# How to Compare B Coefficients within and between models in R?

##### New Member
Hello people,

I am new to this forum and it would be great if some experienced people could help met out. I would like to know what the appropriate statistical method is, to compare B Coefficients between multinomial logit models in R.

My dataset consist of stated preferences data that I obtained from a choice based conjoint experiment and has the so-called long shape.

For my experiment there were two experimental conditions, the 'brand' condition and the 'retail' condition. The same independent variables were used (dealer, fuel, brand, price and maintain with the same levels).

What I actually want to examine, is whether there are differences between the coefficients of the multinomial logit models. Below the output of the two models (brand12 and retailer12) are summarized

Thus, in the ml.brand12 model, the estimate for price is -1.1159e and in the ml.retailer12 model -1.4122e-04?

How can I examine in a statistical correct way whether this difference is significant?

Brand condition
> summary(ml.brand12)

Call:
mlogit(formula = choice ~ dealer + fuel + brand + price + maintain |
-1, data = brand12, method = "nr", print.level = 0)

Frequencies of alternatives:
a1 a2 a3 a4
0.28487 0.28558 0.32383 0.10573

nr method
5 iterations, 0h:0m:1s
g'(-H)^-1g = 3.33E-05
successive function values within tolerance limits

Coefficients :
Estimate Std. Error t-value Pr(>|t|)
dealer 5.1015e-01 2.9764e-02 17.140 < 2.2e-16 ***
fuel 7.0856e-01 2.5510e-02 27.776 < 2.2e-16 ***
brand 5.1019e-01 2.7346e-02 18.657 < 2.2e-16 ***
price -1.1159e-04 7.5306e-06 -14.818 < 2.2e-16 ***
maintain -2.8398e-03 1.2257e-04 -23.169 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log-Likelihood: -4508.5

Retailer condition
> summary(ml.retailer12)

Call:
mlogit(formula = choice ~ dealer + fuel + brand + price + maintain |
-1, data = retailer12, method = "nr", print.level = 0)

Frequencies of alternatives:
a1 a2 a3 a4
0.27949 0.29038 0.30957 0.12056

nr method
5 iterations, 0h:0m:1s
g'(-H)^-1g = 0.000383
successive function values within tolerance limits

Coefficients :
Estimate Std. Error t-value Pr(>|t|)
dealer 6.3709e-01 3.0155e-02 21.127 < 2.2e-16 ***
fuel 7.0651e-01 2.5560e-02 27.642 < 2.2e-16 ***
brand 4.8755e-01 2.8071e-02 17.369 < 2.2e-16 ***
price -1.4122e-04 7.7595e-06 -18.200 < 2.2e-16 ***
maintain -2.9467e-03 1.2550e-04 -23.479 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Cheers,

Kevin

#### rogojel

##### TS Contributor
hi,
you could just add a discrete factor like "condition" to your regression and analyze all the data together. You can then test the factor and possible interactions for significanve.

regards