singular error when compute a specific variable mlogit (nested) - r

Question

i'm using data from ("TravelMode", package = "AER") and try to follow [Heiss,2002] paper
this is what my code look like initially
Nested Structured Picture
library(mlogit)
data("TravelMode", package = "AER")
TravelMode_frame <- mlogit.data(TravelMode,choice = "choice",shape="long",chid.var="individual",alt.var = "mode")
ml_TM <- mlogit(choice ~travel|income,data=TravelMode_frame,nests = list(public = c('train','bus'), car=('car'),air = c('air')), un.nest.el = FALSE,unscaled=TRUE)
then i want to separate travel time variable between air and the other three as the picture below, so i wrote
air <- idx(TravelMode_frame, 2) %in% c('air')
TravelMode_frame$travel_air <- 0
TravelMode_frame$travel_air[air] <- TravelMode_frame$travel[air]
TravelMode_frame$travel[TravelMode_frame$alt == "air"] <- "0"
then my data look like this
individual mode choice wait vcost travel gcost income size idx travel_air
1 1 air FALSE 69 59 0 70 35 1 1:air 100
2 1 train FALSE 34 31 372 71 35 1 1:rain 0
3 1 bus FALSE 35 25 417 70 35 1 1:bus 0
4 1 car TRUE 0 10 180 30 35 1 1:car 0
~~~ indexes ~~~~
chid alt
1 1 air
2 1 train
3 1 bus
4 1 car
but when i compute it by
ml_TM <- mlogit(choice ~travel+travel_air|income,data=TravelMode_frame,nests = list(public = c('train','bus'), car=('car'), air = c('air')), un.nest.el = FALSE,unscaled=TRUE)
it's say Error in solve.default(H, g[!fixed]) : system is computationally singular: reciprocal condition number = 2.32747e-23
i had no idea why's this happened. could someone pls help me?
i try cutting variable in the formula out 1 by 1 and it's useless
ps. i roll back to the data before i create travel_air and try making travel time a alt specific constant by
ml_TM <- mlogit(choice ~0|income|travel,data=TravelMode_frame,nests = list(public = c('train','bus'), car=('car'),
air = c('air')), un.nest.el = FALSE,unscaled=TRUE)
and it cant compute either (Error in solve.default(crossprod(attr(x, "gradi")[, !fixed])) : system is computationally singular: reciprocal condition number = 1.39039e-20)

Answer 1

i think i get the idea behind this a little bit now. you can tell me if i'm wrong tho, i think my mistakes are
First thing, i forget to rescale income and travel time, so i need to add
TravelMode$travel <- TravelMode$travel/60+TravelMode$wait/60
TravelMode$income <- TravelMode$income/10
about the first question, this one
ml_TM <- mlogit(choice ~travel+travel_air|income,data=TravelMode_frame,nests = list(public = c('train','bus'), car=('car'), air = c('air')), un.nest.el = FALSE,unscaled=TRUE)
my nested have degenerate nested, so IV parameter will not count as dissimilarity anymore but the parameter to proportion the variable instead as the J & L model in the table in the (Heiss,2002) below and maybe because i tried to make it compute 2 variables at once, so come the error because they have to make IV parameter proportion to those variables simultaneously.
for this problem
ml_TM <- mlogit(choice ~0|income|travel,data=TravelMode_frame,nests = list(public = c('train','bus'), car=('car'),
air = c('air')), un.nest.el = FALSE,unscaled=TRUE)
like the above case as model L in the table