2423 0.3034 0.351 0.6088 0.6115 t18 0.3038 0.4459 0.4664 0.492 0.5314 t19 0.2167 0.2377 0.2394 0.3014 0.3943 t20 0.4061 0.4402 0.4582 0.4716 0.5069 t21 0.4005 0.4581 0.4766 0.5066 0.5215 t22 0.4095 0.4298 0.4391 0.4518 0.5709 t23 0.4981 0.507 0.5288 0.5326 0.5699 t24 0.4361 0.4623 0.5692 0.5701 0.6546
模式適合度分析I 、II :
卡方檢定統計量 Chi-squared statistic 自由度 d.f. p-值 p-value 259.5748 166 0
I:使用主成份法(PCA) II:虛無假設:所選的因素其獨特性皆為0
殘差矩陣
變數 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t1 0.4281 -0.1529 -0.0698 -0.117 -0.0163 0.0368 0.0242 -0.0369 0.007 -0.0375 0.0234 0.003 0.0233 -0.0495 -0.0146 -0.0106 0.0261 -0.0153 0.0366 -0.0539 -0.1066 0.0139 -0.0234 0.0032 t2 -0.1529 0.5202 -0.0661 -0.0824 0.0698 0.0677 0.0079 -0.0566 0.0003 0.0737 0.0702 -0.0033 -0.0387 0.0987 0.0456 -0.0048 0.0161 -0.0316 -0.0618 -0.0445 -0.0821 -0.1164 -0.0671 0.0419 t3 -0.0698 -0.0661 0.3526 -0.057 -0.0148 -0.0462 -0.0033 -0.0228 0.02 0.0173 -0.0915 -0.0462 -0.1061 -0.0767 -0.0946 -0.0801 0.0422 0.0797 0.1447 -0.0053 0.0352 0.0416 0.0175 0.0641 t4 -0.117 -0.0824 -0.057 0.4177 0.0157 0.0004 -0.0245 0.0129 0.0041 0.0226 -0.0165 0.0142 -0.0389 0.0415 0.022 -0.0986 0.0762 0.0285 -0.0096 -0.0869 -0.0261 -0.0185 -0.0639 0.0119 t5 -0.0163 0.0698 -0.0148 0.0157 0.2949 -0.0789 -0.0757 -0.0624 0.0053 0.0326 0.0127 -0.0169 -0.0489 0.0041 0.0552 -0.0373 -0.0073 0.0889 -0.0227 -0.0597 -0.0173 0.0054 -0.0593 -0.028 t6 0.0368 0.0677 -0.0462 0.0004 -0.0789 0.2685 -0.0175 -0.1031 -0.0297 0.006 0.0611 -0.0198 0.012 -0.059 0.0106 0.0315 -0.0057 0.0051 0.0141 -0.0449 -0.0135 -0.0613 -0.0412 0.0222 t7 0.0242 0.0079 -0.0033 -0.0245 -0.0757 -0.0175 0.2308 -0.0137 -0.0703 -0.0211 -0.0593 0.0145 0.0173 -0.0269 0.008 0.0291 0.0193 0.0507 0.0236 0.0024 0.0231 -0.0387 -0.0667 -0.0136 t8 -0.0369 -0.0566 -0.0228 0.0129 -0.0624 -0.1031 -0.0137 0.4097 -0.0898 -0.0199 -0.0774 0.0059 -0.0292 -0.0303 -0.0213 0.0498 0.0328 0.0346 0.0411 0.0046 -0.002 -0.0403 0.0234 -0.0427 t9 0.007 0.0003 0.02 0.0041 0.0053 -0.0297 -0.0703 -0.0898 0.224 -0.0061 0.0305 0.0181 0.0061 -0.0461 0.0062 -0.002 0.0123 0.0488 0.0069 -0.0648 -0.017 -0.0151 -0.0152 -0.0264 t10 -0.0375 0.0737 0.0173 0.0226 0.0326 0.006 -0.0211 -0.0199 -0.0061 0.2548 -0.0973 -0.0621 -0.0946 0.0075 0.0636 0.0629 -0.0457 -0.0278 -0.0609 0.0317 0.0103 -0.017 0.0164 -0.0351 t11 0.0234 0.0702 -0.0915 -0.0165 0.0127 0.0611 -0.0593 -0.0774 0.0305 -0.0973 0.4263 -0.1067 -0.0001 -0.0426 -0.0591 0.0062 -0.0559 -0.0545 0.0222 -0.029 -0.0065 0.0926 -0.052 -0.0454 t12 0.003 -0.0033 -0.0462 0.0142 -0.0169 -0.0198 0.0145 0.0059 0.0181 -0.0621 -0.1067 0.3289 -0.0679 0.0434 0.0817 -0.0327 0.0424 -0.0452 -0.1154 0.0993 -0.1169 0.0219 0.0607 -0.0612 t13 0.0233 -0.0387 -0.1061 -0.0389 -0.0489 0.012 0.0173 -0.0292 0.0061 -0.0946 -0.0001 -0.0679 0.3149 0.01 -0.0193 -0.0061 0.0174 -0.0262 0.0891 -0.0084 -0.0737 0.0591 -0.0076 -0.0354 t14 -0.0495 0.0987 -0.0767 0.0415 0.0041 -0.059 -0.0269 -0.0303 -0.0461 0.0075 -0.0426 0.0434 0.01 0.3915 -0.13 -0.0718 -0.1307 -0.095 -0.0321 0.0439 0.0241 0.0332 0.0465 0.0842 t15 -0.0146 0.0456 -0.0946 0.022 0.0552 0.0106 0.008 -0.0213 0.0062 0.0636 -0.0591 0.0817 -0.0193 -0.13 0.5132 -0.1623 -0.108 -0.0318 -0.0927 -0.0165 0.032 -0.0061 0.0209 -0.0258 t16 -0.0106 -0.0048 -0.0801 -0.0986 -0.0373 0.0315 0.0291 0.0498 -0.002 0.0629 0.0062 -0.0327 -0.0061 -0.0718 -0.1623 0.4399 -0.0516 -0.0759 -0.0523 0.0144 0.0082 -0.0636 -0.0171 0.0524 t17 0.0261 0.0161 0.0422 0.0762 -0.0073 -0.0057 0.0193 0.0328 0.0123 -0.0457 -0.0559 0.0424 0.0174 -0.1307 -0.108 -0.0516 0.3885 0.0203 -0.0887 -0.0289 -0.0707 -0.038 0.0292 -0.0935 t18 -0.0153 -0.0316 0.0797 0.0285 0.0889 0.0051 0.0507 0.0346 0.0488 -0.0278 -0.0545 -0.0452 -0.0262 -0.095 -0.0318 -0.0759 0.0203 0.4686 -0.046 -0.0534 -0.1014 -0.0673 -0.1398 -0.0247 t19 0.0366 -0.0618 0.1447 -0.0096 -0.0227 0.0141 0.0236 0.0411 0.0069 -0.0609 0.0222 -0.1154 0.0891 -0.0321 -0.0927 -0.0523 -0.0887 -0.046 0.6057 -0.1804 0.0135 -0.0598 -0.0542 -0.0517 t20 -0.0539 -0.0445 -0.0053 -0.0869 -0.0597 -0.0449 0.0024 0.0046 -0.0648 0.0317 -0.029 0.0993 -0.0084 0.0439 -0.0165 0.0144 -0.0289 -0.0534 -0.1804 0.4931 0.0266 -0.048 -0.001 -0.0292 t21 -0.1066 -0.0821 0.0352 -0.0261 -0.0173 -0.0135 0.0231 -0.002 -0.017 0.0103 -0.0065 -0.1169 -0.0737 0.0241 0.032 0.0082 -0.0707 -0.1014 0.0135 0.0266 0.4785 -0.0324 -0.0309 -0.0048 t22 0.0139 -0.1164 0.0416 -0.0185 0.0054 -0.0613 -0.0387 -0.0403 -0.0151 -0.017 0.0926 0.0219 0.0591 0.0332 -0.0061 -0.0636 -0.038 -0.0673 -0.0598 -0.048 -0.0324 0.4291 -0.0313 -0.087 t23 -0.0234 -0.0671 0.0175 -0.0639 -0.0593 -0.0412 -0.0667 0.0234 -0.0152 0.0164 -0.052 0.0607 -0.0076 0.0465 0.0209 -0.0171 0.0292 -0.1398 -0.0542 -0.001 -0.0309 -0.0313 0.4301 -0.0294 t24 0.0032 0.0419 0.0641 0.0119 -0.028 0.0222 -0.0136 -0.0427 -0.0264 -0.0351 -0.0454 -0.0612 -0.0354 0.0842 -0.0258 0.0524 -0.0935 -0.0247 -0.0517 -0.0292 -0.0048 -0.087 -0.0294 0.3454
分數表(下載完整CSV檔):
觀察值 主成份1 主成份2 主成份3 主成份4 主成份5 1 -1.319 -0.7665 -0.6135 0.6205 1.2332 2 -0.0672 0.2399 0.3454 0.2581 -1.3819 3 -0.3419 -1.5065 1.5778 -0.5131 -0.4854 4 -0.5004 0.6217 -0.4445 -1.1765 -2.7142 5 0.0229 -0.3853 -1.4694 0.7684 -0.847 。 。 。 141 -0.8342 -0.0811 0.1349 -2.0756 1.1226 142 -1.0446 0.7997 -0.0254 -1.1382 0.4377 143 1.0405 0.6338 -1.0395 -0.6918 0.9042 144 -0.3703 0.0449 -1.1789 -0.3334 0.6587 145 1.4078 0.2834 -0.58 1.3278 -0.2639
變數及資料與前三個主成份分數散佈圖I,II :
第一、二個主成份:
第一、三個主成份:
第二、三個主成份:
I:圖中黑色數字表示樣本點
II:圖中紅色數字及箭頭表示變數位置及方向
[重新分析]