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ASCs in RRM example

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cybey
Posts: 60
Joined: 26 Apr 2020, 19:38

ASCs in RRM example

Post by cybey »

I've just tried to specify my first RRM model within Apollo and everything seems fine, except for the alternative-specific constants (ASCs). The specification is based on the RRM example on the Apollo homepage. The following statement can be found in the manual on page 51:
For the alternative specific constants (ASCs), we adopt the convention of entering them directly into the regret function rather than using Equation 5.13.
I did the same. The ASCs are intended to capture left-right effects. My results look like this:

Code: Select all

                           Estimate        s.e.   t.rat.(0)  p(1-sided)    Rob.s.e. Rob.t.rat.(0)  p(1-sided)
b_asc_1                    0.033875    0.034216      0.9900     0.16108    0.034215        0.9901    0.161074
b_asc_2                   -0.147582    0.032767     -4.5039   3.336e-06    0.034023       -4.3377   7.199e-06
b_asc_3                    0.000000          NA          NA          NA          NA            NA          NA
b_Frequency                0.007539    0.006017      1.2531     0.10509    0.008125        0.9279    0.176733
b_Duration                -0.053585    0.010776     -4.9727   3.301e-07    0.013338       -4.0175   2.941e-05
b_Temperature_22           0.000000          NA          NA          NA          NA            NA          NA
b_Temperature_24          -0.026134    0.013532     -1.9313     0.02673    0.015229       -1.7161    0.043073
b_Temperature_26          -0.223475    0.015105    -14.7944     0.00000    0.021716      -10.2909    0.000000
b_Temperature_27          -0.334757    0.016328    -20.5021     0.00000    0.024956      -13.4141    0.000000
b_Compensation_Company     0.000000          NA          NA          NA          NA            NA          NA
b_Compensation_IceDrink    0.056305    0.014259      3.9487   3.928e-05    0.019549        2.8802    0.001987
b_Compensation_Donation   -0.020718    0.014813     -1.3986     0.08096    0.021257       -0.9746    0.164871
b_Warning_None             0.000000          NA          NA          NA          NA            NA          NA
b_Warning_15min            0.073235    0.014498      5.0515   2.192e-07    0.014889        4.9188   4.354e-07
b_Warning_DayBefore        0.105387    0.014232      7.4047   6.573e-14    0.015260        6.9063   2.488e-12
In contrast, the MNL model:

Code: Select all

                           Estimate        s.e.   t.rat.(0)  p(1-sided)    Rob.s.e. Rob.t.rat.(0)  p(1-sided)
b_asc_1                    -0.03381    0.034225     -0.9880     0.16159     0.03423       -0.9878    0.161627
b_asc_2                     0.14764    0.032775      4.5046   3.325e-06     0.03405        4.3364   7.241e-06
b_asc_3                     0.00000          NA          NA          NA          NA            NA          NA
b_Frequency                 0.01139    0.009028      1.2617     0.10352     0.01220        0.9340    0.175157
b_Duration                 -0.08034    0.016205     -4.9579   3.564e-07     0.02004       -4.0088   3.052e-05
b_Temperature_22            0.00000          NA          NA          NA          NA            NA          NA
b_Temperature_24           -0.07711    0.039577     -1.9482     0.02569     0.04455       -1.7306    0.041762
b_Temperature_26           -0.64854    0.042497    -15.2609     0.00000     0.06093      -10.6449    0.000000
b_Temperature_27           -0.96542    0.045042    -21.4335     0.00000     0.06865      -14.0621    0.000000
b_Compensation_Company      0.00000          NA          NA          NA          NA            NA          NA
b_Compensation_IceDrink     0.14167    0.035958      3.9399   4.077e-05     0.04934        2.8715    0.002043
b_Compensation_Donation    -0.05158    0.037044     -1.3925     0.08189     0.05318       -0.9700    0.166032
b_Warning_None              0.00000          NA          NA          NA          NA            NA          NA
b_Warning_15min             0.18521    0.036927      5.0157   2.642e-07     0.03792        4.8847   5.179e-07
b_Warning_DayBefore         0.26722    0.036412      7.3389   1.077e-13     0.03905        6.8427   3.886e-12
As you can see, the estimates in the RRM model are as expected: Same signs and relative orders of magnitude, but lower absolute levels. The ASCs also look good, only the sign is "wrong".

Since the ASCs do not enter equation 5.13, shouldn't the sign be reversed in the model specficiation? Otherwise, according to my understanding, one would have to consider in the interpretation that the ASCs are regrets, i.e., a negative sign is positive and vice versa.
stephanehess
Site Admin
Posts: 974
Joined: 24 Apr 2020, 16:29

Re: ASCs in RRM example

Post by stephanehess »

Hi Nico

the manual wasn't clear. Your signs make sense.

What the manual should say (and will from the next version onwards) is:

"For the alternative specific constants (ASCs), we adopt the convention of entering them directly into the regret function rather than using them in the comparison across alternatives - i.e. they would appear outside the sum across alternatives in Equation 13"

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk
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