ApolloChoiceModelling forum

Dear prof Hess & Dr Palma

We have estimated a LC model including interactions for sex and age in the class-allocation part of the model. The model runs well, but having the results we are somewhat uncertain about how to interpret the estimated parameters (gamma_sex, gamma_age)? Are these parameters to be treated like the deltas, and be transformed into class-allocations? Or can the estimated parameters in the model output (see below) be interpreted directly? In the latter case, how do we interpret positive parameters that are above 1, between 0-1, and negative parameters? If they have to be transformed, could you inform us where to find the code for the correct transformation?

Thank you for any help in this matter.

BR, Margrethe

Here is the full LC-model. Class B is used for normalisation:

Model run by snf52282 using Apollo 0.2.8 on R 4.2.0 for Windows.
www.ApolloChoiceModelling.com

Model name : LC_mining_6c_socio
Model description : Simple LC model on mining data with 6 classes - preference space
Model run at : 2023-02-24 16:16:25
Estimation method : bfgs
Model diagnosis : successful convergence
Number of individuals : 874
Number of rows in database : 6992
Number of modelled outcomes : 48944
1 : 6992
2 : 6992
3 : 6992
4 : 6992
5 : 6992
6 : 6992
model : 6992

Number of cores used : 3
Model without mixing

LL(start) : -7855.36
LL (whole model) at equal shares, LL(0) : -7681.5
LL (whole model) at observed shares, LL(C) : -7624.37
LL(final, whole model) : -4975.16
Rho-squared vs equal shares : 0.3523
Adj.Rho-squared vs equal shares : 0.3466
Rho-squared vs observed shares : 0.3475
Adj.Rho-squared vs observed shares : 0.3417
AIC : 10038.33
BIC : 10339.84

LL(0,component_1) : -7681.5
LL(final,component_1) : -16847.53
LL(0,component_2) : -7681.5
LL(final,component_2) : -18703.26
LL(0,component_3) : -7681.5
LL(final,component_3) : -18865.03
LL(0,component_4) : -7681.5
LL(final,component_4) : -10004.35
LL(0,component_5) : -7681.5
LL(final,component_5) : -8657.48
LL(0,component_6) : -7681.5
LL(final,component_6) : -37913.01

Estimated parameters : 44
Time taken (hh:mm:ss) : 00:09:39.36
pre-estimation : 00:00:26.48
estimation : 00:05:20.05
post-estimation : 00:03:52.84
Iterations : 121
Min abs eigenvalue of Hessian : 0.510339

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_a -5.462285 0.872569 -6.2600 0.912629 -5.98522
asc_b 4.114880 0.819783 5.0195 0.849996 4.84106
asc_c -3.187890 1.290441 -2.4704 1.573985 -2.02536
asc_d -2.012112 0.261743 -7.6874 0.495902 -4.05748
asc_e -0.681651 0.358088 -1.9036 0.473365 -1.44001
asc_f 0.000000 NA NA NA NA
seabed_a -0.143539 0.044055 -3.2582 0.054137 -2.65143
seabed_b -0.031247 0.036740 -0.8505 0.032915 -0.94935
seabed_c -0.181305 0.023772 -7.6267 0.037356 -4.85349
seabed_d -0.029162 0.007426 -3.9268 0.007238 -4.02885
seabed_e 0.005944 0.016016 0.3711 0.015766 0.37702
seabed_f -1.173473 0.639191 -1.8359 0.899571 -1.30448
salmon_a -0.051310 0.051338 -0.9995 0.041933 -1.22362
salmon_b -0.049509 0.071756 -0.6900 0.079679 -0.62135
salmon_c 0.043669 0.036177 1.2071 0.031168 1.40109
salmon_d -0.070358 0.014830 -4.7443 0.017158 -4.10064
salmon_e -0.021930 0.029689 -0.7387 0.028090 -0.78072
salmon_f -0.370813 0.099677 -3.7201 0.139316 -2.66166
job_a 0.073576 0.026008 2.8290 0.034676 2.12183
job_b 0.003472 0.015182 0.2287 0.015827 0.21936
job_c 0.044455 0.012302 3.6137 0.011965 3.71556
job_d -0.007769 0.003965 -1.9595 0.004399 -1.76621
job_e 0.008962 0.006977 1.2844 0.006823 1.31336
job_f 0.329620 0.155772 2.1160 0.213414 1.54451
cost_a -0.001570 2.9428e-04 -5.3337 3.0156e-04 -5.20491
cost_b -1.5508e-04 2.3052e-04 -0.6727 2.7289e-04 -0.56827
cost_c 6.2605e-04 1.5364e-04 4.0747 1.3058e-04 4.79442
cost_d -3.3901e-04 6.519e-05 -5.2007 1.0014e-04 -3.38536
cost_e -6.4725e-04 1.4222e-04 -4.5511 2.8430e-04 -2.27660
cost_f -0.007151 0.003452 -2.0714 0.004942 -1.44699
delta_a -0.649325 0.615022 -1.0558 0.619977 -1.04734
gamma_sex_a 1.095391 0.276718 3.9585 0.290902 3.76549
gamma_age_a -0.025720 0.008405 -3.0600 0.008696 -2.95771
delta_b 0.000000 NA NA NA NA
gamma_sex_b 0.000000 NA NA NA NA
gamma_age_b 0.000000 NA NA NA NA
delta_c -1.721741 0.627135 -2.7454 0.660136 -2.60816
gamma_sex_c 1.267914 0.269938 4.6971 0.283918 4.46578
gamma_age_c -0.006909 0.007907 -0.8738 0.007800 -0.88568
delta_d -0.333364 0.484720 -0.6877 0.484250 -0.68841
gamma_sex_d 1.162662 0.221214 5.2558 0.223418 5.20398
gamma_age_d -0.014913 0.006471 -2.3045 0.006467 -2.30606
delta_e -1.143919 0.652040 -1.7544 0.672726 -1.70043
gamma_sex_e 0.734089 0.288348 2.5458 0.316989 2.31582
gamma_age_e -0.004824 0.008482 -0.5687 0.009210 -0.52373
delta_f 1.378297 1.276650 1.0796 1.766749 0.78013
gamma_sex_f -0.075044 0.628020 -0.1195 0.809995 -0.09265
gamma_age_f -0.069287 0.022134 -3.1303 0.031132 -2.22562


Summary of class allocation for model component :
Mean prob.
Class_1 0.13370
Class_2 0.20865
Class_3 0.14939
Class_4 0.34085
Class_5 0.13534
Class_6 0.03206

Margrethe

this is really more a general choice modelling question than an Apollo question, and you can find details in papers on latent class, or even in my book chapter at http://www.stephanehess.me.uk/papers/bo ... s_2014.pdf

The gamma parameters are part of your class allocation model. For example, the fact that gamma_sex_a is positive means that for someone with that covariate, the likelihood of class a is increased relative to your base class, which is class b (where the gammas are fixed to zero)

Hope this helps

Stephane

Yes, very helpful indeed!
Thank you.
will try to keep posts to the Forum strictly apollo-related!!
I am very happy that this forum exists.

BR,
Margrethe