Plackett-Luce Trees
KauĂȘ de Sousa
2021
Set up
For this lecture we need to packages following packages. We load the packages with library().
library("PlackettLuce")
library("qvcalc")
library("gosset")
library("patchwork")
library("ggparty")
library("climatrends")
library("nasapower")
library("ClimMobTools")Example 1: Sweetpotato data
We first read the .csv file with the function read.csv()
dt <- read.csv("data/sweet_potato.csv")str(dt)## 'data.frame': 1433 obs. of 20 variables:
## $ id : int 6 18 24 25 27 56 62 63 73 74 ...
## $ country : chr "Uganda" "Uganda" "Uganda" "Uganda" ...
## $ district : chr "Gulu" "Gulu" "Gulu" "Gulu" ...
## $ gender : chr "Woman" "Woman" "Man" "Man" ...
## $ trial : chr "community" "community" "community" "community" ...
## $ item_A : chr "NASPOT 10 (Kabode)" "Kakamega" "NASPOT 13" "NASPOT 12" ...
## $ item_B : chr "NASPOT 12" "NASPOT 8" "NASPOT 10 (Kabode)" "NASPOT 10 (Kabode)" ...
## $ item_C : chr "NASPOT 13" "NASPOT 13" "Kakamega" "NASPOT 13" ...
## $ best_overall : chr "B" "B" "A" "A" ...
## $ worst_overall : chr "A" "A" "C" "B" ...
## $ best_taste : chr "C" "B" "A" "A" ...
## $ worst_taste : chr "B" "C" "C" "B" ...
## $ best_color : chr "B" "C" "B" "C" ...
## $ worst_color : chr "C" "B" "A" "A" ...
## $ best_describe : chr "It has high dry matter content" "nice, sweet" "sweet" "very sweet and nice" ...
## $ worst_describe: chr "not too sweet" "sweet" "wet" "it is wet and not sweet" ...
## $ community : chr NA NA NA NA ...
## $ age : chr NA NA NA NA ...
## $ geno_test : chr NA NA NA NA ...
## $ region : chr NA NA NA NA ...For this analysis we keep only the Ghana data
dt <- dt[dt$country == "Ghana", ]And then we transform the tricot rankings into a PlackettLuce rankings. We use the overall preference on the genotypes
R <- rank_tricot(data = dt,
items = c("item_A","item_B","item_C"),
input = c("best_overall","worst_overall"))
head(R)## 419
## "SARI-Nan > SARI-Diedi (Tu-Purple) > ..."
## 420
## "PG17305-N1 > SARI-Diedi (Tu-Purple) ..."
## 421
## "SARI-Diedi (Tu-Purple) > PG17305-N1 ..."
## 422
## "SARI-Nyumingre (Obare) > PG17305-N1 ..."
## 423
## "SARI-Nyumingre (Obare) > PG17265-N1 ..."
## 424
## "SARI-Nyumingre (Obare) > PG17140-N2 ..."Fit a PlackettLuce model
To fit a PlackettLuce model we use the function PlackettLuce(). To know more about the model read the paper by Turner et al (2020).
mod <- PlackettLuce(R)
summary(mod)## Call: PlackettLuce(rankings = R)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CIP442162 0.00000 NA NA NA
## CRI-Apomuden -0.50383 0.18382 -2.741 0.006128 **
## CRI-Ligri -0.29860 0.18349 -1.627 0.103664
## PG17136-N1 0.60760 0.20933 2.903 0.003700 **
## PG17140-N2 -0.97825 0.21498 -4.550 5.35e-06 ***
## PG17206-N5 -0.42867 0.20743 -2.067 0.038774 *
## PG17265-N1 -0.30215 0.20639 -1.464 0.143194
## PG17305-N1 -0.03831 0.20502 -0.187 0.851767
## PG17362-N1 -0.19461 0.20701 -0.940 0.347154
## PG17412-N2 -0.64490 0.20807 -3.099 0.001939 **
## PGN14011-24 -0.46418 0.22658 -2.049 0.040494 *
## PGN16021-39 -0.38181 0.22402 -1.704 0.088322 .
## PGN16024-27 -0.53794 0.22304 -2.412 0.015870 *
## PGN16024-28 -0.39930 0.22308 -1.790 0.073469 .
## PGN16030-30 -0.88195 0.23026 -3.830 0.000128 ***
## PGN16092-6 -0.43790 0.22537 -1.943 0.052011 .
## PGN16130-4 -0.45238 0.22236 -2.034 0.041904 *
## PGN16203-18 -0.52260 0.22491 -2.324 0.020149 *
## SARI-Diedi (Tu-Purple) -0.53984 0.18336 -2.944 0.003239 **
## SARI-Nan 0.14675 0.18539 0.792 0.428611
## SARI-Nyumingre (Obare) 0.16792 0.18411 0.912 0.361734
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 3501.8 on 3025 degrees of freedom
## AIC: 3541.8
## Number of iterations: 16We define a reference item (variety). This helps us in identifying whether a widely used variety is better of worse than the new genotypes.
ref = "SARI-Nyumingre (Obare)"
summary(mod, ref = ref)## Call: PlackettLuce(rankings = R)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CIP442162 -0.16792 0.18411 -0.912 0.361734
## CRI-Apomuden -0.67175 0.14676 -4.577 4.71e-06 ***
## CRI-Ligri -0.46652 0.14647 -3.185 0.001447 **
## PG17136-N1 0.43968 0.18730 2.347 0.018905 *
## PG17140-N2 -1.14617 0.19745 -5.805 6.44e-09 ***
## PG17206-N5 -0.59659 0.18389 -3.244 0.001178 **
## PG17265-N1 -0.47007 0.18375 -2.558 0.010521 *
## PG17305-N1 -0.20623 0.18108 -1.139 0.254754
## PG17362-N1 -0.36253 0.18769 -1.932 0.053420 .
## PG17412-N2 -0.81282 0.18591 -4.372 1.23e-05 ***
## PGN14011-24 -0.63210 0.18666 -3.386 0.000708 ***
## PGN16021-39 -0.54973 0.18557 -2.962 0.003054 **
## PGN16024-27 -0.70586 0.18201 -3.878 0.000105 ***
## PGN16024-28 -0.56722 0.18167 -3.122 0.001794 **
## PGN16030-30 -1.04987 0.19282 -5.445 5.19e-08 ***
## PGN16092-6 -0.60582 0.18555 -3.265 0.001094 **
## PGN16130-4 -0.62030 0.18331 -3.384 0.000715 ***
## PGN16203-18 -0.69052 0.18389 -3.755 0.000173 ***
## SARI-Diedi (Tu-Purple) -0.70776 0.14694 -4.817 1.46e-06 ***
## SARI-Nan -0.02117 0.14910 -0.142 0.887103
## SARI-Nyumingre (Obare) 0.00000 NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 3501.8 on 3025 degrees of freedom
## AIC: 3541.8
## Number of iterations: 16The model coefficients can be obtained using the function coef(). The first example take the coefficients in the log format, the log-worth. If we apply the argument log = FALSE this returns the probability of winning (worth). The sum of these probabilities should always be 1.
coef(mod, ref = ref)## CIP442162 CRI-Apomuden CRI-Ligri
## -0.16791946 -0.67174879 -0.46652334
## PG17136-N1 PG17140-N2 PG17206-N5
## 0.43967813 -1.14617258 -0.59659002
## PG17265-N1 PG17305-N1 PG17362-N1
## -0.47007388 -0.20623080 -0.36253350
## PG17412-N2 PGN14011-24 PGN16021-39
## -0.81282308 -0.63209741 -0.54972776
## PGN16024-27 PGN16024-28 PGN16030-30
## -0.70586233 -0.56721708 -1.04987293
## PGN16092-6 PGN16130-4 PGN16203-18
## -0.60581769 -0.62029882 -0.69052107
## SARI-Diedi (Tu-Purple) SARI-Nan SARI-Nyumingre (Obare)
## -0.70775981 -0.02116773 0.00000000coef(mod, log = FALSE)## CIP442162 CRI-Apomuden CRI-Ligri
## 0.06235524 0.03767581 0.04625843
## PG17136-N1 PG17140-N2 PG17206-N5
## 0.11448517 0.02344353 0.04061661
## PG17265-N1 PG17305-N1 PG17362-N1
## 0.04609448 0.06001151 0.05132786
## PG17412-N2 PGN14011-24 PGN16021-39
## 0.03271861 0.03919973 0.04256530
## PGN16024-27 PGN16024-28 PGN16030-30
## 0.03641223 0.04182734 0.02581341
## PGN16092-6 PGN16130-4 PGN16203-18
## 0.04024354 0.03966497 0.03697515
## SARI-Diedi (Tu-Purple) SARI-Nan SARI-Nyumingre (Obare)
## 0.03634321 0.07221151 0.07375635sum(coef(mod, log = FALSE))## [1] 1We can plot these coefficients with the error bars using the function qvcalc()
plot(qvcalc(mod, ref = ref))
PlackettLuce with covariates
With the function pltree() we can fit a PlackettLuce model recursively to find instabilities in the rankings that are represented by a set of covariates. The rankings are recursively split into two groups according to their value on covariates whose values vary between rankings, and a PlackettLuce model is fitted to each subgroup formed. The method proceeds as follows:
Fit a PlackettâLuce model to the full data.
Assess the stability of the worth parameters with respect to each covariate. That is, test for a structural change in the ranking-level contributions to the first derivatives of the log-likelihood, when these contributions are ordered by covariate values.
If there is significant instability, split the full data by the covariate with the strongest instability, using the cut-point that gives the highest improvement in model fit.
Repeat steps 1-3 for each subgroup until there are no more significant instabilities, or a split produces a subgroup below a given size threshold.
We select the covariates age and gender. We coerce age into integer and gender into factor.
sel <- c("age", "gender")
covar <- dt[sel]
covar$age <- as.integer(covar$age)## Warning: NAs introduced by coercioncovar$gender <- as.factor(covar$gender)Letâs check for NAâs in these variables. We use the function apply() to run over the rows of covar an look for the sum of NAs in each row. A value of 0 means no NA, which is what we are looking for.
sum(is.na(covar))## [1] 8keep <- apply(covar, 1, function(x){
sum(is.na(x))
})
keep <- keep == 0Apply the filter in the dt and covar data frames
covar <- covar[keep, ]
dt <- dt[keep, ]We then use the function rank_tricot() to create the grouped_rankings. This allows the rankings to be linked to the covariates and fit the model using pltree(). The rankings are combined with the covariates using the function cbind().
G <- rank_tricot(data = dt,
items = c("item_A","item_B","item_C"),
input = c("best_overall","worst_overall"),
group = TRUE)
pldt <- cbind(G, covar)
head(pldt)## G age gender
## 419 SARI-Nan > SARI- ... 26 Man
## 420 PG17305-N1 > SAR ... 37 Man
## 421 SARI-Diedi (Tu-P ... 35 Man
## 422 SARI-Nyumingre ( ... 25 Man
## 423 SARI-Nyumingre ( ... 36 Man
## 424 SARI-Nyumingre ( ... 42 ManNow we can fit the tree. The first argument is the formula with response variable being the first followed by the covariates indicated with a ~ sign.
pl <- pltree(G ~ age + gender, data = pldt, alpha = 0.1)
summary(pl)## $`2`
## Call: PlackettLuce(rankings = y, weights = weights, na.action = NULL,
## start = start)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CIP442162 0.000000 NA NA NA
## CRI-Apomuden -0.561385 0.205699 -2.729 0.006350 **
## CRI-Ligri -0.272198 0.205269 -1.326 0.184821
## PG17136-N1 0.439174 0.232960 1.885 0.059404 .
## PG17140-N2 -1.139375 0.245704 -4.637 3.53e-06 ***
## PG17206-N5 -0.653822 0.238588 -2.740 0.006137 **
## PG17265-N1 -0.386940 0.234359 -1.651 0.098727 .
## PG17305-N1 -0.003812 0.232765 -0.016 0.986935
## PG17362-N1 -0.378680 0.235082 -1.611 0.107214
## PG17412-N2 -0.657257 0.237991 -2.762 0.005750 **
## PGN14011-24 -0.403071 0.253849 -1.588 0.112323
## PGN16021-39 -0.369354 0.254594 -1.451 0.146847
## PGN16024-27 -0.600758 0.255263 -2.353 0.018598 *
## PGN16024-28 -0.425007 0.260435 -1.632 0.102698
## PGN16030-30 -0.897314 0.268615 -3.341 0.000836 ***
## PGN16092-6 -0.436958 0.256094 -1.706 0.087963 .
## PGN16130-4 -0.442447 0.247762 -1.786 0.074136 .
## PGN16203-18 -0.691483 0.255624 -2.705 0.006829 **
## SARI-Diedi (Tu-Purple) -0.541247 0.205436 -2.635 0.008423 **
## SARI-Nan 0.069627 0.208161 0.334 0.738013
## SARI-Nyumingre (Obare) 0.397274 0.208438 1.906 0.056656 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 2659.5 on 2311 degrees of freedom
## AIC: 2699.5
## Number of iterations: 13
##
## $`3`
## Call: PlackettLuce(rankings = y, weights = weights, na.action = NULL,
## start = start)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CIP442162 0.00000 NA NA NA
## CRI-Apomuden -0.29731 0.43768 -0.679 0.49695
## CRI-Ligri -0.34969 0.43812 -0.798 0.42477
## PG17136-N1 1.53343 0.51871 2.956 0.00311 **
## PG17140-N2 -0.59500 0.49121 -1.211 0.22578
## PG17206-N5 0.32490 0.45826 0.709 0.47834
## PG17265-N1 -0.02583 0.46488 -0.056 0.95569
## PG17305-N1 0.04864 0.46698 0.104 0.91705
## PG17362-N1 0.67153 0.48942 1.372 0.17003
## PG17412-N2 -0.48299 0.46158 -1.046 0.29538
## PGN14011-24 -0.57525 0.52658 -1.092 0.27465
## PGN16021-39 -0.35483 0.49943 -0.710 0.47741
## PGN16024-27 -0.35840 0.49139 -0.729 0.46577
## PGN16024-28 -0.23410 0.47581 -0.492 0.62272
## PGN16030-30 -0.81432 0.48687 -1.673 0.09441 .
## PGN16092-6 -0.45015 0.50449 -0.892 0.37224
## PGN16130-4 -0.33332 0.53055 -0.628 0.52984
## PGN16203-18 0.09125 0.50900 0.179 0.85772
## SARI-Diedi (Tu-Purple) -0.42444 0.43658 -0.972 0.33095
## SARI-Nan 0.60874 0.43369 1.404 0.16043
## SARI-Nyumingre (Obare) -0.47264 0.43136 -1.096 0.27321
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 770.24 on 670 degrees of freedom
## AIC: 810.24
## Number of iterations: 16The rankings split with the covariate age. We can use the function plot() to see the tree.
plot(pl)
The function plot_tree() is still under development in the package gosset. With this function we can see the tree with the points and error bar.
gosset:::plot_tree(pl)
We can also extract the coefficients from each node like before.
coef(pl)## CIP442162 CRI-Apomuden CRI-Ligri PG17136-N1 PG17140-N2 PG17206-N5
## 2 0 -0.5613845 -0.2721977 0.4391743 -1.1393753 -0.6538218
## 3 0 -0.2973133 -0.3496924 1.5334272 -0.5949976 0.3248989
## PG17265-N1 PG17305-N1 PG17362-N1 PG17412-N2 PGN14011-24 PGN16021-39
## 2 -0.38694033 -0.003811507 -0.3786803 -0.6572568 -0.4030712 -0.3693541
## 3 -0.02583033 0.048636011 0.6715318 -0.4829928 -0.5752502 -0.3548321
## PGN16024-27 PGN16024-28 PGN16030-30 PGN16092-6 PGN16130-4 PGN16203-18
## 2 -0.6007577 -0.4250075 -0.8973138 -0.4369585 -0.4424469 -0.69148324
## 3 -0.3584040 -0.2340996 -0.8143235 -0.4501455 -0.3333179 0.09125216
## SARI-Diedi (Tu-Purple) SARI-Nan SARI-Nyumingre (Obare)
## 2 -0.5412468 0.06962682 0.3972741
## 3 -0.4244423 0.60873996 -0.4726361The model can also be used for predictions with the function predict()
head(predict(pl))## CIP442162 CRI-Apomuden CRI-Ligri PG17136-N1 PG17140-N2 PG17206-N5
## 419 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## 420 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## 421 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## 422 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## 423 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## 424 0.06450597 0.03679542 0.04913443 0.1000762 0.02064313 0.03354662
## PG17265-N1 PG17305-N1 PG17362-N1 PG17412-N2 PGN14011-24 PGN16021-39
## 419 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## 420 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## 421 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## 422 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## 423 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## 424 0.04380804 0.06426057 0.0441714 0.03343158 0.04310705 0.04458528
## PGN16024-27 PGN16024-28 PGN16030-30 PGN16092-6 PGN16130-4 PGN16203-18
## 419 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## 420 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## 421 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## 422 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## 423 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## 424 0.03537481 0.04217174 0.02629671 0.04167075 0.04144266 0.0323067
## SARI-Diedi (Tu-Purple) SARI-Nan SARI-Nyumingre (Obare)
## 419 0.0375439 0.06915737 0.09596964
## 420 0.0375439 0.06915737 0.09596964
## 421 0.0375439 0.06915737 0.09596964
## 422 0.0375439 0.06915737 0.09596964
## 423 0.0375439 0.06915737 0.09596964
## 424 0.0375439 0.06915737 0.09596964Example 2: Breadwheat data
The breadwheat is a dataframe from tricot trials of bread wheat (Triticum aestivum L.) varieties in India. This is a sample data available at ClimMob that can be fetched using the function getDataCM() from ClimMobTools.
key <- "d39a3c66-5822-4930-a9d4-50e7da041e77"
dt <- getDataCM(key = key,
project = "breadwheat",
pivot.wider = TRUE)
names(dt)## [1] "id" "package_participant_name"
## [3] "package_item_A" "package_item_B"
## [5] "package_item_C" "package_project_name"
## [7] "registration_surveyid" "registration_survey_deviceimei"
## [9] "registration_survey_start" "registration_survey_end"
## [11] "registration_participant_name" "registration_district"
## [13] "registration_village" "registration_familiyofthefarmer"
## [15] "registration_age" "registration_gender"
## [17] "registration_telephone" "registration_farm_geo_longitude"
## [19] "registration_farm_geo_latitude" "lastassessment_surveyid"
## [21] "lastassessment_survey_deviceimei" "lastassessment_survey_start"
## [23] "lastassessment_survey_end" "lastassessment_grainquality_pos"
## [25] "lastassessment_grainquality_neg" "lastassessment_yield_pos"
## [27] "lastassessment_yield_neg" "lastassessment_overallperf_pos"
## [29] "lastassessment_overallperf_neg" "firstassessment_surveyid"
## [31] "firstassessment_survey_deviceimei" "firstassessment_survey_start"
## [33] "firstassessment_survey_end" "firstassessment_earlygrowth_pos"
## [35] "firstassessment_earlygrowth_neg" "firstassessment_plantingdate"
## [37] "firstassessment_farm_geo_longitude" "firstassessment_farm_geo_latitude"We remove some strings in the colunm names
names(dt) <- gsub("firstassessment_|package_|lastassessment_|registration_",
"",
names(dt))Tricot data with environmental covariates
We can add environmental covariates from package climatrends. Here we use the function temperature() to compute the temperature indices for the first 80 days after planting. We first convert the planting dates into an object of class Date, and the longitude and latitude into numeric.
dt$plantingdate <- as.Date(dt$plantingdate, format = "%Y-%m-%d")
dt$lon <- as.numeric(dt$farm_geo_longitude)
dt$lat <- as.numeric(dt$farm_geo_latitude)
temp <- temperature(dt[, c("lon","lat")],
day.one = dt[, "plantingdate"],
span = 80)## Getting climate data from NASA POWERtemp## maxDT minDT maxNT minNT DTR SU TR CFD WSDI CSDI T10p T90p
## <dbl> <dbl> <dbl> <dbl> <int> <int> <int> <int> <int> <int> <dbl> <dbl>
## 1: 30.75 20.65 17.67 4.63 15 2 0 0 3 2 5.50 27.73
## 2: 29.16 20.65 16.52 4.63 15 0 0 0 4 2 5.50 27.45
## 3: 32.77 20.65 18.49 4.63 15 7 0 0 8 2 5.50 29.17
## 4: 29.16 20.65 16.52 4.63 15 0 0 0 3 2 5.50 27.25
## 5: 29.16 20.65 16.52 4.63 15 0 0 0 4 2 5.50 26.22
## ---
## 489: 29.16 20.65 16.52 4.63 15 0 0 0 3 2 5.50 27.25
## 490: 29.16 20.65 16.52 4.63 15 0 0 0 3 2 5.50 27.25
## 491: 32.77 20.65 17.67 4.63 15 5 0 0 6 2 5.50 28.41
## 492: 29.16 20.65 16.52 4.63 15 0 0 0 3 2 5.50 27.25
## 493: 29.16 20.65 16.52 4.63 15 0 0 0 3 2 5.50 27.25We build the farmersâ rankings as an object of class âgrouped_rankingsâ.
G <- rank_tricot(dt,
items = c("item_A","item_B","item_C"),
input = c("overallperf_pos","overallperf_neg"),
group = TRUE)
dat <- cbind(G, temp)We fit the model using the function pltree()
pl <- pltree(G ~ maxNT + maxDT,
data = dat)
summary(pl)## $`2`
## Call: PlackettLuce(rankings = y, weights = weights, na.action = NULL,
## start = start)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CSW18 0.0000 NA NA NA
## DBW17 -1.4614 0.4132 -3.537 0.000405 ***
## DPW621-50 -2.0924 0.4376 -4.782 1.74e-06 ***
## HD2824 -3.1032 0.4347 -7.138 9.46e-13 ***
## HD2932 -2.7048 0.4320 -6.261 3.83e-10 ***
## HD2985 -2.0511 0.4413 -4.648 3.35e-06 ***
## HI1563 -3.4131 0.4425 -7.713 1.23e-14 ***
## HP1633 -3.4306 0.4323 -7.936 2.09e-15 ***
## HW2045 -3.5339 0.4396 -8.039 9.03e-16 ***
## K0307 -3.4931 0.4458 -7.835 4.67e-15 ***
## K9107 0.2791 0.4794 0.582 0.560486
## PBW343 -0.6595 0.4512 -1.462 0.143852
## PBW502 -3.1382 0.4539 -6.914 4.71e-12 ***
## PBW550 -3.2180 0.4269 -7.537 4.79e-14 ***
## RAJ4120 -3.0018 0.4331 -6.932 4.16e-12 ***
## WR544 -3.3246 0.4380 -7.590 3.20e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 766.05 on 855 degrees of freedom
## AIC: 796.05
## Number of iterations: 25
##
## $`3`
## Call: PlackettLuce(rankings = y, weights = weights, na.action = NULL,
## start = start)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## CSW18 0.0000 NA NA NA
## DBW17 -0.7026 0.4481 -1.568 0.116904
## DPW621-50 -1.5821 0.4475 -3.535 0.000408 ***
## HD2824 -2.5380 0.4852 -5.231 1.69e-07 ***
## HD2932 -1.5077 0.4469 -3.374 0.000741 ***
## HD2985 -1.1698 0.4286 -2.729 0.006343 **
## HI1563 -2.3205 0.4502 -5.154 2.54e-07 ***
## HP1633 -2.1386 0.4676 -4.574 4.79e-06 ***
## HW2045 -1.9125 0.4482 -4.267 1.98e-05 ***
## K0307 -2.3455 0.4467 -5.251 1.51e-07 ***
## K9107 1.1110 0.5217 2.129 0.033215 *
## PBW343 0.2557 0.4366 0.586 0.558045
## PBW502 -1.9471 0.4245 -4.586 4.51e-06 ***
## PBW550 -2.1052 0.4693 -4.486 7.26e-06 ***
## RAJ4120 -2.5301 0.4974 -5.087 3.64e-07 ***
## WR544 -2.1327 0.4498 -4.741 2.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual deviance: 559.08 on 594 degrees of freedom
## AIC: 589.08
## Number of iterations: 16gosset:::plot_tree(pl)
desousakaue 
k.desousa@cgiar.org