17: MTC Expanded MNL Mode Choice
17: MTC Expanded MNL Mode Choice¶
For this example, we’re going to re-create model 17 from the Self Instructing Manual. (pp. 128)
d = larch.examples.MTC()
m = larch.Model(dataservice=d)
We will use the usual choice and availability variables.
m.availability_var = '_avail_'
m.choice_ca_var = '_choice_'
from larch.roles import P, X
m.utility_ca = (
+ X("totcost/hhinc") * P("costbyincome")
+ X("tottime * (altnum <= 4)") * P("motorized_time")
+ X("tottime * (altnum >= 5)") * P("nonmotorized_time")
+ X("ovtt/dist * (altnum <= 4)") * P("motorized_ovtbydist")
)
The “totcost/hhinc” data is computed once as a new variable when loading the model data. The same applies for tottime filtered by motorized modes (we harness the convenient fact that all the motorized modes have identifying numbers 4 or less), and “ovtt/dist”.
for a in [4,5,6]:
m.utility_co[a] += X("hhinc") * P("hhinc#{}".format(a))
Since the model we want to create groups together DA, SR2 and SR3+ jointly as reference alternatives with respect to income, we can simply omit all of these alternatives from the block that applies to hhinc.
For vehicles per worker, the preferred model include a joint parameter on SR2 and SR3+, but not including DA and not fixed at zero. Here we might use a shadow_parameter (also called an alias in some places), which allows us to specify one or more parameters that are simply a fixed proportion of another parameter. For example, we can say that vehbywrk_SR2 will be equal to vehbywrk_SR.
for a,name in m.dataservice.alternative_pairs[1:3]:
m.utility_co[a] += (
+ X("vehbywrk") * P("vehbywrk_SR")
+ X("wkccbd+wknccbd") * P("wkcbd_"+name)
+ X("wkempden") * P("wkempden_"+name)
+ P("ASC_"+name)
)
for a,name in m.dataservice.alternative_pairs[3:]:
m.utility_co[a] += (
+ X("vehbywrk") * P("vehbywrk_"+name)
+ X("wkccbd+wknccbd") * P("wkcbd_"+name)
+ X("wkempden") * P("wkempden_"+name)
+ P("ASC_"+name)
)
We didn’t explicitly define our parameters first, which is fine; Larch will find them in the utility functions (or elsewhere in more complex models). But they may be found in a weird order that is hard to read in reports. We can define an ordering scheme by assigning to the parameter_groups attribute, like this:
m.ordering = (
('LOS', ".*cost.*", ".*time.*", ".*dist.*",),
('Zonal', "wkcbd.*", "wkempden.*",),
('Household', "hhinc.*", "vehbywrk.*",),
('ASCs', "ASC.*",),
)
Each item in parameter_ordering is a tuple, with a label and one or more regular expressions, which will be compared against all the parameter names. Any names that match will be pulled out and put into the reporting order sequentially. Thus if a parameter name would match more than one regex, it will appear in the ordering only for the first match.
Having created this model, we can then estimate it:
>>> m.load_data()
>>> m.maximize_loglike()
┣ ...Optimization terminated successfully...
>>> m.calculate_parameter_covariance()
>>> m.loglike()
-3444.1...
>>> print(m.pfo()[['value','std_err','t_stat','robust_std_err','robust_t_stat']])
value std_err t_stat robust_std_err robust_t_stat
Category Parameter
LOS costbyincome -0.052 1.040e-02 -5.036 1.334e-02 -3.927
motorized_time -0.020 3.815e-03 -5.292 3.898e-03 -5.178
nonmotorized_time -0.045 5.768e-03 -7.878 5.760e-03 -7.890
motorized_ovtbydist -0.133 1.964e-02 -6.763 2.410e-02 -5.513
Zonal wkcbd_BIKE 0.489 3.611e-01 1.355 3.665e-01 1.335
wkcbd_SR2 0.260 1.234e-01 2.107 1.234e-01 2.106
wkcbd_SR3 1.069 1.913e-01 5.590 1.899e-01 5.630
wkcbd_TRANSIT 1.309 1.657e-01 7.899 1.585e-01 8.259
wkcbd_WALK 0.102 2.521e-01 0.404 2.588e-01 0.393
wkempden_BIKE 0.002 1.215e-03 1.586 1.176e-03 1.640
wkempden_SR2 0.002 3.903e-04 4.042 4.128e-04 3.822
wkempden_SR3 0.002 4.520e-04 4.994 4.537e-04 4.975
wkempden_TRANSIT 0.003 3.607e-04 8.684 3.831e-04 8.178
wkempden_WALK 0.003 7.421e-04 3.895 7.107e-04 4.067
Household hhinc#4 -0.005 1.977e-03 -2.692 2.047e-03 -2.600
hhinc#5 -0.009 5.154e-03 -1.677 5.967e-03 -1.449
hhinc#6 -0.006 3.149e-03 -1.905 3.431e-03 -1.748
vehbywrk_BIKE -0.702 2.583e-01 -2.718 3.094e-01 -2.270
vehbywrk_SR -0.317 6.663e-02 -4.752 7.560e-02 -4.188
vehbywrk_TRANSIT -0.946 1.183e-01 -7.999 1.370e-01 -6.907
vehbywrk_WALK -0.722 1.694e-01 -4.261 2.032e-01 -3.552
ASCs ASC_BIKE -1.629 4.274e-01 -3.811 4.861e-01 -3.351
ASC_SR2 -1.808 1.061e-01 -17.035 1.170e-01 -15.451
ASC_SR3 -3.434 1.519e-01 -22.610 1.557e-01 -22.048
ASC_TRANSIT -0.685 2.478e-01 -2.764 2.690e-01 -2.547
ASC_WALK 0.068 3.480e-01 0.196 3.493e-01 0.195
Tip
If you want access to the model in this example without worrying about assembling all the code blocks together on your own, you can load a read-to-estimate copy like this:
m = larch.example(17)