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Research Problem ? Istheanalysisexploratory orconfirm atory ? Selectobjectivess: D atasum arization and Identifiying structures Datareduction Structure Equation M odeling Confirm atory FactorA nalysis W hatisbeing grouped variables orcases Research D esign W hatvariblesare included? H ow are the variablesm easured? W hatisthe desired sam ple size? Assum ption Statisticalconsiderationsofnorm ality, linearity, and hom osecedasticity H om ogeneity ofsam ple Conceptuallinkages Go

Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

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Page 1: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Research Problem?Is the analysis exploratory or confirmatory ?

Select objectivess:Data sumarization and Identifiying structures

Data reduction

Structure Equation Modeling

Confirmatory

Factor AnalysisWhat is being grouped variables or cases

Research DesignWhat varibles are included?How are the variables measured?What is the desired sample size?

AssumptionStatistical considerations of normality, linearity, and homosecedasticityHomogeneity of sample Conceptual linkages

Go

Page 2: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Go

Selecting a Factor MethodIs the total variance or only common variance analyzed

Specifying the Factor MatrixDetermine the number of factors to be retained

Total Variance Common Variance

Select a Rotational MethodShould the factors be correlated (Oblique) or

uncorrelated (Orthogonal)

Interpreting the Rotated Factor MatrixCan significant loadings be found?Can factors be named?Are communalities sufficient?

Factor Model RespectificationWere any variables deleted?

Do you want to change the number of factors?Do you want another type of rotation?

Validation of the Factor MatrixSplit/Multiple samplesSeparate analysis for subgroupsIdentify influencial cases

Selection of Surrogate Variables

Computation of Factor Scores

Creation of Summated Scales

Orthogoral Method Oblique Method

Yes

No

Page 3: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Factor Analysis

• 理論模式

• Zj 是第 j 個標準化分數• Fi 是共同因素• Uj 是 Zj 的唯一因素• aij 是因素負荷量

jmjmjjjj UFaFaFaFaz .....332211

Page 4: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 5: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 6: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

步驟 1

• 計算變相之間相關矩陣或共變數矩陣– KMO ( 抽樣適當性 , KMO>0.5)– Bartlett’s test( 抽樣適當性 , Bartlett 顯著 )– Correlation Matrix

研究者可以從相關矩陣分布 ,簡扼看出哪一些題項之間關係較為密切

Page 7: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 8: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

步驟 2

• 估計因素負荷量– 決定方法

• Principal component• Unweighted least squares• Generalized least square• Maxium likelihood

– 決定分析方式• Correlation matrix• Covariance matrix

Page 9: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 10: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 11: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

步驟 3

• 決定轉軸方式– None

– Varimax

– Quartimax

– Equamax

• 決定因子數目– Unrotated factor soluti

on

– Screet Plot

– Eigenvalue over>1

– Number of factors

Page 12: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 13: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

步驟 4

• 決定因素原則– 選取較少的題項 , 獲得最大的解釋

• Factor Loading

• % of variance

• Eigenvalue

• Cumulative %

– 給予相關性高的題項一個適當名稱

Page 14: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量
Page 15: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

結果Correlation Matrix

1.000 .658 .694 .461 .647 .695 .542 .558 .335 .419 .301 .388 .223 .194 .099 .197 .304 .138 .333 .395 .297 .393.658 1.000 .647 .493 .545 .617 .503 .455 .274 .386 .231 .406 .263 .129 .114 .077 .266 .167 .297 .409 .266 .471.694 .647 1.000 .659 .550 .682 .541 .547 .360 .385 .268 .420 .223 .188 .129 .149 .305 .175 .305 .444 .308 .345.461 .493 .659 1.000 .481 .509 .277 .437 .315 .231 .054 .191 -.003 -.009 -.121 .058 .204 .219 .290 .286 .152 .250.647 .545 .550 .481 1.000 .615 .489 .379 .290 .274 .230 .349 .039 .176 .202 .135 .145 .142 .373 .304 .413 .407.695 .617 .682 .509 .615 1.000 .488 .607 .430 .573 .337 .488 .251 .295 .174 .236 .371 .303 .396 .420 .291 .430.542 .503 .541 .277 .489 .488 1.000 .465 .152 .176 .239 .328 .261 .140 .257 .207 .240 .104 .319 .380 .382 .286.558 .455 .547 .437 .379 .607 .465 1.000 .215 .524 .467 .513 .352 .273 .238 .196 .259 .226 .363 .510 .327 .431.335 .274 .360 .315 .290 .430 .152 .215 1.000 .491 .336 .363 .305 .368 .161 .153 .523 .140 .281 .280 .220 .290.419 .386 .385 .231 .274 .573 .176 .524 .491 1.000 .643 .622 .519 .637 .406 .299 .416 .325 .387 .335 .202 .299.301 .231 .268 .054 .230 .337 .239 .467 .336 .643 1.000 .794 .526 .570 .512 .213 .391 .160 .222 .348 .258 .288.388 .406 .420 .191 .349 .488 .328 .513 .363 .622 .794 1.000 .504 .589 .513 .203 .377 .220 .233 .377 .331 .383.223 .263 .223 -.003 .039 .251 .261 .352 .305 .519 .526 .504 1.000 .481 .462 .378 .315 .285 .143 .261 .205 .229.194 .129 .188 -.009 .176 .295 .140 .273 .368 .637 .570 .589 .481 1.000 .587 .334 .317 .324 .284 .168 .239 .204.099 .114 .129 -.121 .202 .174 .257 .238 .161 .406 .512 .513 .462 .587 1.000 .272 .239 .109 .182 .290 .257 .236.197 .077 .149 .058 .135 .236 .207 .196 .153 .299 .213 .203 .378 .334 .272 1.000 .254 .198 .222 .302 .114 .108.304 .266 .305 .204 .145 .371 .240 .259 .523 .416 .391 .377 .315 .317 .239 .254 1.000 .213 .382 .579 .302 .232.138 .167 .175 .219 .142 .303 .104 .226 .140 .325 .160 .220 .285 .324 .109 .198 .213 1.000 .325 .250 .225 .131.333 .297 .305 .290 .373 .396 .319 .363 .281 .387 .222 .233 .143 .284 .182 .222 .382 .325 1.000 .338 .254 .205.395 .409 .444 .286 .304 .420 .380 .510 .280 .335 .348 .377 .261 .168 .290 .302 .579 .250 .338 1.000 .553 .444.297 .266 .308 .152 .413 .291 .382 .327 .220 .202 .258 .331 .205 .239 .257 .114 .302 .225 .254 .553 1.000 .358.393 .471 .345 .250 .407 .430 .286 .431 .290 .299 .288 .383 .229 .204 .236 .108 .232 .131 .205 .444 .358 1.000

A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22

CorrelationA1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22

Page 16: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Inverse of Correlation Matrix

3.245 -.662 -.899 .476 -1.069 -.421 -.244 -.585 -.021 -.156 -.197 .350 -.065 -.113 .512 -.154 -.284 .164 .109 .081 .136 .013-.662 2.739 -.384 -.343 -.291 -.191 -.432 .503 .307 -.572 .563 -.567 -.504 .231 .188 .392 .049 .080 -.077 -.412 .253 -.497-.899 -.384 3.495 -1.372 .251 -.727 -.509 .087 -.122 .149 .121 -.293 -.137 -.239 -.100 .151 .226 .215 .124 -.477 -.051 .269.476 -.343 -1.372 2.525 -.697 .220 .319 -.751 -.389 .029 .249 -.047 .269 .257 .357 -.105 -.187 -.349 -.055 .125 .229 .064

-1.069 -.291 .251 -.697 3.003 -.838 -.223 .545 -.209 .354 -.388 -.075 .610 .107 -.605 -.164 .597 .034 -.407 .312 -.714 -.238-.421 -.191 -.727 .220 -.838 3.652 -.298 -.693 -.273 -1.097 .665 -.529 .360 .252 .151 -.204 -.375 -.435 .127 .210 .256 -.188-.244 -.432 -.509 .319 -.223 -.298 2.129 -.463 .081 .802 -.109 .065 -.248 .101 -.323 -.168 -.132 .078 -.252 .172 -.307 .183-.585 .503 .087 -.751 .545 -.693 -.463 2.821 .474 -.579 -.401 -.241 -.314 .068 .106 .202 .592 .167 -.311 -.771 -.036 -.343-.021 .307 -.122 -.389 -.209 -.273 .081 .474 1.942 -.516 .041 .023 -.345 -.285 .241 .151 -.710 .261 -.027 .100 -.078 -.268-.156 -.572 .149 .029 .354 -1.097 .802 -.579 -.516 3.614 -1.012 .164 -.341 -.945 -.133 -.097 .070 -.087 -.369 .037 .121 .239-.197 .563 .121 .249 -.388 .665 -.109 -.401 .041 -1.012 3.693 -2.210 -.377 -.046 -.085 .178 -.333 .187 .062 -.243 .204 .032.350 -.567 -.293 -.047 -.075 -.529 .065 -.241 .023 .164 -2.210 3.848 -.100 -.644 -.303 .117 -.093 -.022 .272 .158 -.199 -.126

-.065 -.504 -.137 .269 .610 .360 -.248 -.314 -.345 -.341 -.377 -.100 2.185 .106 -.464 -.525 -.087 -.417 .236 .413 -.171 -.058-.113 .231 -.239 .257 .107 .252 .101 .068 -.285 -.945 -.046 -.644 .106 2.825 -.887 -.381 -.142 -.461 -.149 .756 -.324 -.076.512 .188 -.100 .357 -.605 .151 -.323 .106 .241 -.133 -.085 -.303 -.464 -.887 2.178 .027 .043 .260 -.026 -.526 .172 -.103

-.154 .392 .151 -.105 -.164 -.204 -.168 .202 .151 -.097 .178 .117 -.525 -.381 .027 1.451 .021 .047 -.083 -.564 .261 .054-.284 .049 .226 -.187 .597 -.375 -.132 .592 -.710 .070 -.333 -.093 -.087 -.142 .043 .021 2.324 .065 -.422 -1.187 .036 .164.164 .080 .215 -.349 .034 -.435 .078 .167 .261 -.087 .187 -.022 -.417 -.461 .260 .047 .065 1.459 -.286 -.286 -.148 .050.109 -.077 .124 -.055 -.407 .127 -.252 -.311 -.027 -.369 .062 .272 .236 -.149 -.026 -.083 -.422 -.286 1.596 .012 .022 .065.081 -.412 -.477 .125 .312 .210 .172 -.771 .100 .037 -.243 .158 .413 .756 -.526 -.564 -1.187 -.286 .012 3.003 -.969 -.409.136 .253 -.051 .229 -.714 .256 -.307 -.036 -.078 .121 .204 -.199 -.171 -.324 .172 .261 .036 -.148 .022 -.969 1.862 -.117.013 -.497 .269 .064 -.238 -.188 .183 -.343 -.268 .239 .032 -.126 -.058 -.076 -.103 .054 .164 .050 .065 -.409 -.117 1.651

A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22

Page 17: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Reproduced Correlations

.719b .683 .723 .587 .649 .712 .555 .599 .321 .420 .302 .441 .208 .186 .134 .138 .241 .188 .357 .398 .311 .445

.683 .656b .687 .553 .620 .664 .525 .561 .311 .373 .284 .417 .171 .144 .116 8.246E-02 .231 .125 .306 .387 .311 .447

.723 .687 .734b .625 .645 .725 .528 .589 .369 .427 .281 .420 .184 .170 8.795E-02 .124 .281 .201 .378 .407 .301 .440

.587 .553 .625 .675b .505 .610 .321 .398 .363 .277 1.923E-02 .147 -2.430E-02 -2.047E-02 -.201 3.702E-02 .238 .216 .362 .253 .112 .255

.649 .620 .645 .505 .612b .614 .563 .540 .201 .289 .219 .353 .149 .101 .122 .124 .174 .143 .308 .396 .345 .422

.712 .664 .725 .610 .614 .755b .502 .614 .439 .554 .375 .497 .296 .310 .167 .223 .354 .307 .446 .419 .286 .419

.555 .525 .528 .321 .563 .502 .631b .520 3.185E-02 .214 .233 .347 .219 .142 .275 .238 .128 .171 .297 .457 .462 .416

.599 .561 .589 .398 .540 .614 .520 .572b .294 .481 .428 .524 .354 .345 .320 .248 .282 .235 .351 .424 .357 .423

.321 .311 .369 .363 .201 .439 3.185E-02 .294 .706b .556 .418 .429 .255 .346 .106 5.538E-02 .623 .186 .310 .370 .178 .297

.420 .373 .427 .277 .289 .554 .214 .481 .556 .784b .664 .682 .569 .668 .434 .323 .461 .353 .370 .295 .150 .287

.302 .284 .281 1.923E-02 .219 .375 .233 .428 .418 .664 .756b .747 .593 .655 .608 .226 .382 .125 .168 .317 .263 .363

.441 .417 .420 .147 .353 .497 .347 .524 .429 .682 .747 .774b .576 .623 .581 .225 .375 .139 .217 .365 .305 .432

.208 .171 .184 -2.430E-02 .149 .296 .219 .354 .255 .569 .593 .576 .564b .618 .553 .375 .294 .287 .246 .262 .215 .212

.186 .144 .170 -2.047E-02 .101 .310 .142 .345 .346 .668 .655 .623 .618 .706b .566 .393 .347 .330 .266 .223 .147 .178

.134 .116 8.795E-02 -.201 .122 .167 .275 .320 .106 .434 .608 .581 .553 .566 .662b .323 .217 .138 .118 .302 .329 .269

.138 8.246E-02 .124 3.702E-02 .124 .223 .238 .248 5.538E-02 .323 .226 .225 .375 .393 .323 .500b .217 .475 .383 .270 .217 5.092E-02

.241 .231 .281 .238 .174 .354 .128 .282 .623 .461 .382 .375 .294 .347 .217 .217 .748b .295 .414 .609 .433 .341

.188 .125 .201 .216 .143 .307 .171 .235 .186 .353 .125 .139 .287 .330 .138 .475 .295 .554b .474 .253 .134 6.613E-03

.357 .306 .378 .362 .308 .446 .297 .351 .310 .370 .168 .217 .246 .266 .118 .383 .414 .474 .502b .426 .289 .191

.398 .387 .407 .253 .396 .419 .457 .424 .370 .295 .317 .365 .262 .223 .302 .270 .609 .253 .426 .767b .675 .488

.311 .311 .301 .112 .345 .286 .462 .357 .178 .150 .263 .305 .215 .147 .329 .217 .433 .134 .289 .675 .654b .450

.445 .447 .440 .255 .422 .419 .416 .423 .297 .287 .363 .432 .212 .178 .269 5.092E-02 .341 6.613E-03 .191 .488 .450 .471b

-2.521E-02 -2.905E-02 -.127 -2.643E-03 -1.668E-02 -1.345E-02 -4.096E-02 1.343E-02 -1.513E-03 -1.210E-03 -5.297E-02 1.480E-02 8.052E-03 -3.426E-02 5.892E-02 6.252E-02 -5.008E-02 -2.390E-02 -3.022E-03 -1.454E-02 -5.222E-02-2.521E-02 -3.934E-02 -6.002E-02 -7.577E-02 -4.742E-02 -2.275E-02 -.106 -3.757E-02 1.346E-02 -5.349E-02 -1.118E-02 9.216E-02 -1.521E-02 -2.335E-03 -5.875E-03 3.481E-02 4.220E-02 -9.442E-03 2.216E-02 -4.505E-02 2.377E-02-2.905E-02 -3.934E-02 3.440E-02 -9.451E-02 -4.251E-02 1.276E-02 -4.175E-02 -9.613E-03 -4.209E-02 -1.317E-02 -2.858E-04 3.883E-02 1.830E-02 4.091E-02 2.460E-02 2.402E-02 -2.665E-02 -7.320E-02 3.747E-02 7.082E-03 -9.509E-02

-.127 -6.002E-02 3.440E-02 -2.422E-02 -.102 -4.330E-02 3.862E-02 -4.732E-02 -4.672E-02 3.461E-02 4.464E-02 2.150E-02 1.147E-02 7.941E-02 2.057E-02 -3.383E-02 3.366E-03 -7.181E-02 3.253E-02 3.945E-02 -4.712E-03-2.643E-03 -7.577E-02 -9.451E-02 -2.422E-02 9.696E-05 -7.358E-02 -.161 8.908E-02 -1.566E-02 1.082E-02 -3.242E-03 -.110 7.496E-02 7.988E-02 1.092E-02 -2.944E-02 -5.265E-04 6.577E-02 -9.206E-02 6.735E-02 -1.469E-02-1.668E-02 -4.742E-02 -4.251E-02 -.102 9.696E-05 -1.355E-02 -7.666E-03 -9.330E-03 1.931E-02 -3.801E-02 -9.308E-03 -4.559E-02 -1.509E-02 7.616E-03 1.274E-02 1.669E-02 -3.371E-03 -5.025E-02 1.567E-03 4.955E-03 1.046E-02-1.345E-02 -2.275E-02 1.276E-02 -4.330E-02 -7.358E-02 -1.355E-02 -5.506E-02 .120 -3.783E-02 5.946E-03 -1.872E-02 4.164E-02 -2.288E-03 -1.786E-02 -3.131E-02 .112 -6.624E-02 2.249E-02 -7.739E-02 -7.977E-02 -.130-4.096E-02 -.106 -4.175E-02 3.862E-02 -.161 -7.666E-03 -5.506E-02 -7.876E-02 4.277E-02 3.928E-02 -1.162E-02 -2.570E-03 -7.125E-02 -8.178E-02 -5.194E-02 -2.355E-02 -9.239E-03 1.251E-02 8.543E-02 -2.965E-02 8.647E-031.343E-02 -3.757E-02 -9.613E-03 -4.732E-02 8.908E-02 -9.330E-03 .120 -7.876E-02 -6.433E-02 -8.146E-02 -6.637E-02 4.912E-02 2.269E-02 5.549E-02 9.718E-02 -9.934E-02 -4.579E-02 -2.822E-02 -9.065E-02 4.255E-02 -7.081E-03

-1.513E-03 1.346E-02 -4.209E-02 -4.672E-02 -1.566E-02 1.931E-02 -3.783E-02 4.277E-02 -6.433E-02 -2.199E-02 -6.051E-02 -5.000E-02 -3.120E-02 -2.730E-02 -2.462E-02 -4.426E-02 -2.790E-02 1.666E-02 4.093E-02 5.252E-02 1.202E-02-1.210E-03 -5.349E-02 -1.317E-02 3.461E-02 1.082E-02 -3.801E-02 5.946E-03 3.928E-02 -8.146E-02 -2.199E-02 4.686E-02 -6.684E-02 -8.499E-02 -9.608E-02 -1.292E-02 9.348E-03 3.497E-02 5.367E-02 3.153E-02 -4.949E-03 -7.581E-02-5.297E-02 -1.118E-02 -2.858E-04 4.464E-02 -3.242E-03 -9.308E-03 -1.872E-02 -1.162E-02 -6.637E-02 -6.051E-02 4.686E-02 -7.203E-02 -3.358E-02 -6.739E-02 -2.216E-02 1.818E-03 8.110E-02 1.593E-02 1.129E-02 2.559E-02 -4.910E-021.480E-02 9.216E-02 3.883E-02 2.150E-02 -.110 -4.559E-02 4.164E-02 -2.570E-03 4.912E-02 -5.000E-02 -6.684E-02 -7.203E-02 -.137 -9.085E-02 3.434E-03 2.078E-02 -2.340E-03 -.103 -1.032E-03 -1.009E-02 1.714E-028.052E-03 -1.521E-02 1.830E-02 1.147E-02 7.496E-02 -1.509E-02 -2.288E-03 -7.125E-02 2.269E-02 -3.120E-02 -8.499E-02 -3.358E-02 -.137 2.074E-02 -5.954E-02 -2.984E-02 -5.844E-03 1.790E-02 -5.455E-02 9.168E-02 2.517E-02

-3.426E-02 -2.335E-03 4.091E-02 7.941E-02 7.988E-02 7.616E-03 -1.786E-02 -8.178E-02 5.549E-02 -2.730E-02 -9.608E-02 -6.739E-02 -9.085E-02 2.074E-02 -5.164E-02 2.183E-02 -2.926E-02 6.424E-02 -1.215E-02 -7.228E-02 -3.229E-025.892E-02 -5.875E-03 2.460E-02 2.057E-02 1.092E-02 1.274E-02 -3.131E-02 -5.194E-02 9.718E-02 -2.462E-02 -1.292E-02 -2.216E-02 3.434E-03 -5.954E-02 -5.164E-02 3.711E-02 -.277 -.161 3.193E-02 -.103 5.662E-026.252E-02 3.481E-02 2.402E-02 -3.383E-02 -2.944E-02 1.669E-02 .112 -2.355E-02 -9.934E-02 -4.426E-02 9.348E-03 1.818E-03 2.078E-02 -2.984E-02 2.183E-02 3.711E-02 -8.218E-02 -3.208E-02 -2.985E-02 -.131 -.109

-5.008E-02 4.220E-02 -2.665E-02 3.366E-03 -5.265E-04 -3.371E-03 -6.624E-02 -9.239E-03 -4.579E-02 -2.790E-02 3.497E-02 8.110E-02 -2.340E-03 -5.844E-03 -2.926E-02 -.277 -8.218E-02 -.149 -2.531E-03 9.119E-02 .124-2.390E-02 -9.442E-03 -7.320E-02 -7.181E-02 6.577E-02 -5.025E-02 2.249E-02 1.251E-02 -2.822E-02 1.666E-02 5.367E-02 1.593E-02 -.103 1.790E-02 6.424E-02 -.161 -3.208E-02 -.149 -8.731E-02 -3.561E-02 1.406E-02-3.022E-03 2.216E-02 3.747E-02 3.253E-02 -9.206E-02 1.567E-03 -7.739E-02 8.543E-02 -9.065E-02 4.093E-02 3.153E-02 1.129E-02 -1.032E-03 -5.455E-02 -1.215E-02 3.193E-02 -2.985E-02 -2.531E-03 -8.731E-02 -.122 -4.364E-02-1.454E-02 -4.505E-02 7.082E-03 3.945E-02 6.735E-02 4.955E-03 -7.977E-02 -2.965E-02 4.255E-02 5.252E-02 -4.949E-03 2.559E-02 -1.009E-02 9.168E-02 -7.228E-02 -.103 -.131 9.119E-02 -3.561E-02 -.122 -9.203E-02-5.222E-02 2.377E-02 -9.509E-02 -4.712E-03 -1.469E-02 1.046E-02 -.130 8.647E-03 -7.081E-03 1.202E-02 -7.581E-02 -4.910E-02 1.714E-02 2.517E-02 -3.229E-02 5.662E-02 -.109 .124 1.406E-02 -4.364E-02 -9.203E-02

A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22

Reproduced Correlation

Residuala

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22

Extraction Method: Principal Component Analysis.Residuals are computed between observed and reproduced correlations. There are 79 (34.0%) nonredundant residuals with absolute values > 0.05.a. Reproduced communalitiesb.

Page 18: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

113132121111 ..... UFaFaFaFaz mm

223232221212 ..... UFaFaFaFaz mm

333332321313 ..... UFaFaFaFaz mm

變項 F1 因素 F2 因素 共同性 (h) (communality)

唯一因素

X1 a11 a12 1-h1

X2 a21 a22 1-h2

X3 a31 a32 1-h3

特徵值解釋量

212

211 aa

222

221 aa

232

231 aa

231

221

211 aaa

3/)( 231

221

211 aaa

232

222

212 aaa

3/)( 232

222

212 aaa

依序選擇最重要的 Fi

下一張投影片

Page 19: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

KMO and Bartlett's Test

.857

1187.740231.000

Kaiser-Meyer-Olkin Measure of Sampling Adequacy.

Approx. Chi-SquaredfSig.

Bartlett's Test of Sphericity >0.5

Communalities

1.000 .7191.000 .6561.000 .7341.000 .6751.000 .6121.000 .7551.000 .6311.000 .5721.000 .7061.000 .7841.000 .7561.000 .7741.000 .5641.000 .7061.000 .6621.000 .5001.000 .7481.000 .5541.000 .5021.000 .7671.000 .6541.000 .471

A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22

Initial Extraction

Extraction Method: Principal Component Analysis.

Page 20: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Scree Plot

Component Number

21191715131197531

Eig

envalu

e10

8

6

4

2

0

Page 21: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

113132121111 ..... UFaFaFaFaz mm

223232221212 ..... UFaFaFaFaz mm

333332321313 ..... UFaFaFaFaz mm

變項 F1 因素 F2 因素 共同性 (h) (communality)

唯一因素

X1 a11 a12 1-h1

X2 a21 a22 1-h2

X3 a31 a32 1-h3

特徵值解釋量

212

211 aa

222

221 aa

232

231 aa

231

221

211 aaa

3/)( 231

221

211 aaa

232

222

212 aaa

3/)( 232

222

212 aaa

下一張投影片藍色字體

Page 22: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Total Variance Explained

8.145 37.024 37.024 8.145 37.024 37.024 5.113 23.242 23.2422.728 12.400 49.424 2.728 12.400 49.424 3.917 17.807 41.0491.300 5.908 55.332 1.300 5.908 55.332 2.035 9.249 50.2981.262 5.736 61.068 1.262 5.736 61.068 1.728 7.856 58.1541.066 4.845 65.913 1.066 4.845 65.913 1.707 7.759 65.913.922 4.193 70.106.869 3.951 74.057.740 3.365 77.422.681 3.096 80.518.620 2.818 83.336.526 2.391 85.727.492 2.235 87.962.422 1.919 89.882.410 1.864 91.746.343 1.560 93.306.298 1.354 94.661.258 1.172 95.833.249 1.134 96.966.211 .957 97.923.176 .798 98.721.146 .664 99.385.135 .615 100.000

Component12345678910111213141516171819202122

Total % of VarianceCumulative % Total % of VarianceCumulative % Total % of VarianceCumulative %Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings

Extraction Method: Principal Component Analysis.

特徵值 共同性除 22

Page 23: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Component Matrixa

.730 -.391 -.104 -.137 6.070E-02

.682 -.397 -.139 -.118 -1.091E-02

.731 -.419 -2.988E-02 -.150 1.910E-02

.501 -.556 .255 -.224 -3.154E-03

.635 -.413 -.171 -4.802E-03 9.379E-02

.796 -.273 6.517E-02 -.194 7.051E-02

.598 -.270 -.295 .236 .242

.727 -.108 -.137 -4.038E-02 .106

.547 9.443E-02 .378 -.193 -.467

.726 .355 .145 -.332 -1.374E-02

.637 .505 -.216 -.158 -.156

.734 .354 -.253 -.178 -.119

.527 .509 -6.587E-02 -5.190E-02 .142

.545 .607 2.993E-02 -.164 .113

.455 .561 -.332 .142 9.294E-02

.366 .278 .209 .196 .455

.567 .181 .426 .247 -.390

.375 .130 .469 8.301E-02 .413

.527 -5.333E-02 .397 .146 .206

.653 -4.221E-02 9.516E-02 .544 -.184

.516 -3.076E-02 -.116 .599 -.123

.567 -.115 -.223 .164 -.243

A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A19A20A21A22

1 2 3 4 5Component

Extraction Method: Principal Component Analysis.5 components extracted.a.

特徵值計算方式… .

Page 24: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

特徵值計算方式… .

Page 25: Factor Analysis 理論模式 Z j 是第 j 個標準化分數 F i 是共同因素 U j 是 Z j 的唯一因素 a ij 是因素負荷量

Component Transformation Matrix

.687 .515 .338 .271 .273-.640 .749 -.020 .151 .072-.170 -.341 -.169 .634 .651-.274 -.237 .888 .219 -.179.116 .022 -.262 .673 -.681

Component12345

1 2 3 4 5

Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization.