探索的分析妙课件.ppt

1、因子数-探索的分析妙-SAS因子数決定方法指定指定指定指定省略形省略形意味：概略意味：概略意味：意味：NFACTORS=?NFACTORS=?NFACT=?NFACT=?N=?N=?因子数因子数直接指定直接指定因子数因子数直接指定直接指定MINEIGEN=?MINEIGEN=?MIN=?MIN=?S*大S*大固有値数固有値数?大固有値?大固有値数因子数数因子数事前共通性事前共通性?=1?=1事前共通性事前共通性?=0?=0PROPORTION=?PROPORTION=?P=?P=?PERCENT=?PERCENT=?S*大S*大固有値数固有値数?=1?=1 主 成分分析法 主因子法（m=pr

2、in；m=p r i ni t）主 成分分析法 主因子法（m=pr in；m=p r i ni t）事 前共通性 S=S *（事前共通性 使 意味）事 前共通性 S=S *（事前共通性 使 意味）S*：相 関 行列S 対角要素事前共通性置換行列（p r e li m i n a r y)S*：相 関 行列S 対角要素事前共通性置換行列（p r e li m i n a r y)Reduced Correlation Matrix Reduced Correlation Matrix 観測変数数観測変数数SAS因子数決定方法：続指定指定指定指定省略形省略形意味：概略意味：概略意味：意味：NFAC

3、TORS=?NFACTORS=?NFACT=?NFACT=?N=?N=?因子数因子数直接指定直接指定因子数因子数直接指定直接指定MINEIGEN=?MINEIGEN=?MIN=?MIN=?W*大W*大固有値数固有値数?大固有値?大固有値数因子数数因子数事前共通性事前共通性?=999?=999事前共通性事前共通性?=0?=0PROPORTION=?PROPORTION=?P=?P=?PERCENT=?PERCENT=?W*大W*大固有値数固有値数Proc factor Proc factor 上記 基 準 e x p l ic i t 指 定 ，上記 基 準 e x p l ic i t 指 定

4、 ，SAS，基SAS，基準定因子数中最小採用準定因子数中最小採用Proc factor Proc factor 基準 e x p li c it 指 定 ，基準 e x p li c it 指 定 ，基準優先基準優先NFACTOR指定 因子数大 ，M I N E I G E N 基準適用 NFACTOR指定 因子数大 ，M I N E I G E N 基準適用 観測変数数観測変数数?=1?=1 最 尤法（m=m l）最 尤法（m=m l）事 前共通性 =0 逆数 =1/9 9 9 事 前共通性 =0 逆数 =1/9 9 9 W *=-0.5S*-0.5：S *wei g ht 施 行 列(P

5、r e l i m in a r y)W *=-0.5S*-0.5：S *wei g ht 施 行 列(P r e l i m in a r y)Weighted Reduced Correlation Matrix .事 前共通性Weighted Reduced Correlation Matrix .事 前共通性因子数 選定法-以下客観的解釈可能性考慮総合的判断-Guttman 関連 相関行列固有値値以上個数（）相関行列対角部分事前共通性（多）置換行列方法 Scree 法 相関行列固有値方法 吟味 共通性割合（累積寄与率）適合度検定，AIC Tucker-Lewis 指標Guttman 関

6、連 相関行列 S 固有値，値以上個数（）相関行列 S 対角部分事前共通性（多場合，）置換行列 S*方法 S*固有値，値以上個数 S*固有値大和初 tr(S*)事前共通性和超固有値番号（；prinit）DS*D固有値大和初 trDS*D 超固有値番号，D独自性平方根逆数対角行列（；ml）Guttman 考方Scree Plot(固有値 )真因子数-4-20246810121 2 3 4 5 6固有値番号固有値対角部分真共通性入下固有値以性代入対角部分真共通.hat Remember tSGuttman 実行問題点 正固有値数因子数 未知，S置換 真共通性未知，事前共通性 SMC，置換（S*作成）

7、S*正固有値数数 事前共通性正固有値数 事前共通性以上固有値数 問題点 事前共通性問題SMC真共通性過小評価過小評価 基準求因子真少可能性 S 置換問題？因子数過小推定：視覚説明Scree Plot(固有値 )真因子数-4-20246810121 2 3 4 5 6固有値番号固有値対角部分真共通性入対角部分入対角部分入 S 置換問題点 本来変動，正固有値数真因子数多 共通性過小評価因子数少見積欠点，上記相殺考方 固有値部分変化固有値手前固有値番号因子数方法 Scree法Scree Plot(固有値 )真因子数-4-2024681012141 2 3 4 5 6 7固有値番号固有値対角部分真共通

8、性入 1 2 3 4 5 6 7 8変形 Guttman 固有値部分合計正部分負部分相殺近従，固有値合計，第固有値真因子数合計近 第固有値固有値加，和固有値合計越固有値数因子数考 固有値合計 対角成分和（事前）共通性合計Scree Plot(固有値 )真因子数-4-2024681012141 2 3 4 5 6 7固有値番号固有値対角部分真共通性入 1 2 3 4 5 6 7 8数最小因子事前共通性合計固有値合計大方個*SGuttman 因子数過小推定：数理改善過小推定置換相関行列対角部分過小推定可能性数決因子数固有値数因子相関行列大，相関行列置換未知実際計算真因子数数大固有値数大固有値数大固

9、有値数大固有値数大固有値，00001111pijjipijjiijjippijjipijjiijjipcrrcsmcrrsmcrrIcrrcsmcrrsmcrrISci真共通性科目例X1X2X3X4X5X6X1X2X3X4X5X6語 1.0000.300英語0.439 1.0000.439 0.297歴史0.410 0.351 1.0000.410 0.351 0.206計算0.288 0.354 0.164 1.0000.288 0.354 0.164 0.420代数0.329 0.320 0.190 0.595 1.0000.329 0.320 0.190 0.595 0.418幾何0.2

10、48 0.329 0.181 0.470 0.464 1.0000.248 0.329 0.181 0.470 0.464 0.295固有値番号 1234556123456固有値2.731.130.620.600.520.402.070.43-0.07-0.12-0.17-0.21Preliminary Eigenvalues:Total=6 Average=1Preliminary Eigenvalues:Total=1.9354749 Average=0.32257915Psi-1/2S*Psi-1/23.200.63-0.11-0.17-0.25-0.33Preliminary Eige

11、nvalues:Total=2.96966246 Average=0.49494374 科 目（相関行列 S）科 目（事前共通性代入 S*）SAS出力（反復主因子法 prinit）Initial Factor Method:Iterated Principal Factor Analysis Initial Factor Method:Iterated Principal Factor Analysis Prior Communality Estimates:SMC Prior Communality Estimates:SMC X1 X2 X3 X4 X5 X6 X1 X2 X3 X4 X5

12、 X6 0.300104 0.296586 0.206095 0.419698 0.417752 0.295240 0.300104 0.296586 0.206095 0.419698 0.417752 0.295240 Preliminary Eigenvalues:Total=1.9354749 Average=0.32257915 Preliminary Eigenvalues:Total=1.9354749 Average=0.32257915 1 2 3 1 2 3 Eigenvalue 2.0729 0.4327 -0.0731 Eigenvalue 2.0729 0.4327

13、-0.0731 Difference 1.6402 0.5058 0.0466 Difference 1.6402 0.5058 0.0466 Proportion 1.0710 0.2236 -0.0378 Proportion 1.0710 0.2236 -0.0378 Cumulative 1.0710 1.2946 1.2568 Cumulative 1.0710 1.2946 1.2568 4 5 6 4 5 6 Eigenvalue -0.1197 -0.1723 -0.2051 Eigenvalue -0.1197 -0.1723 -0.2051 Difference 0.052

14、6 0.0329 Difference 0.0526 0.0329 Proportion -0.0618 -0.0890 -0.1060 Proportion -0.0618 -0.0890 -0.1060 Cumulative 1.1950 1.1060 1.0000 Cumulative 1.1950 1.1060 1.0000 1 factors will be retained by the PROPORTION criterion.1 factors will be retained by the PROPORTION criterion.SAS出力（最尤法ML）Initial Fa

15、ctor Method:Maximum Likelihood Initial Factor Method:Maximum Likelihood Prior Communality Estimates:SMC Prior Communality Estimates:SMC X1 X2 X3 X4 X5 X6 X1 X2 X3 X4 X5 X6 0.300104 0.296586 0.206095 0.419698 0.417752 0.295240 0.300104 0.296586 0.206095 0.419698 0.417752 0.295240 Preliminary Eigenval

16、ues:Total=2.96966246 Average=0.49494374 Preliminary Eigenvalues:Total=2.96966246 Average=0.49494374 1 2 3 1 2 3 Eigenvalue 3.1973 0.6268 -0.1084 Eigenvalue 3.1973 0.6268 -0.1084 Difference 2.5705 0.7352 0.0589 Difference 2.5705 0.7352 0.0589 Proportion 1.0767 0.2111 -0.0365 Proportion 1.0767 0.2111

17、-0.0365 Cumulative 1.0767 1.2877 1.2512 Cumulative 1.0767 1.2877 1.2512 4 5 6 4 5 6 Eigenvalue -0.1673 -0.2468 -0.3319 Eigenvalue -0.1673 -0.2468 -0.3319 Difference 0.0795 0.0851 Difference 0.0795 0.0851 Proportion -0.0563 -0.0831 -0.1118 Proportion -0.0563 -0.0831 -0.1118 Cumulative 1.1949 1.1118 1

18、.0000 Cumulative 1.1949 1.1118 1.0000 1 factors will be retained by the PROPORTION criterion.1 factors will be retained by the PROPORTION criterion.Scree 法固有値，固有値減少量直前固有値番号因子数種固有値相関行列 S相関行列 Sreduced correlation matrix S*reduced correlation matrix S*語語英語英語歴史歴史計算計算代数代数幾何幾何語語英語英語歴史歴史計算計算代数代数幾何幾何X1X11.0

19、001.0000.4390.4390.4100.4100.2880.2880.3290.3290.2480.2480.3000.3000.4390.4390.4100.4100.2880.2880.3290.3290.2480.248X2X20.4390.4391.0001.0000.3510.3510.3540.3540.3200.3200.3290.3290.4390.4390.2970.2970.3510.3510.3540.3540.3200.3200.3290.329X3X30.4100.4100.3510.3511.0001.0000.1640.1640.1900.1900.181

20、0.1810.4100.4100.3510.3510.2060.2060.1640.1640.1900.1900.1810.181X4X40.2880.2880.3540.3540.1640.1641.0001.0000.5950.5950.4700.4700.2880.2880.3540.3540.1640.1640.4200.4200.5950.5950.4700.470X5X50.3290.3290.3200.3200.1900.1900.5950.5951.0001.0000.4640.4640.3290.3290.3200.3200.1900.1900.5950.5950.4180.

21、4180.4640.464X6X60.2480.2480.3290.3290.1810.1810.4700.4700.4640.4641.0001.0000.2480.2480.3290.3290.1810.1810.4700.4700.4640.4640.2950.2951 12 23 34 45 56 6TotalTotalAverageAverage 2.73292.73291.12981.12980.61520.61520.60120.60120.52480.52480.39620.39626 61 1分析方法事前共通性分析方法事前共通性PCAPCAPrior Communality

22、Estimates:ONEPrior Communality Estimates:ONE因子数因子数2 factors will be retained by the MINEIGEN criterion2 factors will be retained by the MINEIGEN criterion *2.07292.07290.43270.4327-0.073-0.073-0.12-0.12-0.172-0.172-0.205-0.2051.93551.93550.32260.3226分析方法事前共通性分析方法事前共通性PCAPCAPrior Communality Estimate

23、s:SMCPrior Communality Estimates:SMC因子数因子数1 factors will be retained by the PROPORTION criterion1 factors will be retained by the PROPORTION criterionPsi-.5S*Psi-.5Psi-.5S*Psi-.53.19733.19730.62680.6268-0.108-0.108-0.167-0.167-0.247-0.247-0.332-0.3322.96972.96970.49490.4949分析方法事前共通性分析方法事前共通性MLMLPrio

24、r Communality Estimates:SMCPrior Communality Estimates:SMC因子数因子数1 factors will be retained by the PROPORTION criterion1 factors will be retained by the PROPORTION criterion固有値固有値種固有値：固有値-1-0.500.511.522.533.5123456固有値番号固有値大 *Psi-.5S*Psi-.5“Psi-.5S*Psi-.5”使意味最終共通性）。最終独自性（、固有値。、ISSddnddnpSSnipkiipkiii

25、2/1*2/12/12/11211),(2)(11)1ln()(trlnlnmin 適合度（乗）統計量値密接関係吟味因子数選択 共通性吟味 各変数共通性 共通因子説明割合（累積寄与率）適合度検定 Tucker-Lewis 指標吟味（SAS）Convergence criterion satisfied.Significance tests based on 220 observations:Test of H0:No common factors.vs HA:At least one common factor.Chi-square=310.841 df=15 Probchi*2=0.0001

26、 Test of H0:1 Factors are sufficient.vs HA:More factors are needed.Chi-square=51.996 df=9 Probchi*2=0.0001 Chi-square without Bartletts correction=52.840208721 Akaikes Information Criterion=34.840208721 Schwarzs Bayesian Criterion=4.2975608035 Tucker and Lewiss Reliability Coefficient=0.7577767173 V

27、ariance explained by each factor FACTOR1 Weighted 3.790389 Unweighted 2.105587 Final Communality Estimates and Variable Weights Total Communality:Weighted=3.790389 Unweighted=2.105587 X1 X2 X3 Comm.0.244586 0.288007 0.121284 Weight 1.324012 1.404759 1.138185 X4 X5 X6 Comm.0.534302 0.538613 0.378794

28、Weight 2.146855 2.166915 1.609663 Convergence criterion satisfied.Significance tests based on 220 observations:Test of H0:No common factors.vs HA:At least one common factor.Chi-square=310.841 df=15 Probchi*2=0.0001 Test of H0:2 Factors are sufficient.vs HA:More factors are needed.Chi-square=2.335 df

29、=4 Probchi*2=0.6745 Chi-square without Bartletts correction=2.3799173231 Akaikes Information Criterion=-5.620082677 Schwarzs Bayesian Criterion=-19.19459286 Tucker and Lewiss Reliability Coefficient=1.0211096922 Variance explained by each factor FACTOR1 FACTOR2 Weighted 4.614155 1.142786 Unweighted

30、2.209431 0.605674 Final Communality Estimates and Variable Weights Total Communality:Weighted=5.756941 Unweighted=2.815105 X1 X2 X3 Comm.0.489826 0.405929 0.356272 Weight 1.960113 1.683306 1.553451 X4 X5 X6 Comm.0.622633 0.568649 0.371796 Weight 2.649925 2.318306 1.591840因子因子出力解説：因子 Convergence crit

31、erion satisfied.Significance tests based on 220 observations:Test of H0:No common factors.vs HA:At least one common factor.Chi-square=310.841 df=15 Probchi*2=0.0001 Test of H0:2 Factors are sufficient.vs HA:More factors are needed.Chi-square=2.335 df=4 Probchi*2=0.6745 Chi-square without Bartletts c

32、orrection=2.3799173231 Akaikes Information Criterion=-5.620082677 Schwarzs Bayesian Criterion=-19.19459286 Tucker and Lewiss Reliability Coefficient=1.0211096922 Variance explained by each factor FACTOR1 FACTOR2 Weighted 4.614155 1.142786 Unweighted 2.209431 0.605674 Final Communality Estimates and

33、Variable Weights Total Communality:Weighted=5.756941 Unweighted=2.815105 X1 X2 X3 Comm.0.489826 0.405929 0.356272 Weight 1.960113 1.683306 1.553451 X4 X5 X6 Comm.0.622633 0.568649 0.371796 Weight 2.649925 2.318306 1.591840.02111.11/1/1/1.1946.194)220ln(3799.2)ln(.6201.5423799.22.3799.2)(tr|ln|ln)1(42/)()(335.2)(tr|ln|ln)3/26/)52(1(:152/)1(841.310|ln|)Diag(|ln)6/)52(1(:122110210IIkkIIIIkkkkkkkkdkkIdIIdTdTdTdTdTTLRCdnTAICsSchwarzdTAICSSnTkpkpdwhereTSSkpnTHvsHppdwhereTSSpnTHvsHkI構造仮定構造仮定対角行列