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Willkommen in der Abteilung Wissenschaftstheorie, Methodologie und Statistisch-Mathematische Methoden
in der Allgemeinen und Integrativen Psychologie, Psychodiagnostik und Psychotherapie, hier:Matrix-Analyse der mit der Thurstone'schen Zentroid-Faktorenanalyse rückgerechneten Korrelationsmatrix
Zu den 46 Zentroid-Faktoren
Erläuterungen zur Matrixanalyse:
Numerische Laien hier und Professionell Interessierte hier
Queldatenfile: MEIDZO.F46
Samp Or MD NumS Condit Determinant HaInRatio R_OutIn K_Norm C_Norm
? 46 0 - 2178017 3,208 D-45 2.79 D-60 9820.6 0(10) 0.006(7)********** Summary of standard correlation matrix analysis ***********
File = MEIDZO.F46 N-order= 46 N-sample=? Rank= 46 Missing data = 0
Positiv Definit=Cholesky successful________= Yes with 0 negat. eigenvalue/s
HEVA: Highest eigenvalue abs.value_________= 12.12756537662934
LEVA: Lowest eigenvalue absolute value_____= 5.5681662152907291D-6
CON: Condition number HEVA/LEVA___________~= 2178017.8442457159
DET: Determinant original matrix (OMIKRON)_= 3.2092299291217788D-45
DET: Determinant (CHOLESKY-Diagonal^2)_____= 3.2092299291217479D-45
DET: Determinant (PESO-CHOLESKY)___________= 3.2092299291217479D-45
DET: Determinant (product eigenvalues)_____= 3.2092299289803024D-45
DET: Determ.abs.val.(PESO prod.red.norms)__= 3.209229929121763D-45
HAC: HADAMARD condition number_____________= 2.797443121049396D-60
HCN: Heuristic condition |DET|CON__________= 1.4734635611918914D-51
D_I: Determinant Inverse absolute value____= 3.1160123209796152D+44
HDA: HADAMARD Inequality absolute value___<= 3.0105320581048941D+190
HIR: HADAMARD RATIO: D_I / HDA ____________= 1.0350370834254195D-146
Highest inverse positive diagonal value____= 31938.863321743
thus multiple r( 42.rest)_________________= .999984345
and 46 multiple r > .99
There are no negative inverse diagonal values.
Maximum range (upp-low) multip-r( 3.rest)_= .497
LES: Numerical stability analysis:
Ratio maximum range output / input _______= 9820.638149276696
PESO-Analysis correlation least Ratio RN/ON= 6D-6 (<-> Angle = 0 )
Number of Ratios correlation RN/ON < .01__ = 10
PESO-Analysis Cholesky least Ratio RN/ON__ = 5.653D-3 (<-> Angle = .32 )
Number of Ratios Cholesky RN/ON < .1 _____ = 7Ncor L1-Norm L2-Norm Max Min m|c| s|c| N_comp M-S S-S
2116 544.5 14.99 1.075 -.619 .241 .169 535095 .19 .147class boundaries and distribution of the correlation coefficients
0 -.89 -.78 -.67 -.56 -.45 -.34 -.23 -.12 -.01 .1
714 408 368 314 156 70 38 2 20 26Original data with 17, input read with 17, computet with 19,
and showed with 3 digit accuracy
(for control here the analysed original matrix):
1.074 .522 .445 .634 .506 .361 .244 .316 .078 .16 .019 -3D-3 .103
.522 1.061 .588 .491 .709 .503 .019 .017 .287 .41 .056 7D-3 .184
.445 .588 .993 .707 .682 .488 .203 .159 .078 .369 -.119 .175 .238
.634 .491 .707 1.05 .463 .447 .322 .136 .078 .384 .084 .027 .034
.506 .709 .682 .463 1.041 .64 .385 .239 .34 .444 .085 .056 .091
.361 .503 .488 .447 .64 .965 .219 .087 .291 .327 -.055 .187 .051
.244 .019 .203 .322 .385 .219 .992 .407 .13 .467 .373 .069 -.262
.316 .017 .159 .136 .239 .087 .407 .997 .398 .105 -.032 .015 -.093
.078 .287 .078 .078 .34 .291 .13 .398 .874 .358 .161 .24 -.19
.16 .41 .369 .384 .444 .327 .467 .105 .358 1.067 .479 -.07 -.119
.019 .056 -.119 .084 .085 -.055 .373 -.032 .161 .479 .842 .038 -.256
-3D-3 7D-3 .175 .027 .056 .187 .069 .015 .24 -.07 .038 .914 .037
.103 .184 .238 .034 .091 .051 -.262 -.093 -.19 -.119 -.256 .037 .928
.231 .343 .572 .426 .37 .42 .044 .172 -.086 .311 .026 -.135 .408
.051 .255 .395 .263 .239 .219 -.171 -.165 -.264 .19 -.1 -.079 .545
.176 .403 .356 .397 .155 .405 .197 .084 .277 .511 .18 .075 .125
-.042 .205 .171 .16 -.088 .299 .074 -.226 -.072 .115 -.124 .222 .229
-.11 -.086 -.033 -.034 -.073 .196 .433 .099 .158 .109 .164 .284 .115
.212 .38 .312 .348 .154 .172 .045 -.155 -.04 -.016 .118 .064 .254
.378 .147 .507 .355 .258 4D-3 .105 .311 -.079 -.048 -1D-3 .124 .33
.227 .276 .226 .25 .255 .05 .173 .121 -1D-3 -.037 4D-3 -.123 -.108
.081 .028 .165 .212 .156 .093 .225 .256 -.01 -.116 .04 -.017 .098
-.458 -.171 -.248 -.142 -.369 -6D-3 .104 -.106 -.011 .247 .158 -.231 -.129
.054 -.037 .27 .21 .035 .117 .265 .175 -.1 .221 .098 .173 .078
.261 -.087 .424 .555 .094 .3 .352 .071 .04 .216 .014 .439 .023
.258 .27 .237 .37 .065 .264 .054 .115 -.105 .141 -.128 .019 .319
-.139 -.271 -.029 -.201 -.219 -.119 -.04 .144 -.035 -.072 -.121 .116 .401
-.139 .034 -.051 -.045 -.012 -.242 .339 .203 -.151 -.117 .011 -.193 .132
.162 .056 .332 .43 .174 .163 .419 .109 -.242 .197 -.072 -4D-3 .407
.231 .091 .316 .242 .316 .447 .192 -.05 -.011 .118 -.044 .25 .334
.275 .426 .647 .572 .346 .503 -.052 -.012 -.081 -6D-3 -.139 .125 .291
.139 .322 .594 .458 .258 .445 -.092 -.128 -.15 -.078 -.235 .147 .235
-.382 .047 .218 3D-3 .18 .103 .258 .044 -.02 .078 -.072 -.18 .149
.411 .244 .401 .481 .305 .507 .122 .176 .091 .055 .013 .154 .338
.091 .125 .356 .371 .195 .527 .03 6D-3 .033 .118 -.068 .167 .241
.196 .273 .203 .278 .121 .345 -.12 -.137 -.103 -8D-3 -.052 .024 .391
-.304 -.124 -.125 -.14 -.27 .047 -.442 -.619 -.286 -.213 -.204 .187 .196
.235 .308 .528 .414 .363 .419 .057 .038 -.046 .101 -.125 .021 .469
.16 .182 .299 .379 .036 .245 -.033 -.177 -.191 .023 -.01 .306 .156
.073 .229 .441 .274 .238 .37 -.094 -.165 -.107 .17 -.143 .367 .12
.271 .353 .492 .41 .325 .421 -4D-3 -.137 -.148 -7D-3 -.158 .056 .23
.106 .021 .201 .163 .121 .316 .142 -.082 -.084 -.093 3D-3 .321 .338
-.054 .027 .173 .141 -.066 .206 -.081 -.216 -.075 -.107 -.174 .423 .069
.232 .395 .348 .293 .311 .439 -.171 -.098 .092 .03 -.083 .106 .316
.222 .219 .095 .055 .281 .18 .183 .092 .05 .12 .235 .367 .194
-.064 .125 .246 .129 .038 .349 .018 -.129 -.023 .13 .103 .477 -8D-3.231 .051 .176 -.042 -.11 .212 .378 .227 .081 -.458 .054 .261 .258
.343 .255 .403 .205 -.086 .38 .147 .276 .028 -.171 -.037 -.087 .27
.572 .395 .356 .171 -.033 .312 .507 .226 .165 -.248 .27 .424 .237
.426 .263 .397 .16 -.034 .348 .355 .25 .212 -.142 .21 .555 .37
.37 .239 .155 -.088 -.073 .154 .258 .255 .156 -.369 .035 .094 .065
.42 .219 .405 .299 .196 .172 4D-3 .05 .093 -6D-3 .117 .3 .264
.044 -.171 .197 .074 .433 .045 .105 .173 .225 .104 .265 .352 .054
.172 -.165 .084 -.226 .099 -.155 .311 .121 .256 -.106 .175 .071 .115
-.086 -.264 .277 -.072 .158 -.04 -.079 -1D-3 -.01 -.011 -.1 .04 -.105
.311 .19 .511 .115 .109 -.016 -.048 -.037 -.116 .247 .221 .216 .141
.026 -.1 .18 -.124 .164 .118 -1D-3 4D-3 .04 .158 .098 .014 -.128
-.135 -.079 .075 .222 .284 .064 .124 -.123 -.017 -.231 .173 .439 .019
.408 .545 .125 .229 .115 .254 .33 -.108 .098 -.129 .078 .023 .319
1.075 .491 .473 .073 -.037 .375 .357 .238 .313 .063 .459 .117 .598
.491 .907 -.029 .295 -.139 .082 .363 -.056 .038 -.045 .175 .174 .386
.473 -.029 .971 .276 .449 .355 -.041 -.081 5D-3 .322 .211 .161 .239
.073 .295 .276 .966 .473 .394 .016 .222 .122 .388 .197 .441 .482
-.037 -.139 .449 .473 1.007 .365 .016 -.084 .122 .43 .232 .299 .02
.375 .082 .355 .394 .365 .997 .272 .503 .412 .261 .377 .217 .37
.357 .363 -.041 .016 .016 .272 1.046 .195 .184 -.287 .318 .388 .141
.238 -.056 -.081 .222 -.084 .503 .195 1.006 .694 .053 .321 .055 .399
.313 .038 5D-3 .122 .122 .412 .184 .694 1.014 .172 .528 .105 .326
.063 -.045 .322 .388 .43 .261 -.287 .053 .172 1.004 .375 .027 .194
.459 .175 .211 .197 .232 .377 .318 .321 .528 .375 .907 .415 .432
.117 .174 .161 .441 .299 .217 .388 .055 .105 .027 .415 .954 .31
.598 .386 .239 .482 .02 .37 .141 .399 .326 .194 .432 .31 .948
.355 .152 .145 .307 .303 .22 .164 .12 .221 .247 .379 .186 .382
.074 -.07 -1D-3 .153 .212 .302 .147 .372 .483 .252 .251 -.087 .201
.457 .372 .155 .329 .2 .135 .286 .309 .494 .138 .516 .419 .583
.445 .134 .294 .166 .33 .161 .052 .108 .228 -.095 .263 .283 .277
.653 .415 .369 .358 .084 .689 .395 .419 .422 .031 .413 .381 .501
.623 .293 .348 .353 .064 .653 .297 .42 .326 .047 .429 .376 .471
.303 .154 .141 .118 .145 .093 .182 .108 .169 .221 .144 .034 .092
.578 .238 .391 .119 .169 .403 .374 .097 .231 -.128 .175 .4 .425
.689 .329 .4 .285 .168 .378 .184 .179 .199 .055 .286 .365 .627
.649 .205 .354 .214 -1D-3 .512 .127 .349 .405 .066 .325 .098 .615
-.077 .243 -.114 .19 3D-3 .051 -.221 -.34 -.223 .15 -.02 .092 .058
.732 .443 .341 .251 .167 .577 .475 .335 .475 .19 .547 .309 .547
.26 .211 .202 .248 .033 .197 .2 -.011 .051 -.168 .192 .437 .348
.32 .279 .134 .156 -.099 4D-3 .035 -.033 -8D-3 -.188 .163 .284 .269
.565 .355 .184 .325 -6D-3 .576 .279 .405 .197 .059 .31 .304 .529
.241 .279 .053 .424 .387 .297 .507 .092 .19 .039 .386 .519 .337
-.239 .162 -.013 .454 .196 .063 8D-3 -.192 -.145 -.025 .014 .398 .082
.443 .248 .371 .263 .052 .481 .031 .214 .267 -.03 .208 .129 .402
.213 .163 -.069 .189 .084 .172 -.022 .283 .277 -.172 .259 .144 .372
.306 .307 .24 .342 .291 .36 .088 -.026 0 .176 .481 .369 .316-.139 -.139 .162 .231 .275 .139 -.382 .411 .091 .196 -.304 .235 .16
-.271 .034 .056 .091 .426 .322 .047 .244 .125 .273 -.124 .308 .182
-.029 -.051 .332 .316 .647 .594 .218 .401 .356 .203 -.125 .528 .299
-.201 -.045 .43 .242 .572 .458 3D-3 .481 .371 .278 -.14 .414 .379
-.219 -.012 .174 .316 .346 .258 .18 .305 .195 .121 -.27 .363 .036
-.119 -.242 .163 .447 .503 .445 .103 .507 .527 .345 .047 .419 .245
-.04 .339 .419 .192 -.052 -.092 .258 .122 .03 -.12 -.442 .057 -.033
.144 .203 .109 -.05 -.012 -.128 .044 .176 6D-3 -.137 -.619 .038 -.177
-.035 -.151 -.242 -.011 -.081 -.15 -.02 .091 .033 -.103 -.286 -.046 -.191
-.072 -.117 .197 .118 -6D-3 -.078 .078 .055 .118 -8D-3 -.213 .101 .023
-.121 .011 -.072 -.044 -.139 -.235 -.072 .013 -.068 -.052 -.204 -.125 -.01
.116 -.193 -4D-3 .25 .125 .147 -.18 .154 .167 .024 .187 .021 .306
.401 .132 .407 .334 .291 .235 .149 .338 .241 .391 .196 .469 .156
.355 .074 .457 .445 .653 .623 .303 .578 .689 .649 -.077 .732 .26
.152 -.07 .372 .134 .415 .293 .154 .238 .329 .205 .243 .443 .211
.145 -1D-3 .155 .294 .369 .348 .141 .391 .4 .354 -.114 .341 .202
.307 .153 .329 .166 .358 .353 .118 .119 .285 .214 .19 .251 .248
.303 .212 .2 .33 .084 .064 .145 .169 .168 -1D-3 3D-3 .167 .033
.22 .302 .135 .161 .689 .653 .093 .403 .378 .512 .051 .577 .197
.164 .147 .286 .052 .395 .297 .182 .374 .184 .127 -.221 .475 .2
.12 .372 .309 .108 .419 .42 .108 .097 .179 .349 -.34 .335 -.011
.221 .483 .494 .228 .422 .326 .169 .231 .199 .405 -.223 .475 .051
.247 .252 .138 -.095 .031 .047 .221 -.128 .055 .066 .15 .19 -.168
.379 .251 .516 .263 .413 .429 .144 .175 .286 .325 -.02 .547 .192
.186 -.087 .419 .283 .381 .376 .034 .4 .365 .098 .092 .309 .437
.382 .201 .583 .277 .501 .471 .092 .425 .627 .615 .058 .547 .348
.971 .332 .329 .298 .107 .17 .126 .156 .274 .312 .106 .397 .114
.332 1.004 .418 -.133 .015 .051 .482 -.046 -.1 .19 -.148 .22 .157
.329 .418 1.036 .562 .269 .271 .362 .283 .288 .348 -.029 .518 .256
.298 -.133 .562 .941 .254 .322 .042 .379 .405 .341 .171 .442 .174
.107 .015 .269 .254 1.056 .945 .204 .662 .683 .568 .02 .696 .377
.17 .051 .271 .322 .945 1.024 .307 .542 .665 .555 .121 .654 .42
.126 .482 .362 .042 .204 .307 .893 .154 .209 .138 -.132 .278 .067
.156 -.046 .283 .379 .662 .542 .154 .96 .748 .635 .047 .633 .482
.274 -.1 .288 .405 .683 .665 .209 .748 1.026 .741 .207 .684 .51
.312 .19 .348 .341 .568 .555 .138 .635 .741 1.001 .218 .737 .54
.106 -.148 -.029 .171 .02 .121 -.132 .047 .207 .218 1 .219 .448
.397 .22 .518 .442 .696 .654 .278 .633 .684 .737 .219 1.055 .349
.114 .157 .256 .174 .377 .42 .067 .482 .51 .54 .448 .349 1.012
.079 -.1 .188 .307 .292 .324 -.095 .29 .482 .438 .519 .37 .738
.242 .091 .256 .254 .738 .759 .173 .507 .628 .566 .196 .718 .383
.366 .207 .456 .396 .302 .345 .233 .359 .413 .391 .274 .552 .529
-.064 -.071 -.014 1D-3 .16 .184 -.126 -.055 .152 -.038 .468 1D-3 .508
.328 .155 .1 .232 .583 .587 .079 .417 .556 .622 .212 .527 .535
.336 .176 .309 .373 .139 .142 -.125 .112 .126 .202 -6D-3 .113 .284
.109 -.167 .01 .145 .551 .547 -.032 .267 .522 .195 .326 .308 .394.073 .271 .106 -.054 .232 .222 -.064
.229 .353 .021 .027 .395 .219 .125
.441 .492 .201 .173 .348 .095 .246
.274 .41 .163 .141 .293 .055 .129
.238 .325 .121 -.066 .311 .281 .038
.37 .421 .316 .206 .439 .18 .349
-.094 -4D-3 .142 -.081 -.171 .183 .018
-.165 -.137 -.082 -.216 -.098 .092 -.129
-.107 -.148 -.084 -.075 .092 .05 -.023
.17 -7D-3 -.093 -.107 .03 .12 .13
-.143 -.158 3D-3 -.174 -.083 .235 .103
.367 .056 .321 .423 .106 .367 .477
.12 .23 .338 .069 .316 .194 -8D-3
.32 .565 .241 -.239 .443 .213 .306
.279 .355 .279 .162 .248 .163 .307
.134 .184 .053 -.013 .371 -.069 .24
.156 .325 .424 .454 .263 .189 .342
-.099 -6D-3 .387 .196 .052 .084 .291
4D-3 .576 .297 .063 .481 .172 .36
.035 .279 .507 8D-3 .031 -.022 .088
-.033 .405 .092 -.192 .214 .283 -.026
-8D-3 .197 .19 -.145 .267 .277 0
-.188 .059 .039 -.025 -.03 -.172 .176
.163 .31 .386 .014 .208 .259 .481
.284 .304 .519 .398 .129 .144 .369
.269 .529 .337 .082 .402 .372 .316
.079 .242 .366 -.064 .328 .336 .109
-.1 .091 .207 -.071 .155 .176 -.167
.188 .256 .456 -.014 .1 .309 .01
.307 .254 .396 1D-3 .232 .373 .145
.292 .738 .302 .16 .583 .139 .551
.324 .759 .345 .184 .587 .142 .547
-.095 .173 .233 -.126 .079 -.125 -.032
.29 .507 .359 -.055 .417 .112 .267
.482 .628 .413 .152 .556 .126 .522
.438 .566 .391 -.038 .622 .202 .195
.519 .196 .274 .468 .212 -6D-3 .326
.37 .718 .552 1D-3 .527 .113 .308
.738 .383 .529 .508 .535 .284 .394
.988 .387 .292 .468 .399 .26 .395
.387 .929 .397 .165 .553 .258 .475
.292 .397 .98 .453 .361 .307 .326
.468 .165 .453 1.035 .318 .162 .478
.399 .553 .361 .318 .962 .372 .365
.26 .258 .307 .162 .372 .982 .313
.395 .475 .326 .478 .365 .313 1.06i.Eigenvalue Cholesky i.Eigenvalue Cholesky i.Eigenvalue Cholesky
1. 12.12757 1.0362 2. 4.51491 .8984 3. 3.94744 .7985
4. 3.2598 .6569 5. 2.57717 .6438 6. 2.13335 .7312
7. 1.91856 .8073 8. 1.80302 .8584 9. 1.60054 .7021
10. 1.42538 .7524 11. 1.38386 .6535 12. 1.28107 .7299
13. 1.17539 .8287 14. .89053 .5897 15. .82129 .5297
16. .71442 .4667 17. .67414 .5423 18. .55901 .4961
19. .47553 .5227 20. .42816 .6103 21. .32343 .4905
22. .29333 .5064 23. .2238 .4549 24. .19261 .3601
25. .15888 .2625 26. .11546 .3166 27. .08819 .4704
28. .07965 .3514 29. .06248 .2133 30. .05851 .2342
31. .04677 .2558 32. .03101 .1796 33. .02518 .2384
34. .02296 .1663 35. .02076 .1489 36. .01751 .179
37. .01554 .2103 38. 9.04D-3 .1353 39. 5.98D-3 .1743
40. 3.83D-3 .1677 41. 1.79D-3 .1294 42. 1.14D-3 .0509
43. 6.8D-4 .1491 44. 3.4D-4 .0836 45. 2.5D-4 .0893
46. 1D-5 .0165
Cholesky decomposition successful, thus the matrix is (semi) positive definit.Eigenvalues in per cent of trace = 45.510265541603458
1 .2665 2 .0992 3 .0867 4 .0716 5 .0566 6 .0469
7 .0422 8 .0396 9 .0352 10 .0313 11 .0304 12 .0281
13 .0258 14 .0196 15 .018 16 .0157 17 .0148 18 .0123
19 .0104 20 9.4D-3 21 7.1D-3 22 6.4D-3 23 4.9D-3 24 4.2D-3
25 3.5D-3 26 2.5D-3 27 1.9D-3 28 1.8D-3 29 1.4D-3 30 1.3D-3
31 1D-3 32 7D-4 33 6D-4 34 5D-4 35 5D-4 36 4D-4
37 3D-4 38 2D-4 39 1D-4 40 1D-4 41 0 42 0
43 0 44 0 45 0 46 0analysed: 04/23/01 11:16:10 PRG version 05/24/94 MA9.BAS
File = C:\OMI\NUMERIK\MATRIX\SMA\MEIDZO\MEIDZO.SMA
with data from C:\OMI\NUMERIK\MATRIX\SMA\MEIDZO\MEIDZO.F46
Date: 04/23/01 Time:11:16:10
Zitierung
Sponsel, Rudolf (DAS). Matrix-Analyse der mit der Thurstone'schen Zentroid-Faktorenanalyse rückgerechneten Korrelationsmatrix. IP-GIPT. Erlangen: https://www.sgipt.org/wisms/fa/dok02/D03kmzf.htm
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Ende K-Matrix aus ZF _Datenschutz_Überblick _ Relativ Aktuelles _ Rel. Beständiges _ Titelblatt _ Konzept _ Archiv _ Region _ Service iec-verlag _ Mail: _ sekretariat@sgipt.org _