4.4. MFACT. Global significance of the results
MFACT allows us to obtain an average of the individual configurations, and to place each one in relation to this average, thereby providing elements for comparison.
We will use the MFA function of FactoMineR package:
MFA (base, group, type = rep("s",length(group)), excl = NULL, ind.sup = NULL, ncp = 5, name.group = NULL,
num.group.sup = NULL, graph = TRUE, weight.col.mfa = NULL, row.w = NULL, axes = c(1,2), tab.comp=NULL)
base parameter
base is a a data frame joining column-wise:
1.- Dataframe TMul24, (multiple table 8 wines x 393 words). 393 is the number of columns (variables) yuxtaposing the 24 DocumentTerm tables. These variables shall be considered active variables.
dim(TMul24)
8 3932.- The DocumentTerm matrix for 15 French judges (8 wines x 137 terms) ; as.matrix(sum.TD.Fr15$DocTerm)
sum.TD.Fr15$DocTerm
<<DocumentTermMatrix (documents: 8, terms: 137)>>
Non-/sparse entries: 430/666
Sparsity : 61%
Maximal term length: 13
Weighting : term frequency (tf)3.- The DocumentTerm matrix for 9 Catalan judges (8 wines x 95 terms) ; as.matrix(sum.TD.Fr15$DocTerm)
sum.TD.Cat9$DocTerm
<<DocumentTermMatrix (documents: 8, terms: 95)>>
Non-/sparse entries: 267/493
Sparsity : 65%
Maximal term length: 14
Weighting : term frequency (tf)4.- The average scores for each wine from French (FrScore, position 25) and Catalan (CatScore, position 26)
base[,25:26]
FrScore CatScore
PG05 6.27 6.37
PG06 6.63 8.06
EG05 5.10 5.76
EG06 5.17 5.28
PC05 5.57 6.22
PC06 6.23 7.19
EC05 5.67 6.47
EC06 5.43 6.33We join these four objects in the multiple table (8 x 627) MFA.Data24:
MFA.Data24 <- cbind(TMul24, as.matrix(sum.TD.Fr15$DocTerm),
as.matrix(sum.TD.Cat9$DocTerm), base[,25:26])
dim(MFA.Data24)
8 627Tmul24 will be the active table (group). The rest (French sum table -sum.TD.Fr15$DocTerm-, Catalan sum table -sum.TD.Cat9$DocTerm- and scores) will be supplementary groups.
group parameter
group is a vector with the number of variables in each group.
We have 24 groups or DocumentTerm tables.
French panel
The first group is composed by the 15 French judges. # To build a vector with the number of words used for each French judge:
cols.Fr15 <- unlist(lapply(1:15, function(i) res.TD.Fr.list[[i]]$DocTerm$ncol))
cat(cols.Fr15)
23 10 11 24 8 9 38 14 26 29 19 12 21 12 6The names of 15 French judges:
cat(names(res.TD.Fr.list))
FE5 FE6 FE12 FP1 FP3 FP4 FP5 FP6 FP7 FP8 FP9 FP10 FP11 FP12 FP2This way, to obtain the first juxtaposed table for FE5 French judge
cat(names(baseFr)[1])
FE5with texts:
baseFr[1]
FE5
PG05 fruit, fruit mûr, épice doux
PG06 Caramel, lactique, souple, gras, fruit en final
EG05 Curieux, particulier, limite défaut, animal, carton humide, étable
EG06 Curieux, particulier, limite défaut, animal, carton humide, étable
PC05 Fruit, Fraîcheur, épice doux
PC06 Boisé neuf, généreux, matière
EC05 Boisé neuf, généreux, matière
EC06 Fruit, acidité, épice douxhas 23 different words:
cat(res.TD.Fr.list[[1]]$DocTerm$ncol)
23
colnames(res.TD.Fr.list[[1]]$DocTerm)
[1] "acidité" "animal" "boisé" "caramel" "carton"
[6] "curieux" "défaut" "doux" "épice" "étable"
[11] "final" "fraîcheur" "fruit" "généreux" "gras"
[16] "humide" "lactique" "limite" "matière" "mûr"
[21] "neuf" "particulier" "souple" with a total of 43 occurrences
sum(res.TD.Fr.list[[1]]$DocTerm)
43The number total of the words of the French active group is 262:
cat(sum(cols.Fr15))
262Catalan panel
The second group is the Catalan group (9 judges) with the number of words for each judge:
cols.Cat9 <- unlist(lapply(1:9, function(i) res.TD.Cat.list[[i]]$DocTerm$ncol))
cat(cols.Cat9)
16 14 11 14 16 15 22 10 13The total number of columns for Catalan group is 131:
sum(cols.Cat9)
131Grouping the two vectors we hace 24 judges and 393 words:
ColTab24 <- c(cols.Fr15, cols.Cat9)
length(ColTab24)
24sum(ColTab24)
393The number of columns for the French DocTerm is 137m and 95 for the Catalan DocTerm.
The last two positions correspond to the average scores of the French and Catalan judges.
posit.groups <- c(ColTab24,
ncol(sum.TD.Fr15$DocTerm), # 137
ncol(sum.TD.Cat9$DocTerm), # 95
2)
cat(posit.groups)
23 10 11 24 8 9 38 14 26 29 19 12 21 12 6 16 14 11 14 16 15 22 10 13 137 95 2type parameter
There are four possibilities to select the type of groups of variables (columns) of the tables:
"c" or "s" for quantitative variables/groups (the difference is that for "s" variables are scaled to unit variance), "n" for categorical variables and "f" for frequencies (from a contingency tables).
By default, all variables are quantitative and scaled to unit variance
It will be 24 variables or judges for frequencies, two "f" for the sum tables for French and Catalan, and finally "s" for the FrScore and CatScore group,
quantitative variables scaled to unit variance that will be noted as "Liking.score":
type=c(rep ('f',24),"f","f","s")
ncp parameter
Where ncp is the number of dimensions to keep, in this case 8.
name-group parameter
name.group is a vector containing the names of the groups.
num.group.sup parameter
The indexes of the illustrative groups (by default, NULL and no group are illustrative).
In our case: num.group.sup=c(27)
The complete MFA function:
res.mfact.24 <- FactoMineR::MFA(MFA.Data24,group=posit.groups,
ncp=8,
type=c(rep ('f',24),"f","f","s"),
name.group=c(names(res.TD.Fr.list), names(res.TD.Cat.list),
"SumTable_Fr", "SumTable_Cat","Liking.score"),
num.group.sup=c(25,26,27),graph=FALSE)
Results for MFA and 24 judges
Correlation between judges and dimensions:
res.mfact.24$group$correlation
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
FE5 0.9452986 0.9609679 0.9337074 0.7426019 0.38905418 0.7117801 0.1769334
FE6 0.9008845 0.7805445 0.8657365 0.8182968 0.73452047 0.5375087 0.2390004
FE12 0.7996843 0.6590418 0.5221168 0.6016644 0.73014749 0.8198833 0.2004942
FP1 0.8524275 0.8180392 0.7979427 0.1968318 0.63369510 0.3616580 0.4666581
FP3 0.8433771 0.7992363 0.4187950 0.6898314 0.27575141 0.6701948 0.6258765
FP4 0.7318280 0.7462019 0.5382468 0.6594774 0.67930466 0.4468242 0.5160119
FP5 0.9577002 0.9726749 0.9277071 0.9604978 0.89492234 0.9151603 0.8643823
FP6 0.8133754 0.6552437 0.6602081 0.6642793 0.80168144 0.6436752 0.5948391
FP7 0.9663395 0.8892092 0.8735525 0.9439394 0.88991698 0.8315308 0.9128447
FP8 0.9502423 0.9164794 0.8491146 0.9297292 0.96576383 0.9761179 0.7902801
FP9 0.6000064 0.7617338 0.5347011 0.6896735 0.56738296 0.3235198 0.1648546
FP10 0.9133936 0.7999331 0.5386519 0.5818494 0.08213368 0.3612487 0.7032749
FP11 0.9541351 0.8988026 0.7684001 0.9551831 0.97614925 0.8556253 0.8263432
FP12 0.6215994 0.8953502 0.8263264 0.5065367 0.69132043 0.5528781 0.1343032
FP2 0.2218152 0.7723727 0.6522539 0.6436684 0.09596313 0.4818590 0.5216243
CE1 0.6379835 0.3696531 0.8121680 0.8438325 0.64058633 0.5205072 0.5879528
CE2 0.9379900 0.9662784 0.9612884 0.3547501 0.26450519 0.1963645 0.1306010
CE3 0.9532760 0.9285858 0.7251645 0.6348657 0.27699402 0.3617273 0.2105766
CE4 0.9660998 0.2713663 0.5580112 0.7438663 0.25529755 0.4685639 0.4206373
CE7 0.7100700 0.8788440 0.6892730 0.9379684 0.90968734 0.5674978 0.2232026
CE8 0.8374236 0.9560653 0.9343581 0.3307823 0.25774761 0.1772129 0.1293215
CE9 0.9583886 0.7366960 0.7153680 0.7585589 0.81309797 0.4831496 0.4598697
CE10 0.5701165 0.9302550 0.9303087 0.6626402 0.28654751 0.4994669 0.2311532
CE11 0.7996360 0.7766699 0.6480023 0.5883667 0.41855730 0.6588803 0.2146359The preliminary analysis led us to assign a non-active role to the French judge FP2 because he/she does not share the first global dispersion direction, common to all the other judges, as shown by the very low value of the corresponding canonical # correlation computed by MFACT. Thus, only 23 individual tables are kept.
Correlation between FP2 judge and dimensions:
res.mfact.24$group$correlation["FP2",]
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
0.22181523 0.77237266 0.65225389 0.64366836 0.09596313 0.48185896 0.52162432 As can be seen in the following table, the first judge FP2 has a very low value for the first dimension (0.2218152).
res.mfact.24$group$correlation[order(res.mfact.24$group$correlation[,"Dim.1"]),]
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
FP2 0.2218152 0.7723727 0.6522539 0.6436684 0.09596313 0.4818590 0.5216243
CE10 0.5701165 0.9302550 0.9303087 0.6626402 0.28654751 0.4994669 0.2311532
FP9 0.6000064 0.7617338 0.5347011 0.6896735 0.56738296 0.3235198 0.1648546
FP12 0.6215994 0.8953502 0.8263264 0.5065367 0.69132043 0.5528781 0.1343032
CE1 0.6379835 0.3696531 0.8121680 0.8438325 0.64058633 0.5205072 0.5879528
CE7 0.7100700 0.8788440 0.6892730 0.9379684 0.90968734 0.5674978 0.2232026
FP4 0.7318280 0.7462019 0.5382468 0.6594774 0.67930466 0.4468242 0.5160119
CE11 0.7996360 0.7766699 0.6480023 0.5883667 0.41855730 0.6588803 0.2146359
FE12 0.7996843 0.6590418 0.5221168 0.6016644 0.73014749 0.8198833 0.2004942
FP6 0.8133754 0.6552437 0.6602081 0.6642793 0.80168144 0.6436752 0.5948391
CE8 0.8374236 0.9560653 0.9343581 0.3307823 0.25774761 0.1772129 0.1293215
FP3 0.8433771 0.7992363 0.4187950 0.6898314 0.27575141 0.6701948 0.6258765
FP1 0.8524275 0.8180392 0.7979427 0.1968318 0.63369510 0.3616580 0.4666581
FE6 0.9008845 0.7805445 0.8657365 0.8182968 0.73452047 0.5375087 0.2390004
FP10 0.9133936 0.7999331 0.5386519 0.5818494 0.08213368 0.3612487 0.7032749
CE2 0.9379900 0.9662784 0.9612884 0.3547501 0.26450519 0.1963645 0.1306010
FE5 0.9452986 0.9609679 0.9337074 0.7426019 0.38905418 0.7117801 0.1769334
FP8 0.9502423 0.9164794 0.8491146 0.9297292 0.96576383 0.9761179 0.7902801
CE3 0.9532760 0.9285858 0.7251645 0.6348657 0.27699402 0.3617273 0.2105766
FP11 0.9541351 0.8988026 0.7684001 0.9551831 0.97614925 0.8556253 0.8263432
FP5 0.9577002 0.9726749 0.9277071 0.9604978 0.89492234 0.9151603 0.8643823
CE9 0.9583886 0.7366960 0.7153680 0.7585589 0.81309797 0.4831496 0.4598697
CE4 0.9660998 0.2713663 0.5580112 0.7438663 0.25529755 0.4685639 0.4206373
FP7 0.9663395 0.8892092 0.8735525 0.9439394 0.88991698 0.8315308 0.9128447For this reason we repeat the MFA eliminating the French judge FP2.
TMul24 multiple table is now TMul23 taking into account. For this reason we repeat the MFA eliminating the French judge FP2 taking into account that this judge ranks 15th in the dataframe. The dimension is 8 wines x 256 words for the French table and 8 x 387 for the French and Catalan table Tmul23:
TMulFr14<-do.call(cbind, lapply(lapply(1:14, function(i) as.matrix(res.TD.Fr.list[[i]]$DocTerm)), unlist))
TMulFr14 <- data.frame(TMulFr14, check.names=TRUE)
cat(dim(TMulFr14))
8 256TMul23 <- cbind(TMulFr14, TMulCat9)
cat(dim(TMul23))
8 387Sub table for the 14 French judges:
sum.TD.Fr14 <- TextData(baseFr, var.text=c(1:14), Fmin=1,stop.word.user = str.Fr.stopworduser)
sum.TD.Fr14$DocTerm
<<DocumentTermMatrix (documents: 8, terms: 135)>>
Non-/sparse entries: 420/660
Sparsity : 61%
Maximal term length: 13
Weighting : term frequency (tf)It has 595 occurrences, 135 distinct words retained after stopwords:
sum.TD.Fr14$summGen
Before After
Documents 8.00 8.00
Occurrences 639.00 595.00
Words 147.00 135.00
Mean-length 79.88 74.38To build the data frame MFA.Data23 with the 8 rows (wines) and 619 columns (variables)
MFA.Data23 <- cbind(TMul23, as.matrix(sum.TD.Fr14$DocTerm),
as.matrix(sum.TD.Cat9$DocTerm), base[,25:26])
cat(dim(MFA.Data23))
8 619To compute the positions (in this case the same vector as cols.Fr14 but eliminating the last position from FP2):
cols.Fr14 <- unlist(lapply(1:14, function(i) res.TD.Fr.list[[i]]$DocTerm$ncol))
cat(cols.Fr14)
23 10 11 24 8 9 38 14 26 29 19 12 21 12Grouping the two vectors (French and Catalan) (23 judges and 387 words)
ColTab23 <- c(cols.Fr14, cols.Cat9)
cat(length(ColTab23))
23cat(sum(ColTab23))
387Joining the group positions:
posit.groups.23 <- c(ColTab23,
ncol(sum.TD.Fr14$DocTerm),
ncol(sum.TD.Cat9$DocTerm),
2)
cat(posit.groups.23)
23 10 11 24 8 9 38 14 26 29 19 12 21 12 16 14 11 14 16 15 22 10 13 135 95 2cat(length(posit.groups.23))
26The new MFA for the 23 judges:
res.mfact.23 <- FactoMineR::MFA(MFA.Data23,group=posit.groups.23,
ncp=8,
type=c(rep ('f',23),"f","f","s"),
name.group=c(names(res.TD.Fr.list)[1:14], names(res.TD.Cat.list),
"SumTable_Fr","SumTable_Cat","Liking.score"),
num.group.sup=c(24,25,26),graph=FALSE)
cat(dim(MFA.Data23))
8 619names(res.mfact.23)
[1] "separate.analyses" "eig" "group"
[4] "inertia.ratio" "ind" "summary.quanti"
[7] "summary.quali" "quanti.var.sup" "freq"
[10] "freq.sup" "partial.axes" "call"
[13] "global.pca"
The inertia of the first factor is equal to 13.3 (13.268381). It should be noted that the maximum value would be 23, that is, the number of active judges (= active groups). Thus, the first global axis of the MFACT does not correspond to the first direction of inertia in each of the 23 active individual configurations.
Eigenvalues and barplot
res.mfact.23$eig
eigenvalue percentage of variance cumulative percentage of variance
comp 1 13.268381 22.675591 22.67559
comp 2 12.066693 20.621913 43.29750
comp 3 10.191452 17.417136 60.71464
comp 4 8.571333 14.648362 75.36300
comp 5 5.812204 9.933026 85.29603
comp 6 5.393299 9.217120 94.51315
comp 7 3.210573 5.486852 100.00000barplot(res.mfact.23$eig[,1], main="Eigenvalues")
Nevertheless, the correlation coefficient between the first factor and the projection of the 23 configurations on this axis, called the canonical correlation coefficient in MFACT , is over 0.70 for 19 of the judges.
round(res.mfact.23$group$correlation,2)
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
FE5 0.95 0.97 0.95 0.78 0.43 0.63 0.17
FE6 0.90 0.86 0.80 0.86 0.71 0.51 0.28
FE12 0.79 0.66 0.52 0.63 0.76 0.77 0.24
FP1 0.85 0.74 0.84 0.26 0.60 0.46 0.43
FP3 0.84 0.74 0.57 0.65 0.33 0.71 0.55
FP4 0.73 0.75 0.49 0.67 0.67 0.51 0.52
FP5 0.96 0.96 0.92 0.97 0.90 0.90 0.87
FP6 0.81 0.64 0.73 0.70 0.78 0.62 0.62
FP7 0.96 0.89 0.85 0.94 0.88 0.88 0.89
FP8 0.95 0.87 0.89 0.91 0.97 0.96 0.81
FP9 0.58 0.78 0.48 0.73 0.60 0.31 0.11
FP10 0.92 0.79 0.62 0.53 0.07 0.33 0.71
FP11 0.95 0.89 0.78 0.97 0.97 0.87 0.85
FP12 0.62 0.83 0.85 0.53 0.65 0.62 0.22
CE1 0.65 0.42 0.77 0.89 0.62 0.52 0.53
CE2 0.95 0.96 0.96 0.34 0.25 0.22 0.14
CE3 0.96 0.95 0.75 0.59 0.29 0.29 0.21
CE4 0.97 0.24 0.63 0.66 0.29 0.51 0.37
CE7 0.70 0.94 0.62 0.95 0.92 0.55 0.16
CE8 0.84 0.95 0.92 0.33 0.25 0.20 0.13
CE9 0.96 0.58 0.86 0.75 0.75 0.53 0.50
CE10 0.56 0.91 0.93 0.67 0.30 0.55 0.22
CE11 0.79 0.85 0.56 0.59 0.48 0.64 0.17cat(nrow(res.mfact.23$group$correlation[res.mfact.23$group$correlation[,1] > 0.70,]))
19The inertia of the second factor is equal to 12.1. The canonical correlation coefficients are over 0.70 for 18 judges, so this second axis also corresponds to the direction of inertia present in the majority of the individual configurations.
cat(nrow(res.mfact.23$group$correlation[res.mfact.23$group$correlation[,2] > 0.70,]))
18Some numerical results of MFACT
RV coefficients. The RV respective values are 0.96 (French sum table) and 0.98 (Catalan sum table), while 1 indicates a perfect homothety:
round(res.mfact.23$group$RV,2)
FE5 FE6 FE12 FP1 FP3 FP4 FP5 FP6 FP7 FP8 FP9 FP10 FP11 FP12 CE1 CE2 CE3 CE4 CE7 CE8
FE5 1.00 0.77 0.43 0.47 0.48 0.46 0.84 0.54 0.56 0.61 0.41 0.60 0.59 0.59 0.42 0.94 0.80 0.48 0.69 0.92
FE6 0.77 1.00 0.54 0.52 0.36 0.41 0.67 0.59 0.66 0.64 0.43 0.44 0.60 0.46 0.62 0.70 0.72 0.40 0.68 0.70
FE12 0.43 0.54 1.00 0.39 0.36 0.42 0.53 0.40 0.51 0.66 0.51 0.29 0.51 0.38 0.38 0.38 0.40 0.32 0.40 0.35
FP1 0.47 0.52 0.39 1.00 0.43 0.59 0.56 0.41 0.61 0.56 0.31 0.52 0.61 0.52 0.62 0.59 0.38 0.30 0.32 0.52
FP3 0.48 0.36 0.36 0.43 1.00 0.35 0.66 0.27 0.77 0.57 0.48 0.69 0.55 0.26 0.44 0.44 0.64 0.65 0.45 0.40
FP4 0.46 0.41 0.42 0.59 0.35 1.00 0.53 0.44 0.56 0.53 0.28 0.32 0.55 0.49 0.44 0.48 0.33 0.27 0.61 0.46
FP5 0.84 0.67 0.53 0.56 0.66 0.53 1.00 0.66 0.78 0.83 0.57 0.70 0.76 0.69 0.51 0.83 0.77 0.62 0.73 0.74
FP6 0.54 0.59 0.40 0.41 0.27 0.44 0.66 1.00 0.59 0.64 0.29 0.47 0.61 0.47 0.32 0.48 0.52 0.44 0.70 0.34
FP7 0.56 0.66 0.51 0.61 0.77 0.56 0.78 0.59 1.00 0.82 0.57 0.68 0.79 0.42 0.68 0.50 0.66 0.57 0.73 0.45
FP8 0.61 0.64 0.66 0.56 0.57 0.53 0.83 0.64 0.82 1.00 0.53 0.63 0.84 0.57 0.51 0.59 0.59 0.60 0.62 0.49
FP9 0.41 0.43 0.51 0.31 0.48 0.28 0.57 0.29 0.57 0.53 1.00 0.23 0.56 0.45 0.28 0.31 0.33 0.30 0.51 0.31
FP10 0.60 0.44 0.29 0.52 0.69 0.32 0.70 0.47 0.68 0.63 0.23 1.00 0.63 0.34 0.37 0.60 0.83 0.66 0.36 0.43
FP11 0.59 0.60 0.51 0.61 0.55 0.55 0.76 0.61 0.79 0.84 0.56 0.63 1.00 0.52 0.50 0.51 0.53 0.50 0.64 0.46
FP12 0.59 0.46 0.38 0.52 0.26 0.49 0.69 0.47 0.42 0.57 0.45 0.34 0.52 1.00 0.31 0.61 0.39 0.26 0.42 0.55
CE1 0.42 0.62 0.38 0.62 0.44 0.44 0.51 0.32 0.68 0.51 0.28 0.37 0.50 0.31 1.00 0.48 0.47 0.31 0.50 0.54
CE2 0.94 0.70 0.38 0.59 0.44 0.48 0.83 0.48 0.50 0.59 0.31 0.60 0.51 0.61 0.48 1.00 0.74 0.47 0.56 0.95
CE3 0.80 0.72 0.40 0.38 0.64 0.33 0.77 0.52 0.66 0.59 0.33 0.83 0.53 0.39 0.47 0.74 1.00 0.64 0.57 0.64
CE4 0.48 0.40 0.32 0.30 0.65 0.27 0.62 0.44 0.57 0.60 0.30 0.66 0.50 0.26 0.31 0.47 0.64 1.00 0.38 0.31
CE7 0.69 0.68 0.40 0.32 0.45 0.61 0.73 0.70 0.73 0.62 0.51 0.36 0.64 0.42 0.50 0.56 0.57 0.38 1.00 0.59
CE8 0.92 0.70 0.35 0.52 0.40 0.46 0.74 0.34 0.45 0.49 0.31 0.43 0.46 0.55 0.54 0.95 0.64 0.31 0.59 1.00
CE9 0.58 0.56 0.43 0.68 0.51 0.47 0.71 0.58 0.62 0.69 0.31 0.79 0.57 0.48 0.40 0.66 0.72 0.65 0.36 0.44
CE10 0.62 0.53 0.48 0.48 0.50 0.51 0.64 0.32 0.52 0.55 0.64 0.25 0.54 0.75 0.44 0.59 0.41 0.36 0.51 0.65
CE11 0.72 0.65 0.43 0.20 0.44 0.26 0.65 0.45 0.48 0.51 0.55 0.41 0.60 0.43 0.32 0.59 0.67 0.55 0.58 0.55
SumTable_Fr 0.82 0.75 0.61 0.69 0.71 0.61 0.94 0.67 0.86 0.85 0.64 0.76 0.83 0.65 0.57 0.79 0.79 0.64 0.70 0.69
SumTable_Cat 0.85 0.78 0.52 0.64 0.69 0.55 0.89 0.57 0.78 0.76 0.50 0.71 0.71 0.58 0.70 0.86 0.85 0.69 0.68 0.80
Liking.score 0.59 0.45 0.21 0.33 0.31 0.45 0.51 0.36 0.39 0.40 0.39 0.33 0.36 0.39 0.06 0.51 0.50 0.06 0.50 0.49
MFA 0.85 0.80 0.62 0.67 0.69 0.63 0.94 0.67 0.86 0.86 0.60 0.72 0.82 0.66 0.64 0.82 0.81 0.65 0.76 0.75
CE9 CE10 CE11 SumTable_Fr SumTable_Cat Liking.score MFA
FE5 0.58 0.62 0.72 0.82 0.85 0.59 0.85
FE6 0.56 0.53 0.65 0.75 0.78 0.45 0.80
FE12 0.43 0.48 0.43 0.61 0.52 0.21 0.62
FP1 0.68 0.48 0.20 0.69 0.64 0.33 0.67
FP3 0.51 0.50 0.44 0.71 0.69 0.31 0.69
FP4 0.47 0.51 0.26 0.61 0.55 0.45 0.63
FP5 0.71 0.64 0.65 0.94 0.89 0.51 0.94
FP6 0.58 0.32 0.45 0.67 0.57 0.36 0.67
FP7 0.62 0.52 0.48 0.86 0.78 0.39 0.86
FP8 0.69 0.55 0.51 0.85 0.76 0.40 0.86
FP9 0.31 0.64 0.55 0.64 0.50 0.39 0.60
FP10 0.79 0.25 0.41 0.76 0.71 0.33 0.72
FP11 0.57 0.54 0.60 0.83 0.71 0.36 0.82
FP12 0.48 0.75 0.43 0.65 0.58 0.39 0.66
CE1 0.40 0.44 0.32 0.57 0.70 0.06 0.64
CE2 0.66 0.59 0.59 0.79 0.86 0.51 0.82
CE3 0.72 0.41 0.67 0.79 0.85 0.50 0.81
CE4 0.65 0.36 0.55 0.64 0.69 0.06 0.65
CE7 0.36 0.51 0.58 0.70 0.68 0.50 0.76
CE8 0.44 0.65 0.55 0.69 0.80 0.49 0.75
CE9 1.00 0.29 0.50 0.80 0.77 0.36 0.76
CE10 0.29 1.00 0.52 0.67 0.66 0.44 0.71
CE11 0.50 0.52 1.00 0.69 0.74 0.34 0.71
SumTable_Fr 0.80 0.67 0.69 1.00 0.93 0.52 0.98
SumTable_Cat 0.77 0.66 0.74 0.93 1.00 0.43 0.96
Liking.score 0.36 0.44 0.34 0.52 0.43 1.00 0.52
MFA 0.76 0.71 0.71 0.98 0.96 0.52 1.00round(res.mfact.23$group$RV[24:27, 24:27],2)
SumTable_Fr SumTable_Cat Liking.score MFA
SumTable_Fr 1.00 0.93 0.52 0.98
SumTable_Cat 0.93 1.00 0.43 0.96
Liking.score 0.52 0.43 1.00 0.52
MFA 0.98 0.96 0.52 1.00Lg coefficients:
round(res.mfact.23$group$Lg,2)
FE5 FE6 FE12 FP1 FP3 FP4 FP5 FP6 FP7 FP8 FP9 FP10 FP11 FP12 CE1 CE2 CE3 CE4 CE7 CE8
FE5 1.71 1.49 0.80 0.76 0.92 0.80 1.79 0.78 1.16 1.41 0.73 0.94 1.17 1.02 0.71 1.97 1.61 0.81 1.43 1.53
FE6 1.49 2.15 1.13 0.94 0.77 0.82 1.58 0.96 1.53 1.66 0.86 0.78 1.33 0.89 1.16 1.64 1.62 0.75 1.58 1.32
FE12 0.80 1.13 2.00 0.69 0.75 0.81 1.20 0.63 1.14 1.65 0.98 0.49 1.10 0.70 0.69 0.87 0.85 0.58 0.89 0.64
FP1 0.76 0.94 0.69 1.55 0.78 0.99 1.13 0.57 1.19 1.23 0.52 0.77 1.15 0.84 0.99 1.17 0.72 0.49 0.63 0.83
FP3 0.92 0.77 0.75 0.78 2.11 0.69 1.56 0.44 1.77 1.46 0.95 1.20 1.21 0.49 0.83 1.02 1.42 1.23 1.04 0.74
FP4 0.80 0.82 0.81 0.99 0.69 1.81 1.15 0.66 1.19 1.26 0.51 0.52 1.12 0.87 0.75 1.02 0.67 0.47 1.30 0.80
FP5 1.79 1.58 1.20 1.13 1.56 1.15 2.60 1.18 1.99 2.38 1.25 1.36 1.87 1.45 1.07 2.14 1.89 1.29 1.85 1.52
FP6 0.78 0.96 0.63 0.57 0.44 0.66 1.18 1.24 1.03 1.26 0.43 0.64 1.04 0.69 0.46 0.85 0.88 0.64 1.23 0.48
FP7 1.16 1.53 1.14 1.19 1.77 1.19 1.99 1.03 2.47 2.29 1.21 1.29 1.88 0.86 1.36 1.25 1.59 1.17 1.82 0.91
FP8 1.41 1.66 1.65 1.23 1.46 1.26 2.38 1.26 2.29 3.13 1.27 1.35 2.28 1.33 1.15 1.66 1.60 1.37 1.74 1.12
FP9 0.73 0.86 0.98 0.52 0.95 0.51 1.25 0.43 1.21 1.27 1.84 0.38 1.15 0.80 0.50 0.68 0.69 0.53 1.09 0.54
FP10 0.94 0.78 0.49 0.77 1.20 0.52 1.36 0.64 1.29 1.35 0.38 1.45 1.15 0.54 0.57 1.15 1.53 1.03 0.69 0.66
FP11 1.17 1.33 1.10 1.15 1.21 1.12 1.87 1.04 1.88 2.28 1.15 1.15 2.32 1.05 0.98 1.25 1.23 0.99 1.54 0.90
FP12 1.02 0.89 0.70 0.84 0.49 0.87 1.45 0.69 0.86 1.33 0.80 0.54 1.05 1.72 0.52 1.28 0.79 0.44 0.86 0.93
CE1 0.71 1.16 0.69 0.99 0.83 0.75 1.07 0.46 1.36 1.15 0.50 0.57 0.98 0.52 1.65 0.98 0.93 0.51 1.01 0.89
CE2 1.97 1.64 0.87 1.17 1.02 1.02 2.14 0.85 1.25 1.66 0.68 1.15 1.25 1.28 0.98 2.54 1.81 0.98 1.41 1.93
CE3 1.61 1.62 0.85 0.72 1.42 0.67 1.89 0.88 1.59 1.60 0.69 1.53 1.23 0.79 0.93 1.81 2.33 1.26 1.37 1.26
CE4 0.81 0.75 0.58 0.49 1.23 0.47 1.29 0.64 1.17 1.37 0.53 1.03 0.99 0.44 0.51 0.98 1.26 1.68 0.79 0.51
CE7 1.43 1.58 0.89 0.63 1.04 1.30 1.85 1.23 1.82 1.74 1.09 0.69 1.54 0.86 1.01 1.41 1.37 0.79 2.49 1.19
CE8 1.53 1.32 0.64 0.83 0.74 0.80 1.52 0.48 0.91 1.12 0.54 0.66 0.90 0.93 0.89 1.93 1.26 0.51 1.19 1.64
CE9 0.89 0.97 0.71 0.99 0.86 0.75 1.33 0.75 1.15 1.42 0.49 1.11 1.02 0.73 0.59 1.24 1.29 0.98 0.66 0.66
CE10 1.11 1.06 0.93 0.81 0.99 0.93 1.41 0.48 1.12 1.32 1.19 0.41 1.13 1.35 0.77 1.28 0.85 0.64 1.10 1.14
CE11 1.19 1.21 0.76 0.31 0.80 0.44 1.32 0.63 0.94 1.13 0.94 0.62 1.15 0.71 0.52 1.18 1.28 0.89 1.14 0.88
SumTable_Fr 1.70 1.75 1.37 1.37 1.64 1.29 2.40 1.19 2.13 2.38 1.38 1.45 2.01 1.36 1.15 2.00 1.92 1.31 1.76 1.40
SumTable_Cat 1.67 1.71 1.10 1.19 1.49 1.11 2.13 0.95 1.82 2.00 1.02 1.28 1.61 1.14 1.34 2.05 1.93 1.34 1.61 1.52
Liking.score 0.77 0.66 0.30 0.41 0.45 0.61 0.83 0.40 0.62 0.71 0.53 0.40 0.55 0.51 0.08 0.82 0.76 0.07 0.79 0.63
MFA 2.01 2.13 1.58 1.51 1.81 1.53 2.74 1.35 2.44 2.75 1.47 1.55 2.26 1.57 1.48 2.36 2.22 1.51 2.17 1.73
CE9 CE10 CE11 SumTable_Fr SumTable_Cat Liking.score MFA
FE5 0.89 1.11 1.19 1.70 1.67 0.77 2.01
FE6 0.97 1.06 1.21 1.75 1.71 0.66 2.13
FE12 0.71 0.93 0.76 1.37 1.10 0.30 1.58
FP1 0.99 0.81 0.31 1.37 1.19 0.41 1.51
FP3 0.86 0.99 0.80 1.64 1.49 0.45 1.81
FP4 0.75 0.93 0.44 1.29 1.11 0.61 1.53
FP5 1.33 1.41 1.32 2.40 2.13 0.83 2.74
FP6 0.75 0.48 0.63 1.19 0.95 0.40 1.35
FP7 1.15 1.12 0.94 2.13 1.82 0.62 2.44
FP8 1.42 1.32 1.13 2.38 2.00 0.71 2.75
FP9 0.49 1.19 0.94 1.38 1.02 0.53 1.47
FP10 1.11 0.41 0.62 1.45 1.28 0.40 1.55
FP11 1.02 1.13 1.15 2.01 1.61 0.55 2.26
FP12 0.73 1.35 0.71 1.36 1.14 0.51 1.57
CE1 0.59 0.77 0.52 1.15 1.34 0.08 1.48
CE2 1.24 1.28 1.18 2.00 2.05 0.82 2.36
CE3 1.29 0.85 1.28 1.92 1.93 0.76 2.22
CE4 0.98 0.64 0.89 1.31 1.34 0.07 1.51
CE7 0.66 1.10 1.14 1.76 1.61 0.79 2.17
CE8 0.66 1.14 0.88 1.40 1.52 0.63 1.73
CE9 1.36 0.46 0.73 1.48 1.35 0.43 1.59
CE10 0.46 1.87 0.90 1.46 1.35 0.60 1.75
CE11 0.73 0.90 1.58 1.38 1.38 0.43 1.60
SumTable_Fr 1.48 1.46 1.38 2.51 2.19 0.83 2.81
SumTable_Cat 1.35 1.35 1.38 2.19 2.22 0.65 2.57
Liking.score 0.43 0.60 0.43 0.83 0.65 1.00 0.93
MFA 1.59 1.75 1.60 2.81 2.57 0.93 3.25Contributions:
round(res.mfact.23$group$contrib,2)
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
FE5 3.93 7.53 5.51 2.44 1.82 2.29 0.43
FE6 4.52 5.94 4.90 4.39 6.52 3.07 1.76
FE12 3.60 2.61 2.30 3.24 8.40 10.46 1.62
FP1 4.26 2.11 6.06 0.70 3.94 2.72 5.10
FP3 4.89 4.35 2.70 4.35 1.57 6.61 6.11
FP4 3.47 3.23 2.15 4.86 6.66 3.00 5.37
FP5 6.10 6.36 6.39 6.11 6.35 7.33 8.75
FP6 4.39 2.02 0.96 3.70 6.19 4.22 2.39
FP7 4.99 4.65 3.62 8.95 7.13 9.50 12.20
FP8 5.46 4.43 5.58 8.66 10.50 11.17 14.16
FP9 2.28 4.90 1.58 5.73 6.05 1.51 0.36
FP10 5.68 3.25 2.83 2.55 0.06 1.16 6.92
FP11 4.38 4.87 3.85 6.42 8.45 5.59 19.49
FP12 1.86 3.59 6.72 3.15 4.08 5.29 1.08
CE1 2.96 1.12 5.69 5.64 3.67 3.28 4.85
CE2 5.92 7.00 8.76 1.30 1.01 0.79 0.58
CE3 6.73 6.61 4.38 3.49 1.00 1.55 1.07
CE4 6.03 0.20 3.78 4.91 1.11 3.61 1.69
CE7 2.84 6.41 2.87 9.49 9.33 4.64 0.56
CE8 2.85 6.49 7.14 0.83 1.03 0.43 0.53
CE9 6.92 1.40 3.60 1.89 2.12 2.61 2.91
CE10 1.61 6.20 6.31 3.96 1.15 4.78 1.39
CE11 4.33 4.73 2.33 3.21 1.85 4.40 0.69And the inertia:
round(res.mfact.23$inertia.ratio,2)
Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
0.70 0.64 0.56 0.48 0.38 0.34 0.22