Predicted Probabilities and Logits for "nestedLogit" Models

The predict and fitted methods compute predicted values from a fitted "nestedLogit" model. The confint method computes point-wise confidence limits for predicted response-category probabilities or logits.

predict, fitted: Compute predicted response-category probabilities (or predicted logits for each binary logit model in the dichotomies) from a fitted "nestedLogit" model.
confint: Compute point-wise confidence limits for predicted response-category probabilities or logits.
print methods: Print predicted probabilities, logits, and their standard errors, with control over how many rows to display.

Usage

# S3 method for class 'nestedLogit'
predict(object, newdata, model = c("nested", "dichotomies"), ...)

# S3 method for class 'predictNestedLogit'
print(x, n = min(10L, nrow(x$p)), ...)

# S3 method for class 'predictNestedLogit'
confint(
  object,
  parm = c("prob", "logit"),
  level = 0.95,
  conf.limits.logit = TRUE,
  ...
)

# S3 method for class 'predictDichotomies'
print(x, n = 10L, ...)

# S3 method for class 'nestedLogit'
fitted(object, model = c("nested", "dichotomies"), ...)

Arguments

object: a fitted object of class "nestedLogit"; for confint, an object of class "predictNestedLogit".
newdata: a data frame containing combinations of values of the predictors at which fitted probabilities (or other quantities) are to be computed. If missing, the original data are used.
model: either "nested" (the default), in which case fitted probabilities under the nested logit model are returned, or "dichotomies", in which case predict.glm is invoked for each binary logit model fit to the nested dichotomies and a named list of the results is returned.
...: arguments to be passed down.
x: an object of class "predictNestedLogit" or "predictDichotomies".
n: an integer or "all" to control how many rows are printed for each of the predicted values.
parm: one of "prob" or "logit", indicating whether to generate confidence intervals for probabilities or logits of the responses.
level: confidence level, a number between 0 and 1; default is 0.95.
conf.limits.logit: logical; when parm = "prob", if TRUE (the default), confidence limits are computed on the logit scale and back-transformed to probabilities; if FALSE, Wald-type limits are computed directly on the probability scale.

Value

The predict and fitted methods return an object of class "predictNestedLogit" (when model = "nested") or "predictDichotomies" (when model = "dichotomies").

A "predictNestedLogit" object is a list containing:
p

a data frame of predicted probabilities, with one column per response category.

logit

a data frame of predicted logits.

se.p

a data frame of standard errors of predicted probabilities.

se.logit

a data frame of standard errors of predicted logits.

.data

the newdata data frame, if supplied.

A "predictDichotomies" object is a named list of data frames, one per dichotomy, each produced by predict.glm.
The confint method returns a data frame of point estimates and confidence limits.
The various print methods invisibly return their x arguments.

Details

The predict method provides predicted values for two representations of the model. model = "nested" (the default) gives the fitted probabilities for each of the response categories, along with the corresponding logits and standard errors of each. model = "dichotomies" gives the fitted log odds for each of the binary logit models in the nested dichotomies.

The fitted method (with no newdata) is equivalent to predict applied to the original data used to fit the model.

For the confint method with parm = "prob", setting conf.limits.logit = TRUE (the default) computes confidence limits on the logit scale and back-transforms them to probabilities, which ensures that the limits lie in \([0, 1]\). Setting conf.limits.logit = FALSE computes Wald-type confidence intervals directly on the probability scale, which may extend outside \([0, 1]\).

Author

John Fox and Michael Friendly

Examples

# define continuation dichotomies for level of education
cont.dichots <- continuationLogits(c("<highschool",
                                     "highschool",
                                     "college",
                                     "graduate"))

# fit a nested model for the GSS data
m <- nestedLogit(degree ~ parentdeg + year,
                 cont.dichots,
                 data=GSS)

# predicted probabilities for first few cases
predict(m)
#> 
#> First 10 of 44091 rows:
#> 
#> predicted response-category probabilties
#>    <highschool highschool    college   graduate
#> 2   0.48669496  0.4481946 0.04326738 0.02184305
#> 3   0.48669496  0.4481946 0.04326738 0.02184305
#> 4   0.04093763  0.5328723 0.31960957 0.10658049
#> 5   0.48669496  0.4481946 0.04326738 0.02184305
#> 6   0.03215663  0.4161182 0.34830386 0.20342132
#> 7   0.04093763  0.5328723 0.31960957 0.10658049
#> 8   0.04093763  0.5328723 0.31960957 0.10658049
#> 9   0.11747919  0.6976573 0.13619288 0.04867067
#> 10  0.48669496  0.4481946 0.04326738 0.02184305
#> 13  0.48669496  0.4481946 0.04326738 0.02184305
#>   . . .
#> 
#> predicted response-category logits
#>    <highschool highschool    college  graduate
#> 2  -0.05323272 -0.2079679 -3.0961249 -3.801787
#> 3  -0.05323272 -0.2079679 -3.0961249 -3.801787
#> 4  -3.15390636  0.1316792 -0.7555666 -2.126156
#> 5  -0.05323272 -0.2079679 -3.0961249 -3.801787
#> 6  -3.40445160 -0.3387293 -0.6265031 -1.365047
#> 7  -3.15390636  0.1316792 -0.7555666 -2.126156
#> 8  -3.15390636  0.1316792 -0.7555666 -2.126156
#> 9  -2.01652113  0.8361667 -1.8472774 -2.972784
#> 10 -0.05323272 -0.2079679 -3.0961249 -3.801787
#> 13 -0.05323272 -0.2079679 -3.0961249 -3.801787
#>   . . .
#> 
#> standard errors of predicted probabilities
#>    <highschool  highschool     college    graduate
#> 2  0.006302163 0.005851716 0.001707529 0.001183908
#> 3  0.006302163 0.005851716 0.001707529 0.001183908
#> 4  0.003707404 0.009246535 0.008481557 0.005474035
#> 5  0.006302163 0.005851716 0.001707529 0.001183908
#> 6  0.004011760 0.010684551 0.010589359 0.009031287
#> 7  0.003707404 0.009246535 0.008481557 0.005474035
#> 8  0.003707404 0.009246535 0.008481557 0.005474035
#> 9  0.003595434 0.005098858 0.003676266 0.002182298
#> 10 0.006302163 0.005851716 0.001707529 0.001183908
#> 13 0.006302163 0.005851716 0.001707529 0.001183908
#>   . . .
#> 
#> standard errors of predicted logits
#>    <highschool highschool    college   graduate
#> 2   0.02522651 0.02366087 0.04124933 0.05541104
#> 3   0.02522651 0.02366087 0.04124933 0.05541104
#> 4   0.09442790 0.03714670 0.03900296 0.05748764
#> 5   0.02522651 0.02366087 0.04124933 0.05541104
#> 6   0.12890190 0.04397589 0.04665157 0.05573455
#> 7   0.09442790 0.03714670 0.03900296 0.05748764
#> 8   0.09442790 0.03714670 0.03900296 0.05748764
#> 9   0.03467891 0.02417304 0.03124897 0.04713199
#> 10  0.02522651 0.02366087 0.04124933 0.05541104
#> 13  0.02522651 0.02366087 0.04124933 0.05541104
#>   . . .

# predicted probabilities at specific values of predictors
new <- expand.grid(parentdeg=c("<highschool",  "highschool",
                               "college", "graduate"),
                   year=c(1972, 2016))

fit <- predict(m, newdata=new)
cbind(new, fit)
#>      parentdeg year   parentdeg year    response          p        se.p
#> 1  <highschool 1972 <highschool 1972 <highschool 0.48669496 0.006302163
#> 2   highschool 1972 <highschool 1972  highschool 0.44819461 0.005851716
#> 3      college 1972 <highschool 1972     college 0.04326738 0.001707529
#> 4     graduate 1972 <highschool 1972    graduate 0.02184305 0.001183908
#> 5  <highschool 2016  highschool 1972 <highschool 0.11747919 0.003595434
#> 6   highschool 2016  highschool 1972  highschool 0.69765725 0.005098858
#> 7      college 2016  highschool 1972     college 0.13619288 0.003676266
#> 8     graduate 2016  highschool 1972    graduate 0.04867067 0.002182298
#> 9  <highschool 1972     college 1972 <highschool 0.04093763 0.003707404
#> 10  highschool 1972     college 1972  highschool 0.53287231 0.009246535
#> 11     college 1972     college 1972     college 0.31960957 0.008481557
#> 12    graduate 1972     college 1972    graduate 0.10658049 0.005474035
#> 13 <highschool 2016    graduate 1972 <highschool 0.03215663 0.004011760
#> 14  highschool 2016    graduate 1972  highschool 0.41611819 0.010684551
#> 15     college 2016    graduate 1972     college 0.34830386 0.010589359
#> 16    graduate 2016    graduate 1972    graduate 0.20342132 0.009031287
#> 17 <highschool 1972 <highschool 2016 <highschool 0.26785921 0.006798108
#> 18  highschool 1972 <highschool 2016  highschool 0.58583139 0.006948958
#> 19     college 1972 <highschool 2016     college 0.08374198 0.003523212
#> 20    graduate 1972 <highschool 2016    graduate 0.06256742 0.003072415
#> 21 <highschool 2016  highschool 2016 <highschool 0.04885547 0.001733643
#> 22  highschool 2016  highschool 2016  highschool 0.65346585 0.005313294
#> 23     college 2016  highschool 2016     college 0.19470249 0.004494391
#> 24    graduate 2016  highschool 2016    graduate 0.10297618 0.003441931
#> 25 <highschool 1972     college 2016 <highschool 0.01620361 0.001500524
#> 26  highschool 1972     college 2016  highschool 0.41423386 0.008148392
#> 27     college 1972     college 2016     college 0.38135421 0.008510405
#> 28    graduate 1972     college 2016    graduate 0.18820832 0.007056246
#> 29 <highschool 2016    graduate 2016 <highschool 0.01265796 0.001605067
#> 30  highschool 2016    graduate 2016  highschool 0.30107340 0.008518703
#> 31     college 2016    graduate 2016     college 0.36810041 0.009972667
#> 32    graduate 2016    graduate 2016    graduate 0.31816823 0.009700566
#>          logit   se.logit
#> 1  -0.05323272 0.02522651
#> 2  -0.20796791 0.02366087
#> 3  -3.09612491 0.04124933
#> 4  -3.80178733 0.05541104
#> 5  -2.01652113 0.03467891
#> 6   0.83616665 0.02417304
#> 7  -1.84727739 0.03124897
#> 8  -2.97278366 0.04713199
#> 9  -3.15390636 0.09442790
#> 10  0.13167918 0.03714670
#> 11 -0.75556665 0.03900296
#> 12 -2.12615578 0.05748764
#> 13 -3.40445160 0.12890190
#> 14 -0.33872927 0.04397589
#> 15 -0.62650313 0.04665157
#> 16 -1.36504661 0.05573455
#> 17 -1.00551133 0.03466465
#> 18  0.34675885 0.02863979
#> 19 -2.39255756 0.04591745
#> 20 -2.70690014 0.05238314
#> 21 -2.96879974 0.03730782
#> 22  0.63430892 0.02346361
#> 23 -1.41973906 0.02866441
#> 24 -2.16458467 0.03726159
#> 25 -4.10618498 0.09412952
#> 26 -0.34648993 0.03358165
#> 27 -0.48380426 0.03607278
#> 28 -1.46169432 0.04618387
#> 29 -4.35673022 0.12842860
#> 30 -0.84219163 0.04048270
#> 31 -0.54037476 0.04287429
#> 32 -0.76220268 0.04471601

# use fitted() -- equivalent to predict() on the original data
f <- fitted(m)

# predicted logits for each dichotomy
pred.dichot <- predict(m, newdata=new, model="dichotomies")
pred.dichot
#> 
#>  predictions for binary logit models from nested logit model: m 
#> 
#>  dichotomy: above_.highschool 
#>          fit     se.fit residual.scale
#> 1 0.05323272 0.02522651              1
#> 2 2.01652113 0.03467891              1
#> 3 3.15390636 0.09442790              1
#> 4 3.40445160 0.12890190              1
#> 5 1.00551133 0.03466465              1
#> 6 2.96879974 0.03730782              1
#> 7 4.10618498 0.09412952              1
#> 8 4.35673022 0.12842860              1
#> 
#>  dichotomy: above_highschool 
#>          fit     se.fit residual.scale
#> 1 -1.9291427 0.03501272              1
#> 2 -1.3281099 0.02896659              1
#> 3 -0.2233964 0.03806677              1
#> 4  0.2820807 0.04445165              1
#> 5 -1.3873084 0.03693667              1
#> 6 -0.7862756 0.02531886              1
#> 7  0.3184379 0.03387511              1
#> 8  0.8239151 0.04064027              1
#> 
#>  dichotomy: above_college 
#>          fit     se.fit residual.scale
#> 1 -0.6835162 0.06476680              1
#> 2 -1.0289955 0.05203322              1
#> 3 -1.0981997 0.06219778              1
#> 4 -0.5377960 0.06313624              1
#> 5 -0.2914957 0.06656676              1
#> 6 -0.6369750 0.04354779              1
#> 7 -0.7061792 0.05173419              1
#> 8 -0.1457755 0.05184601              1
#> 
#>  dichotomy: .data 
#>     parentdeg year
#> 1 <highschool 1972
#> 2  highschool 1972
#> 3     college 1972
#> 4    graduate 1972
#> 5 <highschool 2016
#> 6  highschool 2016
#> 7     college 2016
#> 8    graduate 2016

# confidence intervals for predicted probabilities
fit.ci <- confint(fit)
head(fit.ci)
#>   <highschool.p highschool.p  college.p graduate.p <highschool.0.025
#> 1    0.48669496    0.4481946 0.04326738 0.02184305        0.47435358
#> 2    0.11747919    0.6976573 0.13619288 0.04867067        0.11061342
#> 3    0.04093763    0.5328723 0.31960957 0.10658049        0.03425783
#> 4    0.03215663    0.4161182 0.34830386 0.20342132        0.02515812
#> 5    0.26785921    0.5858314 0.08374198 0.06256742        0.25474701
#> 6    0.04885547    0.6534659 0.19470249 0.10297618        0.04556752
#>   highschool.0.025 college.0.025 graduate.0.025 <highschool.0.975
#> 1        0.4367550    0.04004156     0.01963924        0.49905259
#> 2        0.6875711    0.12914674     0.04456744        0.12471137
#> 3        0.5147140    0.30322001     0.09631738        0.04885401
#> 4        0.3953399    0.32784710     0.18629229        0.04102008
#> 5        0.5721494    0.07709029     0.05680926        0.28139148
#> 6        0.6429798    0.18604443     0.09642305        0.05236764
#>   highschool.0.975 college.0.975 graduate.0.975
#> 1        0.4596893    0.04674043     0.02428803
#> 2        0.7075563    0.14356008     0.05313067
#> 3        0.5509440    0.33645724     0.11779464
#> 4        0.4371989    0.36933569     0.22169621
#> 5        0.5993823    0.09091108     0.06886661
#> 6        0.6638049    0.20366267     0.10992051

# confidence intervals for predicted logits
fit.ci.logit <- confint(fit, parm="logit")
head(fit.ci.logit)
#>   <highschool.logit highschool.logit college.logit graduate.logit
#> 1       -0.05323272       -0.2079679    -3.0961249      -3.801787
#> 2       -2.01652113        0.8361667    -1.8472774      -2.972784
#> 3       -3.15390636        0.1316792    -0.7555666      -2.126156
#> 4       -3.40445160       -0.3387293    -0.6265031      -1.365047
#> 5       -1.00551133        0.3467588    -2.3925576      -2.706900
#> 6       -2.96879974        0.6343089    -1.4197391      -2.164585
#>   <highschool.0.025 highschool.0.025 college.0.025 graduate.0.025
#> 1        -0.1026758      -0.25434235    -3.1769721      -3.910391
#> 2        -2.0844905       0.78878837    -1.9085242      -3.065161
#> 3        -3.3389816       0.05887299    -0.8320111      -2.238829
#> 4        -3.6570947      -0.42492042    -0.7179385      -1.474284
#> 5        -1.0734528       0.29062588    -2.4825541      -2.809569
#> 6        -3.0419217       0.58832109    -1.4759203      -2.237616
#>   <highschool.0.975 highschool.0.975 college.0.975 graduate.0.975
#> 1      -0.003789662       -0.1615935    -3.0152777      -3.693184
#> 2      -1.948551711        0.8835449    -1.7860305      -2.880407
#> 3      -2.968831089        0.2044854    -0.6791222      -2.013482
#> 4      -3.151808517       -0.2525381    -0.5350677      -1.255809
#> 5      -0.937569863        0.4028918    -2.3025610      -2.604231
#> 6      -2.895677757        0.6802968    -1.3635578      -2.091553

Predicted Probabilities and Logits for `"nestedLogit"` Models