Plackett-Luce Tree Summaries

Obtain the coefficients, variance-covariance matrix, AIC, or predictions from a Plackett-Luce tree fitted by pltree().

Usage

# S3 method for pltree
coef(object, node = NULL, drop = TRUE, ...)

# S3 method for pltree
vcov(object, node = nodeids(object, terminal = TRUE), ...)

# S3 method for pltree
AIC(object, newdata = NULL, ...)

# S3 method for pltree
predict(
  object,
  newdata = NULL,
  type = c("itempar", "rank", "best", "node"),
  ...
)

Arguments

object

a fitted model object of class "pltree".

node

a vector of node ids specifying the nodes to summarise, by default the ids of the terminal nodes.

drop

if TRUE return the coefficients as a vector when only one node is selected.

...

additional arguments passed to itempar by predict, and to model.frame by AIC.

newdata

an optional data frame to use instead of the original data. For AIC this must include the response variable.

type

the type of prediction to return for each group, one of: "itempar" to give the result of itempar (by default the fitted probability of each item being ranked first out of all objects), "rank" the corresponding rank, "best" the topped ranked item, or "node" the node of the tree the group belongs to.

Details

AIC computes \(-2L + 2p\) where \(L\) is the joint likelihood of the observed rankings under the tree model and \(p\) is the degrees of freedom used to fit the tree model.

Examples

data(beans)
# fit tree based on pairwise comparisons with variety B
pairB <- data.frame(Winner = ifelse(beans$var_b == "Worse",
                                    "Local", beans$variety_b),
                    Loser = ifelse(beans$var_b == "Worse",
                                   beans$variety_b, "Local"),
                    stringsAsFactors = FALSE, row.names = NULL)
beans$G <- as.rankings(pairB, input = "orderings",
                       index = rep(seq(nrow(beans)), 1))

mod <- pltree(G ~ ., data = beans[c("G", "maxTN")])

coef(mod, node = 3)
#>      ALS 0532-6     BRT 103-182 INTA Centro Sur    INTA Ferroso  INTA Matagalpa 
#>      0.00000000     -0.07161137      0.14990568     -0.16583159     -0.48272277 
#>     INTA Precoz       INTA Rojo     INTA Sequia           Local     PM2 Don Rey 
#>     -0.03697466     -0.68305444     -0.43665252     -0.31973562      0.54722786 
#>      SJC 730-79 
#>     -0.37766352 
AIC(mod)
#> [1] 1123.72

# treat first row from each year as new data
newdata <- beans[!duplicated(beans$year),]

## fitted probabilities
predict(mod, newdata)
#>     ALS 0532-6 BRT 103-182 INTA Centro Sur INTA Ferroso INTA Matagalpa
#> 1   0.10191465  0.09487159      0.11839676   0.08634096     0.06289162
#> 482 0.09663466  0.09072365      0.04497423   0.09188975     0.09950195
#>     INTA Precoz  INTA Rojo INTA Sequia      Local PM2 Don Rey SJC 730-79
#> 1    0.09821520 0.05147423  0.06585683 0.07402479  0.17615486 0.06985853
#> 482  0.08239922 0.08743950  0.13071479 0.16470103  0.04214223 0.06887900

## fitted log-abilities, with Local as reference
predict(mod, newdata, log = TRUE, ref = "Local")
#>     ALS 0532-6 BRT 103-182 INTA Centro Sur INTA Ferroso INTA Matagalpa
#> 1    0.3197356   0.2481243       0.4696413    0.1539040     -0.1629871
#> 482 -0.5331945  -0.5963139      -1.2980422   -0.5835425     -0.5039546
#>     INTA Precoz  INTA Rojo INTA Sequia Local PM2 Don Rey SJC 730-79
#> 1     0.2827610 -0.3633188  -0.1169169     0   0.8669635 -0.0579279
#> 482  -0.6925559 -0.6331848  -0.2311141     0  -1.3630816 -0.8717806

## variety ranks
predict(mod, newdata, type = "rank")
#>     ALS 0532-6 BRT 103-182 INTA Centro Sur INTA Ferroso INTA Matagalpa
#> 1            3           5               2            6             10
#> 482          4           6              10            5              3
#>     INTA Precoz INTA Rojo INTA Sequia Local PM2 Don Rey SJC 730-79
#> 1             4        11           9     7           1          8
#> 482           8         7           2     1          11          9

## top ranked variety
predict(mod, newdata, type = "best")
#>             1           482 
#> "PM2 Don Rey"       "Local" 

## node the trial belongs to
predict(mod, newdata, type = "node")
#>   1   2 
#> "3" "2"