17: MTC Expanded MNL Mode Choice¶

For this example, we’re going to re-create model 17 from the Self Instructing Manual. (pp. 128)

import larch.numba as lx
d = lx.examples.MTC(format='dataset')
m = lx.Model(d)

We will use the usual choice and availability variables.

m.availability_var = 'avail'
m.choice_ca_var = 'chose'

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 i in d['alt_names'][1:3]:
    name = str(i.values)
    a = int(i.altid)
    m.utility_co[a] += (
        + X("vehbywrk") * P("vehbywrk_SR")
        + X("wkccbd+wknccbd") * P("wkcbd_"+name)
        + X("wkempden") * P("wkempden_"+name)
        + P("ASC_"+name)
    )

for i in d['alt_names'][3:]:
    name = str(i.values)
    a = int(i.altid)
    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.maximize_loglike()

key

value

loglike

-3444.185105027836

x

	0
ASC_Bike	-1.629
ASC_SR2	-1.808
ASC_SR3+	-3.434
ASC_Transit	-0.685
ASC_Walk	0.068
costbyincome	-0.052
hhinc#4	-0.005
hhinc#5	-0.009
hhinc#6	-0.006
motorized_ovtbydist	-0.133
motorized_time	-0.020
nonmotorized_time	-0.045
vehbywrk_Bike	-0.702
vehbywrk_SR	-0.317
vehbywrk_Transit	-0.946
vehbywrk_Walk	-0.722
wkcbd_Bike	0.489
wkcbd_SR2	0.260
wkcbd_SR3+	1.069
wkcbd_Transit	1.309
wkcbd_Walk	0.102
wkempden_Bike	0.002
wkempden_SR2	0.002
wkempden_SR3+	0.002
wkempden_Transit	0.003
wkempden_Walk	0.003

tolerance

6.02306590679683e-06

steps

array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

message

'Optimization terminated successfully.'

elapsed_time

0:00:00.403184

method

'bhhh'

n_cases

5029

iteration_number

0

logloss

0.6848648051357796

__verbose_repr__

True

m.calculate_parameter_covariance()
m.parameter_summary()

		Value	Std Err	t Stat	Signif	Null Value
Category	Parameter
LOS	costbyincome	-0.0524	0.0104	-5.04	***	0.00
	motorized_time	-0.0202	0.00381	-5.29	***	0.00
	nonmotorized_time	-0.0454	0.00577	-7.88	***	0.00
	motorized_ovtbydist	-0.133	0.0196	-6.76	***	0.00
Zonal	wkcbd_Bike	0.489	0.361	1.36		0.00
	wkcbd_SR2	0.260	0.123	2.11	*	0.00
	wkcbd_SR3+	1.07	0.191	5.59	***	0.00
	wkcbd_Transit	1.31	0.166	7.90	***	0.00
	wkcbd_Walk	0.102	0.252	0.40		0.00
	wkempden_Bike	0.00193	0.00122	1.59		0.00
	wkempden_SR2	0.00158	0.000390	4.04	***	0.00
	wkempden_SR3+	0.00226	0.000452	4.99	***	0.00
	wkempden_Transit	0.00313	0.000361	8.68	***	0.00
	wkempden_Walk	0.00289	0.000742	3.90	***	0.00
Household	hhinc#4	-0.00532	0.00198	-2.69	**	0.00
	hhinc#5	-0.00864	0.00515	-1.68		0.00
	hhinc#6	-0.00600	0.00315	-1.90		0.00
	vehbywrk_Bike	-0.702	0.258	-2.72	**	0.00
	vehbywrk_SR	-0.317	0.0666	-4.75	***	0.00
	vehbywrk_Transit	-0.946	0.118	-8.00	***	0.00
	vehbywrk_Walk	-0.722	0.169	-4.26	***	0.00
ASCs	ASC_Bike	-1.63	0.427	-3.81	***	0.00
	ASC_SR2	-1.81	0.106	-17.03	***	0.00
	ASC_SR3+	-3.43	0.152	-22.61	***	0.00
	ASC_Transit	-0.685	0.248	-2.76	**	0.00
	ASC_Walk	0.0683	0.348	0.20		0.00

v5.7.0

17: MTC Expanded MNL Mode Choice

17: MTC Expanded MNL Mode Choice¶