Thank you for running this forum and helping out!
I am running a MDCEV model (no outside good) to estimate how contextual variables (seven environmental variables, all dummy variables) affect the way people allocate their time to four activities in a given environment. In my case, for the respondents these four activities were simply labelled with different names without any specific attributes. Respondents were asked to allocate a total fixed amount of time to the four activities based on the different environmental configurations given (to ensure independence of environmental variables, we have used a fractional design).
However, I got warning messages of “Singular Hessian, cannot calculate s.e.”, and “some eigenvalues of the Hessian are positive” with the following codes (here I set three alternative specific constants for the three of the four activities, the last one was set to be zero):
Code: Select all
### Clear memory
rm(list = ls())
### Load Apollo library
library(apollo)
### Initialise code
apollo_initialise()
### Set core controls
apollo_control = list(
modelName = "0000_MDCEV_2_attribute_only",
modelDescr = "MDCEV model on time use, gamma profile, no outside good",
indivID = "indivID",
outputDirectory = "output"
)
# ################################################################# #
#### LOAD DATA AND APPLY ANY TRANSFORMATIONS ####
# ################################################################# #
### Loading data from package
### if data is to be loaded from a file (e.g. called data.csv),
### the code would be: database = read.csv("data.csv",header=TRUE)
database <<- read.table("D:/spss_first/00_rmdcev/08_paneldata.csv", header=T, sep=",");
# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #
### Vector of parameters, including any that are kept fixed in estimation
apollo_beta = c(alpha_base = 0,
gamma_open = 1,
gamma_gostation = 1,
gamma_goshop = 1,
gamma_leave = 1,
delta_open = 0,
delta_gostation = 0,
delta_goshop = 0,
open_bdht = 0,
open_otdi = 0,
open_bech = 0,
open_bk = 0,
open_arcd = 0,
open_gras = 0,
open_tree = 0,
gostation_bdht = 0,
gostation_otdi = 0,
gostation_bech = 0,
gostation_bk = 0,
gostation_arcd = 0,
gostation_gras = 0,
gostation_tree = 0,
goshop_bdht = 0,
goshop_otdi = 0,
goshop_bech = 0,
goshop_bk = 0,
goshop_arcd = 0,
goshop_gras = 0,
goshop_tree = 0,
sig = 1)
### 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("sig")
# ################################################################# #
#### 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()
### Define individual alternatives
alternatives = c("open",
"gostation",
"goshop",
"leave")
### Define availabilities
avail = list(open = 1,
gostation = 1,
goshop = 1,
leave = 1)
### Define continuous consumption for individual alternatives
continuousChoice = list(open = open,
gostation = gostation,
goshop = goshop,
leave = leave)
### Define utilities for individual alternatives
V = list()
V[["open"]] = delta_open + open_bdht * bd_ht + open_otdi*out_di + open_bech *bench +open_bk *bike_pk + open_arcd *arcade + open_gras * grass + open_tree * tree
V[["gostation"]] = delta_gostation + gostation_bdht * bd_ht + gostation_otdi*out_di + gostation_bech *bench +gostation_bk *bike_pk + gostation_arcd *arcade + gostation_gras * grass + gostation_tree * tree
V[["goshop"]] = delta_goshop + goshop_bdht * bd_ht + goshop_otdi*out_di + goshop_bech *bench +goshop_bk *bike_pk + goshop_arcd *arcade + goshop_gras * grass + goshop_tree * tree
V[["leave"]] = 0
### Define alpha parameters
alpha = list(open = 1 /(1 + exp(-alpha_base)),
gostation = 1 /(1 + exp(-alpha_base)),
goshop = 1 /(1 + exp(-alpha_base)),
leave = 1 /(1 + exp(-alpha_base)))
### Define gamma parameters
gamma = list(open = gamma_open,
gostation = gamma_gostation,
goshop = gamma_goshop,
leave = gamma_leave)
### Define costs for individual alternatives
cost = list(open = 1,
gostation = 1,
goshop = 1,
leave = 1)
### Define settings for MDCEV model
mdcev_settings <- list(alternatives = alternatives,
avail = avail,
continuousChoice = continuousChoice,
utilities = V,
alpha = alpha,
gamma = gamma,
sigma = sig,
cost = cost,
budget = 30)
### Compute probabilities using MDCEV model
P[["model"]] = apollo_mdcev(mdcev_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 ####
# ################################################################# #
model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs,estimate_settings=list(maxIterations=5000))
# ################################################################# #
#### MODEL OUTPUTS ####
# ################################################################# #
# ----------------------------------------------------------------- #
#---- FORMATTED OUTPUT (TO SCREEN) ----
# ----------------------------------------------------------------- #
apollo_modelOutput(model, modelOutput_settings = list(printPVal=2)) # for two sided t-test
Code: Select all
***** Relative function convergence *****
Additional convergence test using scaled estimation. Parameters will be scaled by their current
estimates and additional iterations will be performed.
BGW is using FD derivatives for model Jacobian. (Caller did not provide derivatives.)
Iterates will be appended to:
output/0000_MDCEV_2_attribute_only_iterations.csv it nf F RELDF PRELDF RELDX MODEL stppar
0 1 5.457461023e+03
***** Singular convergence *****
The estimation of the scaled model failed, and the unscaled version will be returned instead.
Final LL: -5457.461
Calculating log-likelihood at equal shares (LL(0)) for applicable models...
Calculating log-likelihood at observed shares from estimation data (LL(c)) for applicable
models...
Calculating LL of each model component...
Computing covariance matrix using numerical methods (numDeriv).
0%....25%....50%....75%....100%
WARNING: Singular Hessian, cannot calculate s.e.
Hessian written to output/0000_MDCEV_2_attribute_only_hessian.csv
WARNING: Some eigenvalues of the Hessian are positive, indicating convergence to a saddle point!
Computing score matrix...
Your model was estimated using the BGW algorithm. Please acknowledge this by citing Bunch et al.
(1993) - DOI 10.1145/151271.151279
Model name : 0000_MDCEV_2_attribute_only
Model description : MDCEV model on time use, gamma profile, no outside good
Model run at : 2023-11-13 23:16:04.683781
Estimation method : bgw
Model diagnosis : Relative function convergence
Optimisation diagnosis : Saddle point found
hessian properties : Some eigenvalues are positive and others negative
maximum eigenvalue : 0
reciprocal of condition number : not calculated (Hessian is not negative definite)
Number of individuals : 192
Number of rows in database : 768
Number of modelled outcomes : 768
Number of cores used : 1
Model without mixing
LL(start) : -6141.66
LL at equal shares, LL(0) : NA
LL at observed shares, LL(C) : NA
LL(final) : -5457.46
Rho-squared vs equal shares : Not applicable
Adj.Rho-squared vs equal shares : Not applicable
Rho-squared vs observed shares : Not applicable
Adj.Rho-squared vs observed shares : Not applicable
AIC : 10972.92
BIC : 11107.59
Estimated parameters : 29
Time taken (hh:mm:ss) : 00:00:8.37
pre-estimation : 00:00:0.3
estimation : 00:00:2.35
post-estimation : 00:00:5.72
Iterations : 32
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) p(2-sided) Rob.s.e. Rob.t.rat.(0) p(2-sided)
alpha_base -40.273143 NA NA NA NA NA NA
gamma_open 3.463235 NA NA NA NA NA NA
gamma_gostation 4.147158 NA NA NA NA NA NA
gamma_goshop 4.037829 NA NA NA NA NA NA
gamma_leave 7.607748 NA NA NA NA NA NA
delta_open 0.523676 NA NA NA NA NA NA
delta_gostation 0.844225 NA NA NA NA NA NA
delta_goshop 0.192511 NA NA NA NA NA NA
open_bdht -0.596792 NA NA NA NA NA NA
open_otdi 0.725264 NA NA NA NA NA NA
open_bech 0.595906 NA NA NA NA NA NA
open_bk -0.218788 NA NA NA NA NA NA
open_arcd 0.275018 NA NA NA NA NA NA
open_gras 0.823620 NA NA NA NA NA NA
open_tree 0.715244 NA NA NA NA NA NA
gostation_bdht -0.093390 NA NA NA NA NA NA
gostation_otdi -0.095259 NA NA NA NA NA NA
gostation_bech -0.403409 NA NA NA NA NA NA
gostation_bk -0.213423 NA NA NA NA NA NA
gostation_arcd 0.004776 NA NA NA NA NA NA
gostation_gras 0.232169 NA NA NA NA NA NA
gostation_tree 0.061953 NA NA NA NA NA NA
goshop_bdht -0.372858 NA NA NA NA NA NA
goshop_otdi -0.182234 NA NA NA NA NA NA
goshop_bech -0.195470 NA NA NA NA NA NA
goshop_bk -0.078527 NA NA NA NA NA NA
goshop_arcd 0.247201 NA NA NA NA NA NA
goshop_gras 0.544868 NA NA NA NA NA NA
goshop_tree 0.401657 NA NA NA NA NA NA
sig 1.000000 NA NA NA NA NA NA
Code: Select all
### Define utilities for individual alternatives
V = list()
V[["open"]] = const + open_bdht * bd_ht + open_otdi*out_di + open_bech *bench +open_bk *bike_pk + open_arcd *arcade + open_gras * grass + open_tree * tree
V[["gostation"]] = const + gostation_bdht * bd_ht + gostation_otdi*out_di + gostation_bech *bench +gostation_bk *bike_pk + gostation_arcd *arcade + gostation_gras * grass + gostation_tree * tree
V[["goshop"]] = const + goshop_bdht * bd_ht + goshop_otdi*out_di + goshop_bech *bench +goshop_bk *bike_pk + goshop_arcd *arcade + goshop_gras * grass + goshop_tree * tree
V[["leave"]] = 0
Code: Select all
Model name : 0000_MDCEV_2_attribute_only
Model description : MDCEV model on time use, gamma profile, no outside good
Model run at : 2023-11-13 23:49:32.163323
Estimation method : bgw
Model diagnosis : Relative function convergence
Optimisation diagnosis : Maximum found
hessian properties : Negative definite
maximum eigenvalue : -1e-06
reciprocal of condition number : 7.26867e-10
Number of individuals : 192
Number of rows in database : 768
Number of modelled outcomes : 768
Number of cores used : 1
Model without mixing
LL(start) : -6141.66
LL at equal shares, LL(0) : NA
LL at observed shares, LL(C) : NA
LL(final) : -5462.59
Rho-squared vs equal shares : Not applicable
Adj.Rho-squared vs equal shares : Not applicable
Rho-squared vs observed shares : Not applicable
Adj.Rho-squared vs observed shares : Not applicable
AIC : 10979.19
BIC : 11104.57
Estimated parameters : 27
Time taken (hh:mm:ss) : 00:00:7.72
pre-estimation : 00:00:0.28
estimation : 00:00:2.46
post-estimation : 00:00:4.98
Iterations : 33
Unconstrained optimisation.
Estimates:
Estimate s.e. t.rat.(0) p(2-sided) Rob.s.e.
alpha_base -19.78779 1114.0585 -0.01776 0.985829 0.07038
gamma_open 3.45389 0.3919 8.81208 0.000000 0.37897
gamma_gostation 4.42962 0.3760 11.77949 0.000000 0.39609
gamma_goshop 3.85703 0.3317 11.62947 0.000000 0.32124
gamma_leave 7.59876 0.8050 9.43901 0.000000 1.03905
const 0.52765 0.1706 3.09328 0.001980 0.19126
open_bdht -0.59594 0.1338 -4.45307 8.465e-06 0.12894
...
Thank you in advance!
Best regards
Wendy