cmxtmixlogit - expected probabilities and sign of margin effects

[Fernando Romero]

First of all, I would like to say that it is my first thread in Statalist. I apologize for any mistakes I may make.

I am using cmxtmixlogit in Stata 16.0 on Windows 7 to fit a mixed logit model to choice data in which decisions-makers make repeated choices. I have

The coefficient of the alternative-specific variable is negative, but the marginal effects are in the opposite direccion. Both figures are significant. I have read before in other threads about similar problems but it was not clear to me (

https://www.statalist.org/forums/forum/general-stata-discussion/general/1427065-negative-interaction-coefficient-but-positive-marginal-effects

,

https://www.statalist.org/forums/forum/general-stata-discussion/general/1329201-marginal-effects-significance-vs-original-model-effects-significance

,

https://www.statalist.org/forums/forum/general-stata-discussion/general/1362415-interpretation-of-marginal-effects-of-multinomial-logit

)

Here is an example of my data:

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* Example generated by -dataex-. To install: ssc install dataex
clear
input long(ID_orden ID_VEH) double choice long Alternativa str12 ID_VEHICULO long(Tiempos_mostrados Frec_total_bis_fact Hasta_Bahia Noches_fact_1 Tipo_dia_2h_2 Fecha_2h group_PMV_5)
21036 1 1 1 "A//4JrVAStU=" 35 1 2 27 1 1 1
21036 1 0 2 "A//4JrVAStU=" 57 1 2 27 1 1 1
54760 2 1 1 "A/+cM7Qaq80=" 36 1 1 27 3 1 1
54760 2 0 2 "A/+cM7Qaq80=" 56 1 1 27 3 1 1
50259 3 1 1 "a/+OR+K+1M8=" 34 1 2 15 2 7 1
50259 3 0 2 "a/+OR+K+1M8=" 54 1 2 15 2 7 1
73314 4 1 1 "a/+qCASnMoM=" 33 3 2 27 3 7 1
86172 4 1 1 "a/+qCASnMoM=" 34 3 1 27 1 6 1
73314 4 0 2 "a/+qCASnMoM=" 54 3 2 27 3 7 1
86172 4 0 2 "a/+qCASnMoM=" 55 3 1 27 1 6 1
end
label values Alternativa Alternativa
label def Alternativa 1 "AP-4", modify
label def Alternativa 2 "N-IV", modify
label values Frec_total_bis_fact Frec_total_bis_fact
label def Frec_total_bis_fact 1 "1", modify
label def Frec_total_bis_fact 3 "3", modify
label values Hasta_Bahia Hasta_Bahia
label def Hasta_Bahia 1 "Hasta Jerez", modify
label def Hasta_Bahia 2 "Hasta Bahia", modify
label values Noches_fact_1 Noches_fact_1
label def Noches_fact_1 15 "14", modify
label def Noches_fact_1 27 "No consta", modify
label values Tipo_dia_2h_2 Tipo_dia_2h_2
label def Tipo_dia_2h_2 1 "Weekday", modify
label def Tipo_dia_2h_2 2 "Friday", modify
label def Tipo_dia_2h_2 3 "Saturday", modify
label values Fecha_2h Fecha_2h
label def Fecha_2h 1 "12:00:00", modify
label def Fecha_2h 6 "14:00:00", modify
label def Fecha_2h 7 "16:00:00", modify
label values group_PMV_5 group_PMV_5
label def group_PMV_5 1 "EMPTY", modify

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Observations are drivers choosing between two roads. Many drivers choose more than once. I have repeated observations for many drivers.

ID_VEH identifies the vehicle, ID_orden identifies the number of the recurrence, and Alternativa identifies the alternative chosen by the driver.
The alternative-specific variable is Tiempos_motrados that it is travel times estimates of both road alternatives displayed to drivers.


My code is as belows:

cmset ID_VEH ID_orden Alternativa

And the result is:
cmset ID_VEH ID_orden Alternativa
panel data: panels ID_VEH and time ID_orden
note: case identifier _caseid generated from ID_VEH ID_orden
note: panel by alternatives identifier _panelaltid generated from ID_VEH Alternativa caseid variable: _caseid
alternatives variable: Alternativa
panel by alternatives variable: _panelaltid (unbalanced)
time variable: ID_orden, 1 to 104307, but with gaps
delta: 1 unit


Then:

cmxtmixlogit choice, random(Tiempos_mostrados) casevars(ib(first).Hasta_Bahia ib(first).Frec_total_bis_fact ib(first).Noches_fact_1 ib(first).Tipo_dia_2h_2 ib(first).Fecha_2h ib(first).group_PMV_5) intpoints(2500)

margins, dydx(Tiempos_mostrados) alternative(AP-4)

margins, at(Tiempos_mostrados=generate(Tiempos_mostrados)) at(Tiempos_mostrados=generate(Tiempos_mostrados+5)) at(Tiempos_mostrados=generate(Tiempos_mostrados+10)) at(Tiempos_mostrados=generate(Tiempos_mostrados+15)) at(Tiempos_mostrados=generate(Tiempos_mostrados-5)) at(Tiempos_mostrados=generate(Tiempos_mostrados-10)) at(Tiempos_mostrados=generate(Tiempos_mostrados-15)) alternative(AP-4)

As expected, the average coefficient of the travel time estimates is negative. This means that when the travel time shown for a road increases, the probability of choosing that alternative decreases. However, the marginal effect and the expected probabilities are significant and of opposite signs. So I do not know exactly what is the correct interpretation of the problem. Could you help me, please?