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Multiple Correspondence Analysis (MCA) withFactoMineR (hobbies dataset)
Magalie Houée-Bigot & François Husson
Import data
setwd("C:/users/houee/Downloads") # select the working directoryhobbies = read.table("data_MCA_Hobbies.csv", header=TRUE, sep=";")
header=TRUE : indicates that the file contains the names of the variables
sep=";" : indicates the fields separator (usually “;” or “,” for csv files)
It is important to check that the import is well done
summary(hobbies)
## Reading Listening.music Cinema Show Exhibition Computer Sport## n:2757 n:2456 n:5044 n:5978 n:5808 n:5245 n:5308## y:5646 y:5947 y:3359 y:2425 y:2595 y:3158 y:3095############ Walking Travelling Playing.music Collecting Volunteering Mechanic## n:4228 n:5040 n:6943 n:7541 n:7118 n:4864## y:4175 y:3363 y:1460 y: 862 y:1285 y:3539############ Gardening Knitting Cooking Fishing TV Sex## n:5047 n:6990 n:4717 n:7458 Min. :0.000 F:4616## y:3356 y:1413 y:3686 y: 945 1st Qu.:1.000 M:3787## Median :2.000## Mean :2.355## 3rd Qu.:4.000## Max. :4.000#### Age Marital.status Profession nb.activitees## (45,55]:1837 Divorcee : 792 Employee :2552 Min. : 0.000## (35,45]:1646 Married :4333 Manual labourer :1161 1st Qu.: 4.000## (25,35]:1302 Remarried: 404 Management :1052 Median : 7.000## (55,65]:1257 Single :2140 Unskilled worker: 792 Mean : 6.866## (65,75]: 937 Widower : 734 Foreman : 735 3rd Qu.: 9.000## [15,25]: 857 (Other) : 613 Max. :16.000## (Other): 567 NA's :1498
1
Transform the TV variable as factor
hobbies[,"TV"] = as.factor(hobbies[,"TV"])summary(hobbies[,"TV"])
## 0 1 2 3 4## 1017 1223 2156 1775 2232
Loading FactoMineR
library(FactoMineR)
MCA
res.mca <- MCA(hobbies,quali.sup=19:22,quanti.sup=23)
2
−1.0 −0.5 0.0 0.5 1.0
−1.
0−
0.5
0.0
0.5
1.0
MCA factor map
Dim 1 (16.95%)
Dim
2 (
6.91
%)
Reading_nReading_y
Listening.music_n
Listening.music_y
Cinema_n
Cinema_y
Show_n
Show_y
Exhibition_n Exhibition_y
Computer_n
Computer_y
Sport_n
Sport_yWalking_n
Walking_y
Travelling_n Travelling_yPlaying.music_n
Playing.music_yCollecting_n
Collecting_y
Volunteering_n
Volunteering_y
Mechanic_n
Mechanic_y
Gardening_n
Gardening_y
Knitting_n
Knitting_y
Cooking_n
Cooking_y
Fishing_n
Fishing_y
0
1
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3
4F
M
(25,35]
(35,45]
(45,55]
(55,65](65,75]
(75,85]
(85,100]
[15,25]
Divorcee
MarriedRemarried
Single
Widower
EmployeeForeman
Management
Manual labourer
Other
Profession.NATechnician
Unskilled worker
3
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−0.
50.
00.
51.
0MCA factor map
Dim 1 (16.95%)
Dim
2 (
6.91
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4
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Dim 1 (16.95%)
Dim
2 (
6.91
%)
ReadingListening.music
Cinema
ShowExhibition
ComputerSportWalking
TravellingPlaying.music
CollectingVolunteering
Mechanic
Gardening
KnittingCooking
FishingTV
Sex
AgeMarital.status
Profession
nb.activitees
5
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−1.
0−
0.5
0.0
0.5
1.0
Supplementary variables on the MCA factor map
Dim 1 (16.95%)
Dim
2 (
6.91
%)
nb.activitees
Outputs can be summarized with the function summary.
summary(res.mca)
Outputs are given for the first 2 dimensions (by default 3 dimensions are given).
summary(res.mca, ncp=2)
#### Call:## MCA(X = hobbies, quanti.sup = 23, quali.sup = 19:22)###### Eigenvalues## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6## Variance 0.198 0.081 0.072 0.063 0.058 0.056
6
## % of var. 16.947 6.913 6.173 5.389 5.011 4.784## Cumulative % of var. 16.947 23.859 30.033 35.422 40.433 45.217## Dim.7 Dim.8 Dim.9 Dim.10 Dim.11 Dim.12## Variance 0.056 0.053 0.053 0.049 0.046 0.045## % of var. 4.759 4.569 4.547 4.211 3.985 3.864## Cumulative % of var. 49.976 54.545 59.092 63.303 67.288 71.152## Dim.13 Dim.14 Dim.15 Dim.16 Dim.17 Dim.18## Variance 0.044 0.043 0.041 0.038 0.037 0.036## % of var. 3.730 3.717 3.497 3.256 3.200 3.105## Cumulative % of var. 74.881 78.598 82.095 85.351 88.551 91.655## Dim.19 Dim.20 Dim.21## Variance 0.035 0.032 0.030## % of var. 2.997 2.772 2.575## Cumulative % of var. 94.652 97.425 100.000#### Individuals (the 10 first)## Dim.1 ctr cos2 Dim.2 ctr cos2## 1 | 0.667 0.027 0.336 | -0.191 0.005 0.027 |## 2 | 0.140 0.001 0.011 | 0.434 0.028 0.108 |## 3 | -0.155 0.001 0.032 | -0.244 0.009 0.079 |## 4 | -0.108 0.001 0.011 | -0.285 0.012 0.073 |## 5 | -0.022 0.000 0.001 | -0.268 0.011 0.087 |## 6 | -0.636 0.024 0.449 | 0.019 0.000 0.000 |## 7 | -0.206 0.003 0.046 | -0.239 0.008 0.063 |## 8 | 0.284 0.005 0.065 | -0.611 0.055 0.304 |## 9 | 0.598 0.021 0.261 | -0.577 0.049 0.243 |## 10 | 0.204 0.003 0.033 | -0.015 0.000 0.000 |#### Categories (the 10 first)## Dim.1 ctr cos2 v.test Dim.2 ctr## Reading_n | -0.699 4.503 0.239 -44.766 | -0.051 0.058## Reading_y | 0.341 2.199 0.239 44.766 | 0.025 0.028## Listening.music_n | -0.817 5.478 0.275 -48.111 | 0.241 1.170## Listening.music_y | 0.337 2.262 0.275 48.111 | -0.100 0.483## Cinema_n | -0.509 4.369 0.389 -57.170 | 0.287 3.398## Cinema_y | 0.764 6.561 0.389 57.170 | -0.430 5.103## Show_n | -0.394 3.109 0.383 -56.753 | 0.109 0.586## Show_y | 0.972 7.663 0.383 56.753 | -0.270 1.444## Exhibition_n | -0.422 3.461 0.399 -57.885 | -0.005 0.001## Exhibition_y | 0.945 7.745 0.399 57.885 | 0.012 0.003## cos2 v.test## Reading_n 0.001 -3.255 |## Reading_y 0.001 3.255 |## Listening.music_n 0.024 14.202 |## Listening.music_y 0.024 -14.202 |## Cinema_n 0.123 32.200 |## Cinema_y 0.123 -32.200 |## Show_n 0.029 15.735 |## Show_y 0.029 -15.735 |## Exhibition_n 0.000 -0.748 |## Exhibition_y 0.000 0.748 |#### Categorical variables (eta2)## Dim.1 Dim.2
7
## Reading | 0.239 0.001 |## Listening.music | 0.275 0.024 |## Cinema | 0.389 0.123 |## Show | 0.383 0.029 |## Exhibition | 0.399 0.000 |## Computer | 0.327 0.058 |## Sport | 0.287 0.053 |## Walking | 0.172 0.107 |## Travelling | 0.355 0.000 |## Playing.music | 0.209 0.005 |#### Supplementary categories (the 10 first)## Dim.1 cos2 v.test Dim.2 cos2 v.test## F | 0.018 0.000 1.779 | 0.042 0.002 4.253 |## M | -0.021 0.000 -1.779 | -0.051 0.002 -4.253 |## (25,35] | 0.267 0.013 10.495 | -0.315 0.018 -12.358 |## (35,45] | 0.201 0.010 9.092 | -0.020 0.000 -0.916 |## (45,55] | 0.022 0.000 1.064 | 0.213 0.013 10.309 |## (55,65] | -0.153 0.004 -5.885 | 0.380 0.025 14.599 |## (65,75] | -0.447 0.025 -14.526 | 0.301 0.011 9.789 |## (75,85] | -0.701 0.030 -15.862 | 0.101 0.001 2.276 |## (85,100] | -1.015 0.011 -9.400 | -0.214 0.000 -1.986 |## [15,25] | 0.370 0.016 11.416 | -0.860 0.084 -26.580 |#### Supplementary categorical variables (eta2)## Dim.1 Dim.2## Sex | 0.000 0.002 |## Age | 0.097 0.134 |## Marital.status | 0.046 0.099 |## Profession | 0.128 0.017 |#### Supplementary continuous variable## Dim.1 Dim.2## nb.activitees | 0.975 | 0.198 |
Graph of the eigenvalues
barplot(res.mca$eig[,2],main="Eigenvalues", names.arg=1:nrow(res.mca$eig))
8
1 2 3 4 5 6 7 8 9 11 13 15 17 19 21
Eigenvalues0
510
15
Graphs of the individuals
plot(res.mca,invisible=c("var","quali.sup"),cex=.5,label="none",title="Graph of the individuals")
9
−1.0 −0.5 0.0 0.5 1.0 1.5
−0.
50.
00.
51.
0Graph of the individuals
Dim 1 (16.95%)
Dim
2 (
6.91
%)
plot(res.mca,invisible=c("var","quali.sup"),cex=.5,label="none",title="Graph of the individuals", habillage="Gardening")
10
−1.0 −0.5 0.0 0.5 1.0 1.5
−0.
50.
00.
51.
0Graph of the individuals
Dim 1 (16.95%)
Dim
2 (
6.91
%)
Gardening_nGardening_y
Graphs of the categories
plot(res.mca,invis=c("ind","quali.sup"),col.var=c(rep(c("black","red"),17),"black",rep("red",4)),title="Graph of the active categories")
11
−1.0 −0.5 0.0 0.5 1.0
−0.
50.
00.
51.
0Graph of the active categories
Dim 1 (16.95%)
Dim
2 (
6.91
%)
Reading_n
Reading_y
Listening.music_n
Listening.music_y
Cinema_n
Cinema_y
Show_n
Show_y
Exhibition_nExhibition_y
Computer_n
Computer_y
Sport_n
Sport_yWalking_n
Walking_y
Travelling_nTravelling_y
Playing.music_n
Playing.music_yCollecting_n
Collecting_y
Volunteering_n
Volunteering_y
Mechanic_n
Mechanic_y
Gardening_n
Gardening_y
Knitting_n
Knitting_y
Cooking_n
Cooking_y
Fishing_n
Fishing_y
0
1
2
3
4
plot(res.mca,invisible=c("ind","var"),hab="quali",palette=palette(c("blue","maroon","darkgreen","black","red")),title="Graph of the supplementary categories")
12
−1.0 −0.5 0.0 0.5
−1.
0−
0.5
0.0
0.5
Graph of the supplementary categories
Dim 1 (16.95%)
Dim
2 (
6.91
%)
F
M
(25,35]
(35,45]
(45,55]
(55,65](65,75]
(75,85]
(85,100]
[15,25]
Divorcee
MarriedRemarried
Single
Widower
Employee Foreman
Management
Manual labourer
Other
Profession.NA
Technician
Unskilled worker
Graphs of the variables
plot(res.mca,choix="var",title="Graph of the variables")
13
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Graph of the variables
Dim 1 (16.95%)
Dim
2 (
6.91
%)
ReadingListening.music
Cinema
ShowExhibition
ComputerSportWalking
TravellingPlaying.musicCollecting
Volunteering
Mechanic
Gardening
KnittingCooking
FishingTV
Sex
Age
Marital.statusProfession
nb.activitees
plot(res.mca,choix="quanti.sup",title="Graph of the continuous variables")
14
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
−1.
0−
0.5
0.0
0.5
1.0
Graph of the continuous variables
Dim 1 (16.95%)
Dim
2 (
6.91
%)
nb.activitees
Description of the dimensions
dimdesc(res.mca)
## $`Dim 1`## $`Dim 1`$quanti## correlation p.value## nb.activitees 0.9753459 0#### $`Dim 1`$quali## R2 p.value## Reading 0.23851813 0.000000e+00## Listening.music 0.27548544 0.000000e+00## Cinema 0.38900068 0.000000e+00
15
## Show 0.38335191 0.000000e+00## Exhibition 0.39878925 0.000000e+00## Computer 0.32739645 0.000000e+00## Sport 0.28683998 0.000000e+00## Walking 0.17212148 0.000000e+00## Travelling 0.35491399 0.000000e+00## Playing.music 0.20922813 0.000000e+00## Mechanic 0.13493609 8.816716e-267## Cooking 0.12539365 9.423346e-247## Profession 0.12836813 7.201742e-245## Volunteering 0.10877078 2.247113e-212## Age 0.09747901 1.104310e-181## TV 0.05192240 1.282203e-95## Gardening 0.04696289 7.138377e-90## Marital.status 0.04566170 1.135400e-83## Collecting 0.04356310 2.322542e-83## Knitting 0.01143504 8.427145e-23#### $`Dim 1`$category## Estimate p.value## Playing.music_y 0.26839870 0.000000e+00## Travelling_y 0.27033560 0.000000e+00## Walking_y 0.18447699 0.000000e+00## Sport_y 0.24685643 0.000000e+00## Computer_y 0.26265070 0.000000e+00## Exhibition_y 0.30388560 0.000000e+00## Show_y 0.30379833 0.000000e+00## Cinema_y 0.28307598 0.000000e+00## Listening.music_y 0.25657041 0.000000e+00## Reading_y 0.23125560 0.000000e+00## Mechanic_y 0.16540452 8.816716e-267## Cooking_y 0.15865273 9.423346e-247## Volunteering_y 0.20372577 2.247113e-212## Management 0.29445799 4.929397e-132## Gardening_y 0.09837170 7.138377e-90## Collecting_y 0.15293668 2.322542e-83## Single 0.15105015 1.207987e-54## [15,25] 0.24528149 2.108266e-30## (25,35] 0.19984888 6.389909e-26## Foreman 0.14904669 2.149018e-25## 1 0.13159677 3.341439e-25## 2 0.09449946 1.114616e-24## Knitting_y 0.06356668 8.427145e-23## (35,45] 0.17031375 7.998317e-20## (55,65] 0.01289136 3.849963e-09## Technician 0.05991778 6.892575e-04## Profession.NA -0.05116908 3.088722e-04## Married -0.00169137 1.912935e-07## 4 -0.05681694 9.650520e-17## (85,100] -0.37013968 4.325646e-21## Knitting_n -0.06356668 8.427145e-23## Manual labourer -0.18364686 2.978737e-45## Widower -0.20369965 7.479622e-48## (65,75] -0.11794860 2.179375e-48
16
## 0 -0.19424004 7.701514e-56## (75,85] -0.23095998 1.734900e-57## Unskilled worker -0.27848868 1.030645e-70## Collecting_n -0.15293668 2.322542e-83## Gardening_n -0.09837170 7.138377e-90## Volunteering_n -0.20372577 2.247113e-212## Cooking_n -0.15865273 9.423346e-247## Mechanic_n -0.16540452 8.816716e-267## Playing.music_n -0.26839870 0.000000e+00## Travelling_n -0.27033560 0.000000e+00## Walking_n -0.18447699 0.000000e+00## Sport_n -0.24685643 0.000000e+00## Computer_n -0.26265070 0.000000e+00## Exhibition_n -0.30388560 0.000000e+00## Show_n -0.30379833 0.000000e+00## Cinema_n -0.28307598 0.000000e+00## Listening.music_n -0.25657041 0.000000e+00## Reading_n -0.23125560 0.000000e+00###### $`Dim 2`## $`Dim 2`$quanti## correlation p.value## nb.activitees 0.1980007 4.826398e-75#### $`Dim 2`$quali## R2 p.value## Gardening 0.453046316 0.000000e+00## Knitting 0.166169732 0.000000e+00## Mechanic 0.140401965 2.363989e-278## Cooking 0.135420874 8.354586e-268## Age 0.133583530 9.125004e-256## Cinema 0.123401798 1.341384e-242## Walking 0.106756626 2.977082e-208## Marital.status 0.098904206 5.042868e-188## Fishing 0.084751244 8.323766e-164## Computer 0.058202284 1.463850e-111## Sport 0.053442000 2.406308e-102## TV 0.034425908 1.895739e-62## Show 0.029467916 1.375541e-56## Collecting 0.025914681 6.803897e-50## Listening.music 0.024006349 2.627936e-46## Profession 0.017395750 1.450270e-28## Volunteering 0.009426749 4.666146e-19## Playing.music 0.005420573 1.407100e-11## Sex 0.002152884 2.090738e-05## Reading 0.001260776 1.132204e-03#### $`Dim 2`$category## Estimate p.value## Knitting_y 0.154764175 0.000000e+00## Gardening_y 0.195140682 0.000000e+00## Mechanic_y 0.107759030 2.363989e-278## Cooking_y 0.105301934 8.354586e-268
17
## Cinema_n 0.101829204 1.341384e-242## Walking_y 0.092790996 2.977082e-208## Fishing_y 0.130842880 8.323766e-164## Computer_n 0.070728647 1.463850e-111## Sport_n 0.068053382 2.406308e-102## Married 0.058392178 7.920392e-93## Show_n 0.053795386 1.375541e-56## Collecting_y 0.075337113 6.803897e-50## (55,65] 0.122588737 7.341769e-49## Listening.music_n 0.048373115 2.627936e-46## 3 0.082847534 1.990737e-33## (45,55] 0.075130020 4.614026e-25## (65,75] 0.100358876 9.566953e-23## Volunteering_y 0.038304920 4.666146e-19## Manual labourer 0.062446063 2.315841e-16## Playing.music_n 0.027591591 1.407100e-11## Widower 0.059301096 7.755244e-10## 2 0.039534257 6.282529e-08## F 0.013241401 2.090738e-05## Remarried 0.048925026 2.061549e-04## Unskilled worker 0.031284323 7.973605e-04## Reading_y 0.010738269 1.132204e-03## (75,85] 0.043334701 2.283013e-02## (85,100] -0.046130519 4.698967e-02## Reading_n -0.010738269 1.132204e-03## 4 -0.007916798 2.354582e-04## M -0.013241401 2.090738e-05## 1 -0.027119018 3.688650e-07## Management -0.053914699 9.259268e-11## Playing.music_y -0.027591591 1.407100e-11## Profession.NA -0.046307708 8.336614e-12## Volunteering_n -0.038304920 4.666146e-19## 0 -0.087345976 2.743645e-32## (25,35] -0.074668353 2.201473e-35## Listening.music_y -0.048373115 2.627936e-46## Collecting_n -0.075337113 6.803897e-50## Show_y -0.053795386 1.375541e-56## Sport_y -0.068053382 2.406308e-102## Computer_y -0.070728647 1.463850e-111## [15,25] -0.229609518 1.782463e-162## Fishing_n -0.130842880 8.323766e-164## Single -0.150611195 6.342662e-181## Walking_n -0.092790996 2.977082e-208## Cinema_y -0.101829204 1.341384e-242## Cooking_n -0.105301934 8.354586e-268## Mechanic_n -0.107759030 2.363989e-278## Knitting_n -0.154764175 0.000000e+00## Gardening_n -0.195140682 0.000000e+00###### $`Dim 3`## $`Dim 3`$quali## R2 p.value## Mechanic 0.209469073 0.000000e+00
18
## Knitting 0.326760742 0.000000e+00## Fishing 0.331040836 0.000000e+00## Sex 0.256598886 0.000000e+00## Reading 0.103546767 1.057035e-201## TV 0.075506229 2.154507e-141## Cooking 0.068174772 5.148288e-131## Sport 0.062202668 2.431680e-119## Profession 0.062120420 4.080525e-112## Computer 0.041225998 6.762202e-79## Age 0.037096503 1.135166e-64## Gardening 0.030314206 3.475006e-58## Marital.status 0.030381795 7.010460e-55## Listening.music 0.022109556 9.532570e-43## Exhibition 0.012834600 2.072824e-25## Volunteering 0.003760979 1.842666e-08## Cinema 0.003011654 4.812422e-07## Show 0.002498472 4.557774e-06## Playing.music 0.002317306 1.011746e-05## Walking 0.001577370 2.709621e-04#### $`Dim 3`$category## Estimate p.value## M 0.136610232 0.000000e+00## Fishing_y 0.244371238 0.000000e+00## Knitting_n 0.205088669 0.000000e+00## Mechanic_y 0.124382502 0.000000e+00## Reading_n 0.091963576 1.057035e-201## Cooking_n 0.070605355 5.148288e-131## Sport_y 0.069381729 2.431680e-119## Computer_y 0.056252675 6.762202e-79## Gardening_y 0.047701482 3.475006e-58## Listening.music_n 0.043869558 9.532570e-43## Manual labourer 0.074927886 2.425621e-41## 2 0.051269543 9.688900e-39## 0 0.074320988 7.695837e-29## Exhibition_n 0.032903764 2.072824e-25## Technician 0.106451165 3.134871e-23## 1 0.046966483 1.721087e-17## [15,25] 0.089295409 2.250144e-13## (35,45] 0.068211010 6.999672e-13## Single 0.054243734 1.428671e-10## Volunteering_y 0.022864214 1.842666e-08## Cinema_y 0.015033026 4.812422e-07## Management 0.014062563 1.621277e-06## (25,35] 0.057570669 3.068950e-06## Show_n 0.014802663 4.557774e-06## Foreman 0.018757669 9.818621e-06## Playing.music_n 0.017048181 1.011746e-05## Married 0.034417811 1.547920e-05## Walking_n 0.010658779 2.709621e-04## Divorcee -0.010341038 3.409293e-04## Walking_y -0.010658779 2.709621e-04## (55,65] -0.005079741 1.038252e-05## Playing.music_y -0.017048181 1.011746e-05
19
## (85,100] -0.102325499 9.780901e-06## Show_y -0.014802663 4.557774e-06## Cinema_n -0.015033026 4.812422e-07## Volunteering_n -0.022864214 1.842666e-08## 3 -0.065496551 2.227645e-20## (75,85] -0.085282226 7.049703e-21## (65,75] -0.054868462 1.460573e-22## Exhibition_y -0.032903764 2.072824e-25## Listening.music_y -0.043869558 9.532570e-43## Widower -0.118694340 9.651417e-51## Gardening_n -0.047701482 3.475006e-58## Employee -0.103790767 1.329776e-75## Computer_n -0.056252675 6.762202e-79## 4 -0.107060462 1.674088e-84## Sport_n -0.069381729 2.431680e-119## Cooking_y -0.070605355 5.148288e-131## Reading_y -0.091963576 1.057035e-201## F -0.136610232 0.000000e+00## Fishing_n -0.244371238 0.000000e+00## Knitting_y -0.205088669 0.000000e+00## Mechanic_n -0.124382502 0.000000e+00
Confidence ellipses around the categories for the first 4 variables
plotellipses(res.mca, cex=0.2, magnify=12, keepvar=1:4)
20
Dim 1 (16.95%)
Dim
2 (
6.91
%)
−0.5
0.0
0.5
1.0
−0.5 0.0 0.5 1.0
Cinema_nCinema_y
Cinema
Listening.music_nListening.music_y
Listening.music
Reading_nReading_y
Reading
−0.5 0.0 0.5 1.0
−0.5
0.0
0.5
1.0
Show_nShow_y
Show
21
![LisaKewley% Australian%Naonal%University% · [OII]%-2.0 -1.5 -1.0 -0.5 0.0 0.5 LOG ([NII]/H_)-1.0-0.5 0.0 0.5 1.0 1.5 LOG ([OIII]/H `) log(q) 8.30 8.00 7.75 7.50 7.25 7.00 6.75 6.50](https://img.pdfslide.us/doc/110x75/5fee8eb6ee3d1253771f8762/lisakewley-australiannaonaluniversity-oii-20-15-10-05-00-05-log.jpg)
