Implications of nrep(#) on mixlogit analysis

[Dannica Aquino]

Dear All,

I am analyzing discrete choice experiment data through the user-written command mixlogit. Below is the example of my dataset.

* Example generated by -dataex-. To install: ssc install dataex
clear
input int ID byte(Alternatives Choice Price Biodiversity Flood Forest Livelihood SEX AGE YRS_OF_SCHOOLING) double YRS_OF_RESIDENCY byte HH_Size double HH_INCOME
 1 1 1 0 1 1 1 1 0 55  4  5 6  4800
 1 2 0 1 3 2 2 2 0 55  4  5 6  4800
 1 3 0 5 2 3 1 1 0 55  4  5 6  4800
 2 1 1 0 1 1 1 1 0 55  4  5 6  4800
 2 2 0 2 1 2 3 3 0 55  4  5 6  4800
 2 3 0 4 1 3 2 2 0 55  4  5 6  4800
 3 1 1 0 1 1 1 1 0 55  4  5 6  4800
 3 2 0 3 2 2 2 1 0 55  4  5 6  4800
 3 3 0 1 2 2 1 3 0 55  4  5 6  4800
 4 1 1 0 1 1 1 1 0 55  4  5 6  4800
 4 2 0 1 3 3 2 3 0 55  4  5 6  4800
 4 3 0 5 1 2 1 1 0 55  4  5 6  4800
 5 1 1 0 1 1 1 1 0 55  4  5 6  4800
 5 2 0 5 3 1 3 3 0 55  4  5 6  4800
 5 3 0 3 2 3 1 2 0 55  4  5 6  4800
 6 1 1 0 1 1 1 1 0 55  4  5 6  4800
 6 2 0 5 1 2 2 1 0 55  4  5 6  4800
 6 3 0 3 2 1 3 2 0 55  4  5 6  4800
 7 1 1 0 1 1 1 1 0 55  4  5 6  4800
 7 2 0 4 3 3 3 2 0 55  4  5 6  4800
 7 3 0 3 1 1 2 3 0 55  4  5 6  4800
 8 1 0 0 1 1 1 1 1 39 12 20 3 14500
 8 2 1 1 3 2 2 2 1 39 12 20 3 14500
 8 3 0 5 2 3 1 1 1 39 12 20 3 14500
 9 1 0 0 1 1 1 1 1 39 12 20 3 14500
 9 2 1 2 1 2 3 3 1 39 12 20 3 14500
 9 3 0 4 1 3 2 2 1 39 12 20 3 14500
10 1 0 0 1 1 1 1 1 39 12 20 3 14500
10 2 0 3 2 2 2 1 1 39 12 20 3 14500
10 3 1 1 2 2 1 3 1 39 12 20 3 14500
11 1 0 0 1 1 1 1 1 39 12 20 3 14500
11 2 1 1 3 3 2 3 1 39 12 20 3 14500
11 3 0 5 1 2 1 1 1 39 12 20 3 14500
12 1 0 0 1 1 1 1 1 39 12 20 3 14500
12 2 0 5 3 1 3 3 1 39 12 20 3 14500
12 3 1 3 2 3 1 2 1 39 12 20 3 14500
13 1 0 0 1 1 1 1 1 39 12 20 3 14500
13 2 0 5 1 2 2 1 1 39 12 20 3 14500
13 3 1 3 2 1 3 2 1 39 12 20 3 14500
14 1 0 0 1 1 1 1 1 39 12 20 3 14500
14 2 0 4 3 3 3 2 1 39 12 20 3 14500
14 3 1 3 1 1 2 3 1 39 12 20 3 14500
15 1 1 0 1 1 1 1 1 43 14 30 3  4000
15 2 0 1 3 2 2 2 1 43 14 30 3  4000
15 3 0 5 2 3 1 1 1 43 14 30 3  4000
16 1 1 0 1 1 1 1 1 43 14 30 3  4000
16 2 0 2 1 2 3 3 1 43 14 30 3  4000
16 3 0 4 1 3 2 2 1 43 14 30 3  4000
17 1 1 0 1 1 1 1 1 43 14 30 3  4000
17 2 0 3 2 2 2 1 1 43 14 30 3  4000
17 3 0 1 2 2 1 3 1 43 14 30 3  4000
18 1 1 0 1 1 1 1 1 43 14 30 3  4000
18 2 0 1 3 3 2 3 1 43 14 30 3  4000
18 3 0 5 1 2 1 1 1 43 14 30 3  4000
19 1 1 0 1 1 1 1 1 43 14 30 3  4000
19 2 0 5 3 1 3 3 1 43 14 30 3  4000
19 3 0 3 2 3 1 2 1 43 14 30 3  4000
20 1 1 0 1 1 1 1 1 43 14 30 3  4000
20 2 0 5 1 2 2 1 1 43 14 30 3  4000
20 3 0 3 2 1 3 2 1 43 14 30 3  4000
21 1 1 0 1 1 1 1 1 43 14 30 3  4000
21 2 0 4 3 3 3 2 1 43 14 30 3  4000
21 3 0 3 1 1 2 3 1 43 14 30 3  4000
22 1 0 0 1 1 1 1 0 53  7 53 4 60000
22 2 1 1 3 2 2 2 0 53  7 53 4 60000
22 3 0 5 2 3 1 1 0 53  7 53 4 60000
23 1 0 0 1 1 1 1 0 53  7 53 4 60000
23 2 1 2 1 2 3 3 0 53  7 53 4 60000
23 3 0 4 1 3 2 2 0 53  7 53 4 60000
24 1 0 0 1 1 1 1 0 53  7 53 4 60000
24 2 0 3 2 2 2 1 0 53  7 53 4 60000
24 3 1 1 2 2 1 3 0 53  7 53 4 60000
25 1 0 0 1 1 1 1 0 53  7 53 4 60000
25 2 1 1 3 3 2 3 0 53  7 53 4 60000
25 3 0 5 1 2 1 1 0 53  7 53 4 60000
26 1 0 0 1 1 1 1 0 53  7 53 4 60000
26 2 0 5 3 1 3 3 0 53  7 53 4 60000
26 3 1 3 2 3 1 2 0 53  7 53 4 60000
27 1 0 0 1 1 1 1 0 53  7 53 4 60000
27 2 0 5 1 2 2 1 0 53  7 53 4 60000
27 3 1 3 2 1 3 2 0 53  7 53 4 60000
28 1 0 0 1 1 1 1 0 53  7 53 4 60000
28 2 0 4 3 3 3 2 0 53  7 53 4 60000
28 3 1 3 1 1 2 3 0 53  7 53 4 60000
29 1 0 0 1 1 1 1 0 78  2 50 5 20000
29 2 1 1 3 2 2 2 0 78  2 50 5 20000
29 3 0 5 2 3 1 1 0 78  2 50 5 20000
30 1 0 0 1 1 1 1 0 78  2 50 5 20000
30 2 1 2 1 2 3 3 0 78  2 50 5 20000
30 3 0 4 1 3 2 2 0 78  2 50 5 20000
end

I used the following codes and levels of nrep:

Model 1:

mixlogit Choice Price ALT2* ALT3*, group(ID) rand($random) nrep(30) difficult robust

No. of iterations: 8
Log likelihood: -2055.1528
Chi-square: 0.0000

Model 2:

mixlogit Choice Price ALT2* ALT3*, group(ID) rand($random) nrep(90) difficult robust

No. of iterations: 8
Log likelihood: -2054.7891
Chi-square: 0.0049


where:
Choice = dependent variable
Price = additional cost of conserving the natural resource

The model includes:
*3 alternatives, represented as ALT, including the status quo (Alternative 1 as the base alternative)
*6 Random variables (for the resource’s attributes), two of these are interaction variables
*6 Case-specific variables (socio-economic variables of respondents). These were included in the model by creating categorical variables for the alternatives (ALT2 and ALT3) and creating interaction variables between the socio-economic variables and alternatives.

nrep 30 and 90 seem to provide significant and consistent results (i.e. same significant variables and signs), whereas other levels resulted in endless iterations with not concave messages. Further, nrep>90 resulted in insignificant models, i.e. using nrep(300) resulted in a model with chi-square=0.6002.

My questions are:

1. Is there a recommended number of Halton draws (nrep#) for mixed logit? Based on the STATA Journal for mixlogit (https://www.sheffield.ac.uk/polopoly...e/mixlogit.pdf) the default is nrep(50). However, higher levels could give more accurate results.
2. Is it acceptable to use either 30 or 90 for this analysis since it provided almost similar results?

Thank you.