Multinomial Logit Model

[firat85]

Dear all,

I conducted a pre survey for my dissertation with a sample size of 60 respondents and 8 choice sets faced by each respondent. I ran a MNL model suggested by many as the beginning point of analyses. I selected alternative 3 (opt-out) as base outcome for the estimation. The stata output is as belows. So my questions are:

1-) Is it ok that I include attributes as regressors in MNL model? I ask this because I think there is a bit confusion about this issue. Some sources say that MNL model treats the choice behaviour as a function of individual characteristics rather than attributes. However, I came across many papers including also attributes in MNL model. Another thing is how would one have had the prior knowledge about the coefficients of attributes for efficient designs without including them to the MNL model? Therefore, I included them to the model.

2-) Stata estimates the MNL model by determining one of the alternatives as base outcome (in my case alternative 3, opt out). Many coefficients are statistically significant, especially in alternative 2. So can I use these coefficients as prior knowledge in efficient design? Should I include the coefficients to efficienct design even they are statistically insignificant or should I set them to default value as zero?

3-) I have an ASC variable which is coded as "1" for alternatives 1 and 2 and "0" for opt-out alternative. However I still have confusions about the exact role of this variable. What does it really say and should it be included in the analyses? How should the negative and significant coefficient of ASC be interpreted? The mlogit command estimates the ASC coefficient, however, the cmclogit command omits it whereas mixlogit estimates. So what kind of strategy should I follow in this case?

Thank you very much for your answers.

mlogit choice_1 asc plastic glass paper metal freq2 freq3 coll2 time2 comp

Iteration 0: log likelihood = -1052.7335
Iteration 1: log likelihood = -993.09316
Iteration 2: log likelihood = -992.39882
Iteration 3: log likelihood = -992.39753
Iteration 4: log likelihood = -992.39753

Multinomial logistic regression Number of obs = 984
LR chi2(20) = 120.67
Prob > chi2 = 0.0000
Log likelihood = -992.39753 Pseudo R2 = 0.0573


choice_1 Coef. Std. Err. z P>z [95% Conf. Interval]

1
asc -.9777004 .4707047 2.08 0.038 -1.900265 -.0551361
plastic .340762 .3782381 0.90 0.368 -.400571 1.082095
glass .0109795 .4060645 0.03 0.978 -.7848924 .8068514
paper -.0625743 .3386146 0.18 0.853 -.7262468 .6010982
metal -.1083251 .3772892 0.29 0.774 -.8477983 .6311481
freq2 -1.601202 .2923679 5.48 0.000 -2.174232 -1.028171
freq3 -1.089138 .334265 3.26 0.001 -1.744285 -.4339904
coll2 2.55184 .3155387 8.09 0.000 1.933395 3.170284
time2 .3378673 .2091016 1.62 0.106 -.0719644 .747699
comp .0317696 .0092905 3.42 0.001 .0135605 .0499787
_cons -.4471378 .1320645 3.39 0.001 -.7059794 -.1882962

2
asc -.0706359 .4240027 0.17 0.868 -.901666 .7603942
plastic -.4729518 .3672153 1.29 0.198 -1.192681 .2467769
glass -.517307 .3720787 1.39 0.164 -1.246568 .2119538
paper -.616693 .3095361 1.99 0.046 -1.223373 -.0100135
metal -.8127053 .3580536 2.27 0.023 -1.514477 -.1109331
freq2 -.9001698 .2608429 3.45 0.001 -1.411412 -.3889272
freq3 -.885517 .3193243 2.77 0.006 -1.511381 -.2596528
coll2 1.744638 .2960343 5.89 0.000 1.164422 2.324855
time2 .2102194 .2055108 1.02 0.306 -.1925743 .6130132
comp .021949 .0088901 2.47 0.014 .0045246 .0393733
_cons -.5245245 .1352663 3.88 0.000 -.7896416 -.2594074

3 (base outcome)

[Michiel Bliemer]

1. Very good question. McFadden (1973) introduced the terms "multinomial logit", there only socio-demographics are included, and "conditional logit" where only attributes are included. So the correct terminology is actually "conditional logit". However, most people refer to the multinomial logit model when they actually mean the conditional logit model. And most people actually use both attributes and socio-demographics in their utility fuctions. Multinomial logit model has become the default term in the literature, even though it is different from what McFadden originally defined. So YES please use attributes in your utility function.

2. You can also use parameters that are not statistically significant as priors for experimental design, the standard error indicates the unreliability and this is information you can use when optimising your design.

3. I do not know the Stata estimation commands, so this is a question for the Stata forum. I am not sure what model it estimates, since in MNL models there is no need to use a reference alternative. You need to decide whether your data is unlabelled (option A or Option B) or labelled (Surgery or Radiation therapy). If labelled then you can estimate separate parameters for the two alternatives (as you have below) but if it is unlabelled then both need to have the same parameters. It can also be a combination of the two, for example only an alternative-specific constant while the other coefficients are generic. Given that both alternatives have the same attributes, estimating generic coefficients for the attributes may be logical.

It looks like you are using dummy or effects coding for an attribute material[plastic,glass,paper,metal,...] and an attribute frequency[freq1,freq2,freq3] etc. When using dummy of effects coding it becomes more difficult to interpret the ASCs since the reference levels are confounded with the constants. If you would estimate generic parameters across alternatives 1 and 2 then the ASCs would reflect the relative preference of alternative 1 over alternative 2 if the alternatives are labelled, and it also expresses the relative utility of choosing (alt1 and alt2) and not choosing (alt3).

Michiel

[firat85]

Thank you for your answer Mr. Bliemer. Here is my design:

MNL efficiency measures

D error 0.165605
A error 0.609372
B estimate 82.946619
S estimate 53.270587

Prior freq(d0) freq(d1) type(d0) type(d1) type(d2) type(d3) coll(d0) time(d0) comp
Fixed prior value -0.45 -0.44 0 0 -0.31 -0.4 0.87 0.1 0.011
Sp estimates 16.139274 10.838352 Undefined Undefined 35.115258 21.582228 2.486069 53.270587 15.015265
Sp t-ratios 0.487881 0.595353 0 0 0.330756 0.421898 1.243081 0.268542 0.505813

[Michiel Bliemer]

Looks fine to me.