ApolloChoiceModelling forum

Hey,

I have some problems with the estimation, because I get positive eigenvalues, as soon as I use all of my betas.
The more betas I add, the bigger becomes the eigenvalue to a point, where its 0 or positive and my model fails.

I tried it with a subset of my data and checked on every beta, but as soon as a certain amount is activated, it fails and the s.e. get very high or I get NaNs.

This is my code:

### Initialise code
apollo_initialise()

### set core controls
apollo_control = list(
modelName ="Nutzen",
modelDescr ="Simple MNL model on mode choice RP data",
indivID ="FID",
outputDirectory = "output"
)


# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #

### Vector of parameters, including any that are kept fixed in estimation

apollo_beta=c(asc_fuss = 0,
asc_rad = 0,
asc_auto = 0,
asc_mitfahr = 0,
asc_oev = 0,

b_temp_fuss_u0_5= 0,
b_temp_fuss_5_15 = 0,
b_temp_fuss_15_25 = 0,

b_temp_rad_u0_5= 0,
b_temp_rad_5_15 = 0,
b_temp_rad_15_25 = 0,

b_temp_auto_u0_5 = 0,
b_temp_auto_5_15 = 0,
b_temp_auto_15_25= 0,

b_temp_mitfahr_u0_5 = 0,
b_temp_mitfahr_5_15 = 0,
b_temp_mitfahr_15_25 = 0,

b_temp_oev_u0_5= 0,
b_temp_oev_5_15 = 0,
b_temp_oev_15_25 = 0)


### Vector with names (in quotes) of parameters to be kept fixed at their starting value in apollo_beta, use apollo_beta_fixed = c() if none
apollo_fixed = c("asc_fuss", "b_temp_fuss_u0_5", "b_temp_rad_u0_5", "b_temp_auto_u0_5", "b_temp_mitfahr_u0_5", "b_temp_oev_u0_5"
)


# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #

apollo_inputs = apollo_validateInputs()

# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #

apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){

### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))

### Create list of probabilities P
P = list()

### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[['fuss']] = asc_fuss + b_temp_fuss_u0_5 * (KAT_TEMP_NEU == 1) + b_temp_fuss_5_15 * (KAT_TEMP_NEU == 2) + b_temp_fuss_15_25
(KAT_TEMP_NEU == 3)


V[['rad']] = asc_rad + b_temp_rad_u0_5 * (KAT_TEMP_NEU == 1) + b_temp_rad_5_15 * (KAT_TEMP_NEU== 2) + b_temp_rad_15_25 * (KAT_TEMP_NEU== 3)

V[['auto']] = asc_auto+ b_temp_auto_u0_5 * (KAT_TEMP_NEU== 1) + b_temp_auto_5_15 * (KAT_TEMP_NEU == 2) + b_temp_auto_15_25 * (KAT_TEMP_NEU == 3)#


V[['mitfahr']] = asc_mitfahr + b_temp_mitfahr_u0_5 * (KAT_TEMP_NEU == 1) + b_temp_mitfahr_5_15 * (KAT_TEMP_NEU== 2)+ b_temp_mitfahr_15_25 * (KAT_TEMP_NEU == 3)

V[['oev']] = asc_oev + b_temp_oev_u0_5 * (KAT_TEMP_NEU == 1) + b_temp_oev_5_15 * (KAT_TEMP_NEU == 2) + b_temp_oev_15_25 * (KAT_TEMP_NEU == 3)

# ################################################################# #
#### ANALYSIS OF CHOICES ####
# ################################################################# #


choiceAnalysis_settings <- list(
alternatives = c(fuss=1, rad =2, auto=4, mitfahr=5, oev=6),
avail =list(fuss =av_fuss, rad= av_rad, auto=av_auto, mitfahr = av_mitfahr, oev = av_oev),
choiceVar = choice,
V = V
)


### Compute probabilities using MNL model
P[['model']] = apollo_mnl(choiceAnalysis_settings, functionality)

### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)

### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}

# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #


These are the results I get:
Model name : Nutzen
Model description : Simple MNL model on mode choice RP data
Model run at : 2022-11-12 13:47:26
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 1984
Number of rows in database : 100000
Number of modelled outcomes : 1e+05

Number of cores used : 1
Model without mixing

LL(start) : -151142.4
LL at equal shares, LL(0) : -151142.4
LL at observed shares, LL(C) : -122710.1
LL(final) : -122568.6
Rho-squared vs equal shares : 0.1891
Adj.Rho-squared vs equal shares : 0.189
Rho-squared vs observed shares : 0.0012
Adj.Rho-squared vs observed shares : 0.001
AIC : 245165.2
BIC : 245298.4

Estimated parameters : 14
Time taken (hh:mm:ss) : 00:01:7.63
pre-estimation : 00:00:10.41
estimation : 00:00:18.42
post-estimation : 00:00:38.8
Iterations : 24
Min abs eigenvalue of Hessian : 4e-06
Some eigenvalues of Hessian are positive, indicating potential problems!

Unconstrained optimisation.

These outputs have had the scaling used in estimation applied to them.
Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
asc_fuss 0.000000 NA NA NA NA
asc_rad -0.936449 0.04768 -19.64 0.10387 -9.01521
asc_auto 1.331313 0.03150 42.26 0.07231 18.41020
asc_mitfahr -0.389863 0.03694 -10.55 0.07206 -5.41011
asc_oev -0.728414 0.04114 -17.71 0.08340 -8.73384
b_temp_fuss_u0_5 0.000000 NA NA NA NA
b_temp_fuss_5_15 0.065989 NaN NaN 0.35766 0.18450
b_temp_fuss_15_25 0.004563 NaN NaN 0.22437 0.02034
b_temp_rad_u0_5 0.000000 NA NA NA NA
b_temp_rad_5_15 0.333230 NaN NaN 0.41623 0.80059
b_temp_rad_15_25 0.585298 NaN NaN 0.14782 3.95951
b_temp_auto_u0_5 0.000000 NA NA NA NA
b_temp_auto_5_15 -0.104662 NaN NaN 0.28693 -0.36476
b_temp_auto_15_25 -0.153079 NaN NaN NaN NaN
b_temp_mitfahr_u0_5 0.000000 NA NA NA NA
b_temp_mitfahr_5_15 -0.048284 NaN NaN 0.42641 -0.11323
b_temp_mitfahr_15_25 -0.076378 NaN NaN 0.09833 -0.77679
b_temp_oev_u0_5 0.000000 NA NA NA NA
b_temp_oev_5_15 -0.246271 NaN NaN 0.25006 -0.98486
b_temp_oev_15_25 -0.360404 NaN NaN 0.13970 -2.57975


Thank you very much in advance!
Pia

Pia

your model is overspecified. If you use a full set of alternative specific constants, then you need to normalise one to zero, as you do, but it also means that when you add interactions, they can only be added to J-1 of the alternatives as only differences in utility matter

Stephane

Hey Stephane,

thank you very much for your reply!
It works when I set all interactions for one alternative to zero.

Is it then still necassary, as I did in the example, to set one interaction for each alternative to zero too?


Pia

Pia

if your covariates are categorical, then you need that normalisation too, if they are continuous, then you don't

Stephane