conjoint: Conjoint analysis within a mixed effects model framework.
In SensMixed: Analysis of Sensory and Consumer Data in a Mixed Model Framework
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Performs conjoint analysis within a mixed effects model framework. This function is then used in the conjoint analysis of the ConsumerCheck software tool.
Usage
1
2
Arguments
structure
numerical, takes values in c(1,2,3). Specifies the complexity of the conjoint model.
- structure = 1
mixed effects model includes fixed main effects. Random effects consist of random consumer effect and interaction between consumer and the main effects.
- structure = 2
mixed effects model includes main effects and all 2-factor interactions. Random effects consist of consumer effect and interaction between consumer and all fixed effects (both main and interaction ones).
- structure = 3
-
This is a full factorial model with all possible fixed and random effects (i.e. including all main effects and all higher-way interactions). The automated reduction in
random part is followed by an automated reduction in fixed part.
data
a data frame.
response
a vector. Names of the variables that correspond to the liking scores.
fixed
a list. first element is a vector with a name Product includes names of the design variables. second element with a name Consumer includes names of the consumer characteristics variables
random
a string with the name for a consumer variable
facs
a vector with the names of the variables that need to be considered as factors
corr
a logical vaue. TRUE if the correlations between random effects are included in the model. FALSE if correlations between random effects are set to 0.
alpha.random
significance level for elimination of the random part (for LRT test)
alpha.fixed
significance level for elimination of the fixed part (for F test)
Details
Conjoint analysis (Green and Rao 1971; Green and Srinivasan 1978) is a method for analysing
the effects of design factors and consumer characteristics on consumer likings. A
common approach is to analyse it in a mixed effects model framework, where random effects
consist of consumer effect and interactions between consumer effects and design factors, and
fixed effects consist of design factors and consumer characteristics and possibly interactions
between them.
Value
rand.table
data frame with value of Chi square statistics, p-values for the likelihood ratio test for random effects. The order of elimination of non-significant random effects for strucutre = 3
anova.table
data frame with tests for whether the model fixed terms are significant (Analysis of Variance)
lsmeans.table
Least Squares Means data frame with p-values and Confidence intervals
diffs.lsmeans.table
Differences of Least Squares Means data frame with p-values and Confidence intervals. The multiplicity correction for multiple comparisons tests uses Bonferroni method
residuals
These are the residuals of the final model (for structure = 3, the reduced one)
residualsFixed
These are the residuals that are extracted from a fixed effects model with a saturated fixed structure (main effects and all higher-way interactions form fixed part) and one fixed
Consumer effect.
Note
The tests for the random
effects use likelihood ratio tests while the tests for the fixed effects use the F-test
with Satterthwaites approximation to degrees of freedom. The automated reduction
in the fixed part uses the principle of marginality, i.e. the highest order interactions
are tested first: if they are significant, the lower order effects are not eliminated even
if being non-significant.
Author(s)
Alexandra Kuznetsova, Per Bruun Brockhoff
References
Green P, Rao V (1971). Conjoint measurement for quantifying judgemental data. Journal
of Marketing Research, 8, 355 - 363
Green P, Srinivasan V (1978). Conjoint analysis in consumer research: Issues and outlook.
Journal of Consumer Research, 5, 103 - 123
See Also
sensmixed, SensMixedUI
Examples
1
2
3
4
5
6
7
8
9
Example output
[1] "Calculating Liking ..."
Number of levels for interaction Consumer:Product:Information is more or equal to the number of observations in data
Number of levels for interaction Consumer:Product:Information is more or equal to the number of observations in data
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00425257 (tol = 0.002, component 1)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00425258 (tol = 0.002, component 1)
Random effects:
Chi.sq Chi.DF elim.num p.value
Information:Consumer 1.52 1 1 0.218
Product:Consumer 164.26 1 kept <0.001
Consumer 3.01 1 kept 0.083
Fixed effects:
Sum Sq Mean Sq NumDF DenDF F.value elim.num
Product:Information:Gender 5.991542 1.9971805 3 316.02 1.1995135 1
Product:Gender 1.743572 0.5811906 3 237.00 0.3483748 2
Information:Gender 1.407454 1.4074535 1 319.00 0.8436494 3
Gender 1.465605 1.4656048 1 79.00 0.8789376 4
Product:Information 10.387346 3.4624486 3 320.00 2.0764599 5
Product 19.346565 6.4488550 3 240.00 3.8291490 kept
Information 6.520062 6.5200617 1 323.00 3.8714296 kept
Pr(>F)
Product:Information:Gender 0.310
Product:Gender 0.790
Information:Gender 0.359
Gender 0.351
Product:Information 0.103
Product 0.010
Information 0.050
Least squares means:
Product Information Estimate Standard Error DF t-value Lower CI
Product 1 1 NA 5.809 0.232 313 25.0 5.35
Product 2 2 NA 5.105 0.232 313 22.0 4.65
Product 3 3 NA 6.093 0.232 313 26.2 5.64
Product 4 4 NA 5.926 0.232 313 25.5 5.47
Information 1 NA 1 5.633 0.140 106 40.3 5.36
Information 2 NA 2 5.833 0.140 106 41.7 5.56
Upper CI p-value
Product 1 6.27 <2e-16 ***
Product 2 5.56 <2e-16 ***
Product 3 6.55 <2e-16 ***
Product 4 6.38 <2e-16 ***
Information 1 5.91 <2e-16 ***
Information 2 6.11 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Differences of LSMEANS:
Estimate Standard Error DF t-value Lower CI Upper CI
Product 1 - 2 0.7 0.314 240.0 2.240 0.0849 1.323
Product 1 - 3 -0.3 0.314 240.0 -0.900 -0.9027 0.335
Product 1 - 4 -0.1 0.314 240.0 -0.370 -0.7361 0.501
Product 2 - 3 -1.0 0.314 240.0 -3.140 -1.6064 -0.369
Product 2 - 4 -0.8 0.314 240.0 -2.610 -1.4398 -0.202
Product 3 - 4 0.2 0.314 240.0 0.530 -0.4521 0.785
Information 1 - 2 -0.2 0.102 323.0 -1.970 -0.4012 0.000
p-value p-value.adjust
Product 1 - 2 0.0260 0.16
Product 1 - 3 0.3669 1.00
Product 1 - 4 0.7092 1.00
Product 2 - 3 0.0019 0.01 *
Product 2 - 4 0.0095 0.06 .
Product 3 - 4 0.5962 1.00
Information 1 - 2 0.0500 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$rand.table
Chi.sq Chi.DF elim.num p.value
Information:Consumer 1.520722 1 1 0.218
Product:Consumer 164.262745 1 kept <0.001
Consumer 3.010458 1 kept 0.083
$anova.table
Sum Sq Mean Sq NumDF DenDF F.value
Product:Information:Gender 5.991542 1.9971805 3 316.01961 1.1995135
Product:Gender 1.743572 0.5811906 3 236.99997 0.3483748
Information:Gender 1.407454 1.4074535 1 318.99997 0.8436494
Gender 1.465605 1.4656048 1 79.00021 0.8789376
Product:Information 10.387346 3.4624486 3 320.00000 2.0764599
Product 19.346565 6.4488550 3 239.99924 3.8291490
Information 6.520062 6.5200617 1 322.99926 3.8714296
elim.num Pr(>F)
Product:Information:Gender 1 0.310
Product:Gender 2 0.790
Information:Gender 3 0.359
Gender 4 0.351
Product:Information 5 0.103
Product kept 0.010
Information kept 0.050
$lsmeans.table
Product Information Estimate Standard Error DF t-value
Product 1 1 <NA> 5.8086 0.2323 313.1 25.01
Product 2 2 <NA> 5.1049 0.2323 313.1 21.98
Product 3 3 <NA> 6.0926 0.2323 313.1 26.23
Product 4 4 <NA> 5.9259 0.2323 313.1 25.51
Information 1 <NA> 1 5.6327 0.1398 105.8 40.29
Information 2 <NA> 2 5.8333 0.1398 105.8 41.73
Lower CI Upper CI p-value
Product 1 5.3517 6.2656 0
Product 2 4.6479 5.5619 0
Product 3 5.6356 6.5496 0
Product 4 5.4689 6.3829 0
Information 1 5.3555 5.9099 0
Information 2 5.5562 6.1105 0
$diffs.lsmeans.table
Estimate Standard Error DF t-value Lower CI Upper CI p-value
Product 1 - 2 0.7037 0.3141 240 2.24 0.0849 1.3225 0.0260
Product 1 - 3 -0.2840 0.3141 240 -0.90 -0.9027 0.3348 0.3669
Product 1 - 4 -0.1173 0.3141 240 -0.37 -0.7361 0.5015 0.7092
Product 2 - 3 -0.9877 0.3141 240 -3.14 -1.6064 -0.3689 0.0019
Product 2 - 4 -0.8210 0.3141 240 -2.61 -1.4398 -0.2022 0.0095
Product 3 - 4 0.1667 0.3141 240 0.53 -0.4521 0.7854 0.5962
Information 1 - 2 -0.2006 0.1020 323 -1.97 -0.4012 0.0000 0.0500
p-value.adjust
Product 1 - 2 0.1560
Product 1 - 3 1.0000
Product 1 - 4 1.0000
Product 2 - 3 0.0114
Product 2 - 4 0.0570
Product 3 - 4 1.0000
Information 1 - 2 0.0500
$residuals
1 2 3 4 5 6
-0.028055053 -0.228672337 -0.090493749 -0.291111033 -1.087892137 0.711490579
7 8 9 10 11 12
0.157960230 -0.042657054 -0.149932348 -0.350549632 0.235916655 1.035299371
13 14 15 16 17 18
0.422422368 0.221805084 0.246813534 0.046196250 0.314544368 0.113927084
19 20 21 22 23 24
-1.958624929 1.840757788 -0.139927416 0.659455300 2.079098450 -2.121518833
25 26 27 28 29 30
0.393406147 0.192788863 0.093410351 -1.107206933 -0.087892137 -0.288509421
31 32 33 34 35 36
-0.447405070 0.351977646 -1.231616400 0.567766316 -0.294055096 -0.494672380
37 38 39 40 41 42
-0.869992284 0.929390432 0.770494783 -0.430122501 -0.063901316 -0.264518600
43 44 45 46 47 48
0.479025288 -0.721591996 0.508453400 0.307836116 -2.088616633 1.710766083
49 50 51 52 53 54
1.195163542 -0.005453742 -1.131658754 -0.332276038 -0.075404142 0.723978574
55 56 57 58 59 60
0.116795225 -1.083822059 -0.319497943 0.479884773 -0.381936639 0.417446077
61 62 63 64 65 66
-1.168604427 1.630778289 0.471882640 0.271265356 -0.305159438 0.494223278
67 68 69 70 71 72
-0.367598134 0.431784582 0.451099378 0.250482094 -1.329874755 1.469507961
73 74 75 76 77 78
0.448263699 -0.752353585 0.228747402 1.028130119 -0.584746885 1.214635831
79 80 81 82 83 84
0.239644282 0.039026998 0.779021084 0.578403800 -0.758531812 -0.959149096
85 86 87 88 89 90
3.086992200 -3.113625084 0.727479266 -0.473138017 -0.428008495 -0.628625779
91 92 93 94 95 96
-0.701177791 -0.901795075 -0.250288479 0.549094237 0.600929188 0.400311904
97 98 99 100 101 102
0.568290484 0.367673200 -0.758531812 -0.959149096 0.481626900 -0.718990384
103 104 105 106 107 108
0.543575166 0.342957882 1.223840552 0.023223268 -0.708347043 -0.908964327
109 110 111 112 113 114
-0.889649531 -0.090266815 1.172298735 -1.028318549 -0.712282132 0.087100584
115 116 117 118 119 120
-0.142529029 0.656853687 0.254707284 0.054090000 -0.104805650 0.694577066
121 122 123 124 125 126
2.395256658 -2.805360626 -0.694008538 -0.894625822 -0.848484526 0.950898190
127 128 129 130 131 132
-1.207997459 1.591385257 -0.051413322 0.747969394 0.070052082 -0.130565202
133 134 135 136 137 138
-0.111250406 0.688132310 0.080948961 -1.119668323 1.546782726 -0.653834558
139 140 141 142 143 144
0.036056330 -1.164560954 0.065484442 -0.135132842 -0.083297892 0.716084824
145 146 147 148 149 150
0.872221368 0.671604084 -0.665331527 -0.865948811 -0.873460515 -1.074077799
151 152 153 154 155 156
0.004583651 -0.196033633 0.371898389 0.171281105 -0.533462707 -0.734079991
157 158 159 160 161 162
-0.082573395 0.716809321 0.925721872 -1.274895412 0.443590916 0.242973632
163 164 165 166 167 168
-1.067135480 -0.267752764 0.146196732 -1.054420552 -0.607950901 0.191431815
169 170 171 172 173 174
2.268706579 -1.931910705 -0.636654517 -0.837271801 1.182042996 -2.018574288
175 176 177 178 179 180
0.217164762 -0.983452522 0.888410385 -0.312206899 -0.622316011 -0.822933295
181 182 183 184 185 186
-0.619714399 -0.820331683 1.231503268 -1.969114016 0.446413188 0.245795904
187 188 189 190 191 192
0.383974492 0.183357208 0.991941404 -0.208675880 -0.183667429 0.615715287
193 194 195 196 197 198
-0.106916832 -0.307534116 -0.142529029 0.656853687 -0.350658016 0.448724700
199 200 201 202 203 204
-0.104805650 0.694577066 0.998771447 -0.201845837 -0.722685549 -0.923302833
205 206 207 208 209 210
-0.666430937 1.132951779 1.341864330 -1.858752954 -3.547389321 3.251993395
211 212 213 214 215 216
-0.636654517 -0.837271801 0.419600095 0.218982811 -1.204296438 -0.404913722
217 218 219 220 221 222
0.089475262 -0.111142022 1.053863066 -0.146754218 -0.364996522 0.434386194
223 224 225 226 227 228
0.670125245 -0.530492039 -0.348174954 0.451207762 1.010847550 -0.189769734
229 230 231 232 233 234
0.802718562 -0.397898722 0.443205629 0.242588345 0.510936462 0.310319178
235 236 237 238 239 240
-0.578328734 0.221053982 0.451099378 0.250482094 -0.935240055 0.864142661
241 242 243 244 245 246
-1.109739105 0.689643611 -0.593639001 -0.794256285 -1.591037388 0.208345328
247 248 249 250 251 252
1.865545578 -2.335071706 -0.705112879 0.094269837 -0.135359776 0.664022940
253 254 255 256 257 258
0.656511236 -0.544106048 -0.097636397 0.701746319 -1.269313174 1.530069542
259 260 261 262 263 264
-1.147847770 0.651534946 -1.329150258 1.470232458 0.311336808 0.110719524
265 266 267 268 269 270
0.060798252 -0.139819032 0.235916655 1.035299371 0.211691768 0.011074484
271 272 273 274 275 276
1.246813534 -0.953803750 -1.485362516 0.314020200 -0.099513513 0.699869203
277 278 279 280 281 282
0.903088100 -0.297529184 -0.483251333 0.316131383 0.802379352 -0.398237932
283 284 285 286 287 288
-0.076155244 -0.276772528 0.715715769 -1.484901515 0.356202835 -0.844414449
289 290 291 292 293 294
-0.663947874 1.135434842 -0.515655971 1.283726745 -0.934515558 0.864867158
295 296 297 298 299 300
-0.320854991 -0.521472275 -2.471024011 1.328358705 -0.928097407 -0.128714691
301 302 303 304 305 306
0.522791905 0.322174621 1.557913672 -0.642703612 0.175506294 -0.025110989
307 308 309 310 311 312
-0.492297702 0.307085014 0.510303911 -0.690313373 0.334695077 -0.865922207
313 314 315 316 317 318
-0.537397796 0.261984920 -0.178375292 0.621007424 -0.175773680 0.623609036
319 320 321 322 323 324
0.070078687 0.869461403 0.941417426 -0.259199858 1.246786930 -1.953830354
325 326 327 328 329 330
-0.118419658 0.680963058 0.495240909 -0.705376375 -1.759970431 2.039412285
331 332 333 334 335 336
-1.033139728 0.766242988 -0.241268715 -0.441885999 -0.627608148 -0.828225432
337 338 339 340 341 342
0.807698094 0.607080810 -1.492297702 1.307085014 -0.727253189 -0.927870473
343 344 345 346 347 348
0.940060377 -1.260556907 1.971944947 -2.228672337 1.357793951 0.157176667
349 350 351 352 353 354
-2.482526837 2.316855879 -0.895692770 -1.096310054 -0.770607915 -0.971225199
355 356 357 358 359 360
4.220606388 -3.980010896 1.223208001 -0.977409283 -0.795323232 -0.995940516
361 362 363 364 365 366
0.400575400 0.199958116 -0.715516296 -0.916133580 -0.475357584 0.324025132
367 368 369 370 371 372
0.165129483 -0.035487801 -0.514039527 -0.714656811 -0.522825223 1.276557493
373 374 375 376 377 378
-0.730954211 1.068428505 -0.090467144 0.708915572 -0.133743332 -1.334360616
379 380 381 382 383 384
0.068201571 0.867584287 0.676168484 0.475551200 -0.315536250 0.483846466
385 386 387 388 389 390
-0.989386517 0.809996199 -0.419633414 1.379749303 0.582968199 0.382350915
391 392 393 394 395 396
0.618089965 0.417472682 0.757513326 0.556896042 0.062882829 -0.137734454
397 398 399 400 401 402
-0.329150258 0.470232458 -0.926220291 -0.126837575 -0.106916832 -0.307534116
403 404 405 406 407 408
1.673566871 -0.527050413 -0.166753916 -0.367371200 0.895194350 -0.305422934
409 410 411 412 413 414
-0.535547285 -0.736164569 0.061032319 0.860415035 -0.147096669 0.652286047
415 416 417 418 419 420
0.493390398 0.292773114 1.345071889 -1.855545395 -2.506636207 2.292746509
421 422 423 424 425 426
1.312061305 -0.888555979 -2.468912828 2.330469888 -0.190451395 0.608931321
427 428 429 430 431 432
-0.042159491 0.757223225 -0.882480279 -0.083097563 -0.663454412 -0.864071696
433 434 435 436 437 438
-0.121255338 -0.321872621 -0.156867534 0.642515182 -1.154265922 1.645116794
439 440 441 442 443 444
-0.119144155 0.680238561 0.433925194 -0.766692090 0.214408897 1.013791613
445 446 447 448 449 450
-0.599085390 1.200297326 0.436036376 0.235419092 -0.544567048 0.254815668
451 452 453 454 455 456
-0.369448645 1.429934071 1.027787668 -0.172829616 0.641448234 -0.559169050
457 458 459 460 461 462
0.584479500 -0.616137784 0.522040804 -0.678576480 0.919277116 -1.281340168
463 464 465 466 467 468
1.349033583 -1.851583701 0.955755931 -0.244861353 -0.133509265 -0.334126549
469 470 471 472 473 474
-0.130907653 -0.331524937 0.720310014 -0.480307270 -0.178609359 -0.379226643
475 476 477 478 479 480
0.207239644 1.006622360 0.999110657 -0.201506627 1.034232424 -0.166384860
481 482 483 484 485 486
0.512786973 -0.687830311 1.082540077 -0.118077207 -0.941684811 0.857697905
487 488 489 490 491 492
0.488071656 -0.712545628 1.309225626 -1.891391658 1.089709329 -0.110907955
493 494 495 496 497 498
-0.329150258 0.470232458 0.495240909 -0.705376375 0.632813758 0.432196474
499 500 501 502 503 504
-0.667182038 0.132200678 0.124688974 -1.075928310 -0.445554559 -0.646171843
505 506 507 508 509 510
-0.824493706 0.974889011 2.113067598 -2.087549686 -2.911157289 1.888225427
511 512 513 514 515 516
2.150790977 -2.049826307 0.075136757 -0.125480527 1.039524561 -0.161092723
517 518 519 520 521 522
0.831395573 -0.369221711 -0.344213260 0.455169456 2.048956216 -1.151661068
523 524 525 526 527 528
-0.856404880 -0.057022164 -0.880629768 -1.081247052 2.602779699 -2.597837585
529 530 531 532 533 534
-0.712282132 0.087100584 0.462836271 0.262218987 -0.745292716 1.054090000
535 536 537 538 539 540
0.289829050 0.089211766 -0.197620648 0.601762068 -1.286885844 0.512496872
541 542 543 544 545 546
-0.100380131 -1.300997415 -0.616970665 1.182412051 1.878744662 -2.321872621
547 548 549 550 551 552
0.053863066 0.853245782 0.661829978 0.461212694 -0.145970655 -0.346587939
553 554 555 556 557 558
-1.746277885 0.053104831 0.877128218 0.676510935 0.668999231 0.468381947
559 560 561 562 563 564
0.071929198 -0.128688086 -0.362513459 0.436869257 -0.819586855 0.979795861
565 566 567 568 569 570
0.604475957 0.403858673 0.639597723 0.438980440 -0.697943627 0.101439089
571 572 573 574 575 576
0.898635976 0.698018693 -0.573876611 -0.774493895 0.514898156 0.314280872
577 578 579 580 581 582
-2.740959143 2.058423573 -0.355110139 1.444272577 -2.984700327 2.814682389
583 584 585 586 587 588
0.682613240 0.481995956 -2.148081837 0.651300879 -0.340771634 1.458611082
589 590 591 592 593 594
0.240368778 0.039751494 0.696951745 0.496334461 0.864406157 -1.336211127
595 596 597 598 599 600
-1.381936639 1.417446077 0.647491473 0.446874189 0.471882640 0.271265356
601 602 603 604 605 606
-0.065751827 0.733630889 0.477174777 0.276557493 -0.363146011 -0.563763295
607 608 609 610 611 612
0.093436956 -0.107180328 -0.001228553 0.798154163 1.936332751 -1.264284533
613 614 615 616 617 618
0.885281364 -2.315335920 -0.868866270 -0.069483554 0.225691063 0.025073779
619 620 621 622 623 624
-0.258208833 -0.458826117 -0.860972521 -0.061589804 -1.615120154 1.184262562
625 626 627 628 629 630
2.257190346 -1.943426938 1.221578150 0.020960866 1.408083862 -0.792533422
631 632 633 634 635 636
0.021744429 -0.178872855 -2.844150953 1.955231763 -2.274397849 2.524984867
637 638 639 640 641 642
-1.087892137 0.711490579 1.157960230 -1.042657054 0.548633236 -0.651984047
643 644 645 646 647 648
0.302290440 0.101673156 -1.905838547 1.893544169 0.313187319 -0.887429965
$residualsFixed
Product Information Gender Consumer resid
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2 1 2 1 1 4.878049e-02
3 2 1 1 1 -2.439024e-01
4 2 2 1 1 -8.536585e-01
5 3 1 1 1 -1.121951e+00
6 3 2 1 1 3.658537e-01
7 4 1 1 1 9.512195e-01
8 4 2 1 1 8.536585e-01
9 1 1 2 2 -2.115625e+00
10 1 2 2 2 -2.490625e+00
11 2 1 2 2 1.784375e+00
12 2 2 2 2 2.584375e+00
13 3 1 2 2 7.093750e-01
14 3 2 2 2 3.593750e-01
15 4 1 2 2 -6.656250e-01
16 4 2 2 2 -1.656250e-01
17 1 1 1 3 6.250000e-01
18 1 2 1 3 6.737805e-01
19 2 1 1 3 -2.618902e+00
20 2 2 1 3 7.713415e-01
21 3 1 1 3 5.030488e-01
22 3 2 1 3 9.908537e-01
23 4 1 1 3 1.576220e+00
24 4 2 1 3 -2.521341e+00
25 1 1 1 4 2.000000e+00
26 1 2 1 4 2.048780e+00
27 2 1 1 4 -1.243902e+00
28 2 2 1 4 -2.853659e+00
29 3 1 1 4 -1.219512e-01
30 3 2 1 4 -6.341463e-01
31 4 1 1 4 -4.878049e-02
32 4 2 1 4 8.536585e-01
33 1 1 2 5 -1.865625e+00
34 1 2 2 5 -2.406250e-01
35 2 1 2 5 -9.656250e-01
36 2 2 2 5 -1.165625e+00
37 3 1 2 5 -4.062500e-02
38 3 2 2 5 1.609375e+00
39 4 1 2 5 1.584375e+00
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92 2 2 2 12 -2.915625e+00
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102 3 2 2 13 -1.140625e+00
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104 4 2 2 13 2.334375e+00
105 1 1 2 14 4.259375e+00
106 1 2 2 14 2.884375e+00
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112 4 2 2 14 2.093750e-01
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114 1 2 1 15 -1.326220e+00
115 2 1 1 15 3.810976e-01
116 2 2 1 15 7.713415e-01
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118 3 2 1 15 -9.146341e-03
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120 4 2 1 15 1.478659e+00
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122 1 2 2 16 -2.865625e+00
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124 2 2 2 16 -2.790625e+00
125 3 1 2 16 3.343750e-01
126 3 2 2 16 1.984375e+00
127 4 1 2 16 -4.062500e-02
128 4 2 2 16 3.459375e+00
129 1 1 1 17 1.125000e+00
130 1 2 1 17 2.173780e+00
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132 2 2 1 17 -7.286585e-01
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138 1 2 1 18 1.048780e+00
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142 3 2 1 18 -6.341463e-01
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144 4 2 1 18 1.853659e+00
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146 1 2 1 19 5.048780e+00
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170 1 2 2 22 1.343750e-01
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174 3 2 2 22 -2.015625e+00
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178 1 2 2 23 2.384375e+00
179 2 1 2 23 -1.340625e+00
180 2 2 2 23 -1.540625e+00
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182 3 2 2 23 -1.765625e+00
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186 1 2 1 24 2.987805e-01
187 2 1 1 24 6.097561e-03
188 2 2 1 24 -6.036585e-01
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190 3 2 1 24 -3.841463e-01
191 4 1 1 24 -7.987805e-01
192 4 2 1 24 1.036585e-01
193 1 1 1 25 -1.375000e+00
194 1 2 1 25 -1.326220e+00
195 2 1 1 25 3.810976e-01
196 2 2 1 25 7.713415e-01
197 3 1 1 25 -4.969512e-01
198 3 2 1 25 -9.146341e-03
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202 1 2 2 26 1.634375e+00
203 2 1 2 26 -3.090625e+00
204 2 2 2 26 -3.290625e+00
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206 3 2 2 26 2.484375e+00
207 4 1 2 26 4.593750e-01
208 4 2 2 26 -2.040625e+00
209 1 1 2 29 -2.490625e+00
210 1 2 2 29 4.134375e+00
211 2 1 2 29 -1.590625e+00
212 2 2 2 29 -1.790625e+00
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214 3 2 2 29 2.984375e+00
215 4 1 2 29 -3.040625e+00
216 4 2 2 29 -1.540625e+00
217 1 1 2 30 -6.156250e-01
218 1 2 2 30 -9.906250e-01
219 2 1 2 30 2.284375e+00
220 2 2 2 30 1.084375e+00
221 3 1 2 30 -7.906250e-01
222 3 2 2 30 -1.406250e-01
223 4 1 2 30 -1.656250e-01
224 4 2 2 30 -6.656250e-01
225 1 1 1 31 -1.375000e+00
226 1 2 1 31 -3.262195e-01
227 2 1 1 31 1.381098e+00
228 2 2 1 31 -2.286585e-01
229 3 1 1 31 5.030488e-01
230 3 2 1 31 -1.009146e+00
231 4 1 1 31 5.762195e-01
232 4 2 1 31 4.786585e-01
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234 1 2 2 32 1.009375e+00
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238 3 2 2 32 8.593750e-01
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242 1 2 1 33 2.298780e+00
243 2 1 1 33 -9.939024e-01
244 2 2 1 33 -1.603659e+00
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250 1 2 1 34 -1.201220e+00
251 2 1 1 34 5.060976e-01
252 2 2 1 34 8.963415e-01
253 3 1 1 34 6.280488e-01
254 3 2 1 34 -8.841463e-01
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278 3 2 1 37 7.408537e-01
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282 1 2 1 38 1.298780e+00
283 2 1 1 38 6.097561e-03
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288 4 2 1 38 -8.963415e-01
289 1 1 1 39 3.424933e-15
290 1 2 1 39 2.048780e+00
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298 1 2 2 40 -7.406250e-01
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314 1 2 1 42 -9.512195e-01
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321 1 1 1 43 2.000000e+00
322 1 2 1 43 1.048780e+00
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538 1 2 2 70 1.884375e+00
539 2 1 2 70 -1.840625e+00
540 2 2 2 70 -4.062500e-02
541 3 1 2 70 -1.915625e+00
542 3 2 2 70 -3.265625e+00
543 4 1 2 70 7.093750e-01
544 4 2 2 70 3.209375e+00
545 1 1 1 71 3.750000e-01
546 1 2 1 71 -3.576220e+00
547 2 1 1 71 1.131098e+00
548 2 2 1 71 1.521341e+00
549 3 1 1 71 2.253049e+00
550 3 2 1 71 1.740854e+00
551 4 1 1 71 -1.673780e+00
552 4 2 1 71 -1.771341e+00
553 1 1 2 73 -5.490625e+00
554 1 2 2 73 -3.865625e+00
555 2 1 2 73 3.409375e+00
556 2 2 2 73 3.209375e+00
557 3 1 2 73 2.334375e+00
558 3 2 2 73 1.984375e+00
559 4 1 2 73 -1.040625e+00
560 4 2 2 73 -5.406250e-01
561 1 1 2 74 -1.615625e+00
562 1 2 2 74 -9.906250e-01
563 2 1 2 74 -1.715625e+00
564 2 2 2 74 8.437500e-02
565 3 1 2 74 1.209375e+00
566 3 2 2 74 8.593750e-01
567 4 1 2 74 8.343750e-01
568 4 2 2 74 1.334375e+00
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570 1 2 1 75 -1.076220e+00
571 2 1 1 75 3.631098e+00
572 2 2 1 75 3.021341e+00
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574 3 2 1 75 -3.759146e+00
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576 4 2 1 75 1.728659e+00
577 1 1 2 76 -4.865625e+00
578 1 2 2 76 -2.406250e-01
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580 2 2 2 76 2.834375e+00
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582 3 2 2 76 1.609375e+00
583 4 1 2 76 1.584375e+00
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586 1 2 2 77 -2.990625e+00
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588 2 2 2 77 3.084375e+00
589 3 1 2 77 2.093750e-01
590 3 2 2 77 -1.406250e-01
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592 4 2 2 77 2.334375e+00
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594 1 2 1 78 -2.826220e+00
595 2 1 1 78 -2.118902e+00
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597 3 1 1 78 2.003049e+00
598 3 2 1 78 1.490854e+00
599 4 1 1 78 1.076220e+00
600 4 2 1 78 9.786585e-01
601 1 1 2 79 8.843750e-01
602 1 2 2 79 1.509375e+00
603 2 1 2 79 1.784375e+00
604 2 2 2 79 1.584375e+00
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607 4 1 2 79 -6.656250e-01
608 4 2 2 79 -1.656250e-01
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610 1 2 2 80 2.634375e+00
611 2 1 2 80 3.909375e+00
612 2 2 2 80 7.093750e-01
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614 3 2 2 80 -4.515625e+00
615 4 1 2 80 -2.540625e+00
616 4 2 2 80 -1.040625e+00
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618 1 2 1 81 1.798780e+00
619 2 1 1 81 -4.939024e-01
620 2 2 1 81 -1.103659e+00
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622 3 2 1 81 -8.841463e-01
623 4 1 1 81 -1.298780e+00
624 4 2 1 81 1.603659e+00
625 1 1 2 82 1.634375e+00
626 1 2 2 82 -2.740625e+00
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628 2 2 2 82 1.334375e+00
629 3 1 2 82 1.459375e+00
630 3 2 2 82 -8.906250e-01
631 4 1 2 82 -1.915625e+00
632 4 2 2 82 -1.415625e+00
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634 1 2 1 83 1.048780e+00
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638 3 2 1 83 3.658537e-01
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640 4 2 1 83 -1.463415e-01
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642 1 2 1 84 -4.512195e-01
643 2 1 1 84 1.256098e+00
644 2 2 1 84 6.463415e-01
645 3 1 1 84 -1.621951e+00
646 3 2 1 84 1.865854e+00
647 4 1 1 84 -5.487805e-01
648 4 2 1 84 -1.646341e+00
SensMixed documentation built on May 1, 2019, 9:16 p.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Performs conjoint analysis within a mixed effects model framework. This function is then used in the conjoint analysis of the ConsumerCheck software tool.
Usage
1 2 |
Arguments
structure |
numerical, takes values in c(1,2,3). Specifies the complexity of the conjoint model.
|
data |
a data frame. |
response |
a vector. Names of the variables that correspond to the liking scores. |
fixed |
a list. first element is a vector with a name Product includes names of the design variables. second element with a name Consumer includes names of the consumer characteristics variables |
random |
a string with the name for a consumer variable |
facs |
a vector with the names of the variables that need to be considered as factors |
corr |
a logical vaue. TRUE if the correlations between random effects are included in the model. FALSE if correlations between random effects are set to 0. |
alpha.random |
significance level for elimination of the random part (for LRT test) |
alpha.fixed |
significance level for elimination of the fixed part (for F test) |
Details
Conjoint analysis (Green and Rao 1971; Green and Srinivasan 1978) is a method for analysing the effects of design factors and consumer characteristics on consumer likings. A common approach is to analyse it in a mixed effects model framework, where random effects consist of consumer effect and interactions between consumer effects and design factors, and fixed effects consist of design factors and consumer characteristics and possibly interactions between them.
Value
rand.table |
data frame with value of Chi square statistics, p-values for the likelihood ratio test for random effects. The order of elimination of non-significant random effects for strucutre = 3 |
anova.table |
data frame with tests for whether the model fixed terms are significant (Analysis of Variance) |
lsmeans.table |
Least Squares Means data frame with p-values and Confidence intervals |
diffs.lsmeans.table |
Differences of Least Squares Means data frame with p-values and Confidence intervals. The multiplicity correction for multiple comparisons tests uses Bonferroni method |
residuals |
These are the residuals of the final model (for structure = 3, the reduced one) |
residualsFixed |
These are the residuals that are extracted from a fixed effects model with a saturated fixed structure (main effects and all higher-way interactions form fixed part) and one fixed Consumer effect. |
Note
The tests for the random effects use likelihood ratio tests while the tests for the fixed effects use the F-test with Satterthwaites approximation to degrees of freedom. The automated reduction in the fixed part uses the principle of marginality, i.e. the highest order interactions are tested first: if they are significant, the lower order effects are not eliminated even if being non-significant.
Author(s)
Alexandra Kuznetsova, Per Bruun Brockhoff
References
Green P, Rao V (1971). Conjoint measurement for quantifying judgemental data. Journal of Marketing Research, 8, 355 - 363
Green P, Srinivasan V (1978). Conjoint analysis in consumer research: Issues and outlook. Journal of Consumer Research, 5, 103 - 123
See Also
sensmixed, SensMixedUI
Examples
1 2 3 4 5 6 7 8 9 |
Example output
[1] "Calculating Liking ..."
Number of levels for interaction Consumer:Product:Information is more or equal to the number of observations in data
Number of levels for interaction Consumer:Product:Information is more or equal to the number of observations in data
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00425257 (tol = 0.002, component 1)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00425258 (tol = 0.002, component 1)
Random effects:
Chi.sq Chi.DF elim.num p.value
Information:Consumer 1.52 1 1 0.218
Product:Consumer 164.26 1 kept <0.001
Consumer 3.01 1 kept 0.083
Fixed effects:
Sum Sq Mean Sq NumDF DenDF F.value elim.num
Product:Information:Gender 5.991542 1.9971805 3 316.02 1.1995135 1
Product:Gender 1.743572 0.5811906 3 237.00 0.3483748 2
Information:Gender 1.407454 1.4074535 1 319.00 0.8436494 3
Gender 1.465605 1.4656048 1 79.00 0.8789376 4
Product:Information 10.387346 3.4624486 3 320.00 2.0764599 5
Product 19.346565 6.4488550 3 240.00 3.8291490 kept
Information 6.520062 6.5200617 1 323.00 3.8714296 kept
Pr(>F)
Product:Information:Gender 0.310
Product:Gender 0.790
Information:Gender 0.359
Gender 0.351
Product:Information 0.103
Product 0.010
Information 0.050
Least squares means:
Product Information Estimate Standard Error DF t-value Lower CI
Product 1 1 NA 5.809 0.232 313 25.0 5.35
Product 2 2 NA 5.105 0.232 313 22.0 4.65
Product 3 3 NA 6.093 0.232 313 26.2 5.64
Product 4 4 NA 5.926 0.232 313 25.5 5.47
Information 1 NA 1 5.633 0.140 106 40.3 5.36
Information 2 NA 2 5.833 0.140 106 41.7 5.56
Upper CI p-value
Product 1 6.27 <2e-16 ***
Product 2 5.56 <2e-16 ***
Product 3 6.55 <2e-16 ***
Product 4 6.38 <2e-16 ***
Information 1 5.91 <2e-16 ***
Information 2 6.11 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Differences of LSMEANS:
Estimate Standard Error DF t-value Lower CI Upper CI
Product 1 - 2 0.7 0.314 240.0 2.240 0.0849 1.323
Product 1 - 3 -0.3 0.314 240.0 -0.900 -0.9027 0.335
Product 1 - 4 -0.1 0.314 240.0 -0.370 -0.7361 0.501
Product 2 - 3 -1.0 0.314 240.0 -3.140 -1.6064 -0.369
Product 2 - 4 -0.8 0.314 240.0 -2.610 -1.4398 -0.202
Product 3 - 4 0.2 0.314 240.0 0.530 -0.4521 0.785
Information 1 - 2 -0.2 0.102 323.0 -1.970 -0.4012 0.000
p-value p-value.adjust
Product 1 - 2 0.0260 0.16
Product 1 - 3 0.3669 1.00
Product 1 - 4 0.7092 1.00
Product 2 - 3 0.0019 0.01 *
Product 2 - 4 0.0095 0.06 .
Product 3 - 4 0.5962 1.00
Information 1 - 2 0.0500 0.05 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
$rand.table
Chi.sq Chi.DF elim.num p.value
Information:Consumer 1.520722 1 1 0.218
Product:Consumer 164.262745 1 kept <0.001
Consumer 3.010458 1 kept 0.083
$anova.table
Sum Sq Mean Sq NumDF DenDF F.value
Product:Information:Gender 5.991542 1.9971805 3 316.01961 1.1995135
Product:Gender 1.743572 0.5811906 3 236.99997 0.3483748
Information:Gender 1.407454 1.4074535 1 318.99997 0.8436494
Gender 1.465605 1.4656048 1 79.00021 0.8789376
Product:Information 10.387346 3.4624486 3 320.00000 2.0764599
Product 19.346565 6.4488550 3 239.99924 3.8291490
Information 6.520062 6.5200617 1 322.99926 3.8714296
elim.num Pr(>F)
Product:Information:Gender 1 0.310
Product:Gender 2 0.790
Information:Gender 3 0.359
Gender 4 0.351
Product:Information 5 0.103
Product kept 0.010
Information kept 0.050
$lsmeans.table
Product Information Estimate Standard Error DF t-value
Product 1 1 <NA> 5.8086 0.2323 313.1 25.01
Product 2 2 <NA> 5.1049 0.2323 313.1 21.98
Product 3 3 <NA> 6.0926 0.2323 313.1 26.23
Product 4 4 <NA> 5.9259 0.2323 313.1 25.51
Information 1 <NA> 1 5.6327 0.1398 105.8 40.29
Information 2 <NA> 2 5.8333 0.1398 105.8 41.73
Lower CI Upper CI p-value
Product 1 5.3517 6.2656 0
Product 2 4.6479 5.5619 0
Product 3 5.6356 6.5496 0
Product 4 5.4689 6.3829 0
Information 1 5.3555 5.9099 0
Information 2 5.5562 6.1105 0
$diffs.lsmeans.table
Estimate Standard Error DF t-value Lower CI Upper CI p-value
Product 1 - 2 0.7037 0.3141 240 2.24 0.0849 1.3225 0.0260
Product 1 - 3 -0.2840 0.3141 240 -0.90 -0.9027 0.3348 0.3669
Product 1 - 4 -0.1173 0.3141 240 -0.37 -0.7361 0.5015 0.7092
Product 2 - 3 -0.9877 0.3141 240 -3.14 -1.6064 -0.3689 0.0019
Product 2 - 4 -0.8210 0.3141 240 -2.61 -1.4398 -0.2022 0.0095
Product 3 - 4 0.1667 0.3141 240 0.53 -0.4521 0.7854 0.5962
Information 1 - 2 -0.2006 0.1020 323 -1.97 -0.4012 0.0000 0.0500
p-value.adjust
Product 1 - 2 0.1560
Product 1 - 3 1.0000
Product 1 - 4 1.0000
Product 2 - 3 0.0114
Product 2 - 4 0.0570
Product 3 - 4 1.0000
Information 1 - 2 0.0500
$residuals
1 2 3 4 5 6
-0.028055053 -0.228672337 -0.090493749 -0.291111033 -1.087892137 0.711490579
7 8 9 10 11 12
0.157960230 -0.042657054 -0.149932348 -0.350549632 0.235916655 1.035299371
13 14 15 16 17 18
0.422422368 0.221805084 0.246813534 0.046196250 0.314544368 0.113927084
19 20 21 22 23 24
-1.958624929 1.840757788 -0.139927416 0.659455300 2.079098450 -2.121518833
25 26 27 28 29 30
0.393406147 0.192788863 0.093410351 -1.107206933 -0.087892137 -0.288509421
31 32 33 34 35 36
-0.447405070 0.351977646 -1.231616400 0.567766316 -0.294055096 -0.494672380
37 38 39 40 41 42
-0.869992284 0.929390432 0.770494783 -0.430122501 -0.063901316 -0.264518600
43 44 45 46 47 48
0.479025288 -0.721591996 0.508453400 0.307836116 -2.088616633 1.710766083
49 50 51 52 53 54
1.195163542 -0.005453742 -1.131658754 -0.332276038 -0.075404142 0.723978574
55 56 57 58 59 60
0.116795225 -1.083822059 -0.319497943 0.479884773 -0.381936639 0.417446077
61 62 63 64 65 66
-1.168604427 1.630778289 0.471882640 0.271265356 -0.305159438 0.494223278
67 68 69 70 71 72
-0.367598134 0.431784582 0.451099378 0.250482094 -1.329874755 1.469507961
73 74 75 76 77 78
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79 80 81 82 83 84
0.239644282 0.039026998 0.779021084 0.578403800 -0.758531812 -0.959149096
85 86 87 88 89 90
3.086992200 -3.113625084 0.727479266 -0.473138017 -0.428008495 -0.628625779
91 92 93 94 95 96
-0.701177791 -0.901795075 -0.250288479 0.549094237 0.600929188 0.400311904
97 98 99 100 101 102
0.568290484 0.367673200 -0.758531812 -0.959149096 0.481626900 -0.718990384
103 104 105 106 107 108
0.543575166 0.342957882 1.223840552 0.023223268 -0.708347043 -0.908964327
109 110 111 112 113 114
-0.889649531 -0.090266815 1.172298735 -1.028318549 -0.712282132 0.087100584
115 116 117 118 119 120
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121 122 123 124 125 126
2.395256658 -2.805360626 -0.694008538 -0.894625822 -0.848484526 0.950898190
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133 134 135 136 137 138
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0.036056330 -1.164560954 0.065484442 -0.135132842 -0.083297892 0.716084824
145 146 147 148 149 150
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163 164 165 166 167 168
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2.268706579 -1.931910705 -0.636654517 -0.837271801 1.182042996 -2.018574288
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0.217164762 -0.983452522 0.888410385 -0.312206899 -0.622316011 -0.822933295
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211 212 213 214 215 216
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223 224 225 226 227 228
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313 314 315 316 317 318
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319 320 321 322 323 324
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325 326 327 328 329 330
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331 332 333 334 335 336
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355 356 357 358 359 360
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361 362 363 364 365 366
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367 368 369 370 371 372
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373 374 375 376 377 378
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397 398 399 400 401 402
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403 404 405 406 407 408
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409 410 411 412 413 414
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415 416 417 418 419 420
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421 422 423 424 425 426
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427 428 429 430 431 432
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433 434 435 436 437 438
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439 440 441 442 443 444
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445 446 447 448 449 450
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451 452 453 454 455 456
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457 458 459 460 461 462
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463 464 465 466 467 468
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469 470 471 472 473 474
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475 476 477 478 479 480
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481 482 483 484 485 486
0.512786973 -0.687830311 1.082540077 -0.118077207 -0.941684811 0.857697905
487 488 489 490 491 492
0.488071656 -0.712545628 1.309225626 -1.891391658 1.089709329 -0.110907955
493 494 495 496 497 498
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499 500 501 502 503 504
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505 506 507 508 509 510
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511 512 513 514 515 516
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517 518 519 520 521 522
0.831395573 -0.369221711 -0.344213260 0.455169456 2.048956216 -1.151661068
523 524 525 526 527 528
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529 530 531 532 533 534
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535 536 537 538 539 540
0.289829050 0.089211766 -0.197620648 0.601762068 -1.286885844 0.512496872
541 542 543 544 545 546
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547 548 549 550 551 552
0.053863066 0.853245782 0.661829978 0.461212694 -0.145970655 -0.346587939
553 554 555 556 557 558
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559 560 561 562 563 564
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565 566 567 568 569 570
0.604475957 0.403858673 0.639597723 0.438980440 -0.697943627 0.101439089
571 572 573 574 575 576
0.898635976 0.698018693 -0.573876611 -0.774493895 0.514898156 0.314280872
577 578 579 580 581 582
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583 584 585 586 587 588
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589 590 591 592 593 594
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595 596 597 598 599 600
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601 602 603 604 605 606
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607 608 609 610 611 612
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613 614 615 616 617 618
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619 620 621 622 623 624
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625 626 627 628 629 630
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631 632 633 634 635 636
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637 638 639 640 641 642
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643 644 645 646 647 648
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Product Information Gender Consumer resid
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6 3 2 1 1 3.658537e-01
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10 1 2 2 2 -2.490625e+00
11 2 1 2 2 1.784375e+00
12 2 2 2 2 2.584375e+00
13 3 1 2 2 7.093750e-01
14 3 2 2 2 3.593750e-01
15 4 1 2 2 -6.656250e-01
16 4 2 2 2 -1.656250e-01
17 1 1 1 3 6.250000e-01
18 1 2 1 3 6.737805e-01
19 2 1 1 3 -2.618902e+00
20 2 2 1 3 7.713415e-01
21 3 1 1 3 5.030488e-01
22 3 2 1 3 9.908537e-01
23 4 1 1 3 1.576220e+00
24 4 2 1 3 -2.521341e+00
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27 2 1 1 4 -1.243902e+00
28 2 2 1 4 -2.853659e+00
29 3 1 1 4 -1.219512e-01
30 3 2 1 4 -6.341463e-01
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32 4 2 1 4 8.536585e-01
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36 2 2 2 5 -1.165625e+00
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116 2 2 1 15 7.713415e-01
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178 1 2 2 23 2.384375e+00
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196 2 2 1 25 7.713415e-01
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436 2 2 1 57 5.213415e-01
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