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Interpret the estimates of a fitted choice model

Source: R/interpret.R
interpret.Rd

This function translates the posterior draws to scales that are easier to interpret:

  • A compensation says how many units of a reference covariate, for example the price, are worth one unit of another covariate, leaving the utility and hence the choice probabilities unchanged.

  • A marginal effect says by how much the choice probability of an alternative changes per unit of a covariate, computed by finite differences of the predicted probabilities.

Both are reported with their posterior uncertainty.

Usage

interpret(
  object,
  type = c("compensation", "ame", "mea"),
  reference = NULL,
  effects = NULL,
  at = NULL,
  level = 0.95,
  progress = interactive()
)

# S3 method for class 'RprobitB_interpretation'
print(x, digits = 3L, ...)

Arguments

object

[RprobitB_fit]
Fitted choice model.

type

[character(1)]
The quantity to compute:

  • "compensation": how many units of reference compensate one additional unit of every other effect, so that the utility stays the same. With the price as reference, this is the willingness to pay.

  • "ame": the average marginal effect, that is, the derivative of the choice probability of an alternative with respect to a covariate, computed for every observed choice occasion and averaged.

  • "mea": the marginal effect at the average, that is, the same derivative for a single occasion whose covariates equal the averages of the observed ones.

reference

[character(1) | NULL]
The effect in whose units compensations are measured. NULL uses the coefficient that scale fixed when fitting, and requires a choice otherwise. Only used if type = "compensation".

effects

[character() | NULL]
The effects to express in units of reference. NULL uses every effect other than reference. Only used if type = "compensation".

at

[named numeric() | NULL]
Covariate values at which the marginal effects of type = "mea" are evaluated, see the details. NULL uses the average of every covariate.

level

[numeric(1)]
Probability of the equal-tailed posterior credible interval.

progress

[logical(1)]
Show progress?

x

[RprobitB_interpretation]
Output of interpret().

digits

[integer(1)]
Number of significant digits to print.

...

Currently not used.

Value

A data.frame of class RprobitB_interpretation with one row per quantity and the columns mean, sd, lower, and upper of its posterior distribution. Compensations have a column effect and, for a mixture model, a column class; marginal effects have the columns covariate and alternative.

Compensations

The utility of an alternative is linear in the covariates, so an increase of one unit in an effect with coefficient \(\beta_j\) is compensated by a change of \(-\beta_j / \beta_k\) units in the reference effect with coefficient \(\beta_k\). For a random effect, the coefficient of the median decider enters the ratio. Mixture models report one compensation per class. The ratio is computed for every posterior draw, so the reported uncertainty is the posterior uncertainty of the ratio. Compensations are free of the utility scale normalization, which makes them comparable across models.

Marginal effects

Marginal effects are derivatives of choice probabilities and are computed by finite differences of the predicted probabilities. Marginal effects of a mixed model refer to the population distribution of the random coefficients.

  • type = "ame" averages the marginal effects over all observed choices.

  • type = "mea" builds one artificial choice occasion whose covariates are the averages of the observed ones: the mean for numeric covariates and the most frequent value for the others. The argument at can be used to replace the average of the covariates.

Examples

### travel mode choice where travel time has an alternative-specific effect
data("TravelMode", package = "AER")
TravelMode$choice <- TravelMode$choice == "yes"
TravelMode$vcost <- TravelMode$vcost / 1.6196 # cost in Euro
set.seed(1)
model <- fit(
  choice ~ vcost | 1 | travel,
  data = TravelMode,
  format = "long",
  column_decider = "individual",
  column_alternative = "mode",
  scale = c(vcost = -1),
  iterations = 100,
  chains = 1
)

### travel time must be compensated far more in the plane than in the bus
interpret(
  model, type = "compensation", effects = c("travel_bus", "travel_air")
)
#> 1 `travel_bus` compensates -0.26 `vcost` (95% interval -0.451 to -0.143)
#> 1 `travel_air` compensates -1.18 `vcost` (95% interval -2.13 to -0.57)

### the marginal effects at the average covariates, and for a short flight
interpret(model, type = "mea", at = c(travel_air = 40))
#> Marginal effects at the given covariate values
#> Change in the probability of the alternative per unit of the covariate, with 95% interval 
#>  covariate alternative    at      mean       sd     lower     upper
#>      vcost         air  52.6 -0.003552 0.001247 -0.006297 -0.001661
#>      vcost         bus  20.7 -0.001582 0.001040 -0.004136 -0.000535
#>      vcost         car  13.0 -0.003741 0.001817 -0.007971 -0.001693
#>      vcost       train  31.7 -0.003956 0.002487 -0.010021 -0.001285
#>     travel         air  40.0 -0.003739 0.000325 -0.004306 -0.003128
#>     travel         bus 629.5 -0.000359 0.000157 -0.000694 -0.000155
#>     travel         car 573.2 -0.000742 0.000189 -0.001129 -0.000425
#>     travel       train 608.3 -0.000819 0.000258 -0.001333 -0.000458