Multinomial logistic & VPC
Posted: Thu Jan 07, 2016 2:07 pm
Dear all,
I am modelling a multinomial logistic regression and I came across some problems while calculating the Variance Partition Coefficient (VPC). In the binary logistic multilevel case, the VPC is easily calculated through the simulation method, written out on page 133 of the manual. The macro does not work in the case of the multinomial model (as mlwin models it as a three level model). I am wondering if Goldstein, Browne and Rasbash (2002) simulation method can be extended for the multinomial case through the following method:
1. use the higher level variances (of the categories of the dependent variable) to simulate a large number m of higher level residuals from N(0,s²(k)) for each category of the dependent variable. As the dependent variables has k categories, I will do this k-1 times.
2. For each category of the dependent variable, calculate the probability (Pk) for some values of the independent variables. Similarly, calculate the corresponding level 1 variance for each category: V1k=Pk(1-Pk). Is the formula for the variance correct in the multinomial case?
3. From here on it is straightforward to calculate the VPC for each category of the dependent variable.
Would this be a correct approach to model the VPC for each category? Is it sensible to do? And does it also hold if I’m modeling in MCMC?
Kind regards,
Pim Verbunt
I am modelling a multinomial logistic regression and I came across some problems while calculating the Variance Partition Coefficient (VPC). In the binary logistic multilevel case, the VPC is easily calculated through the simulation method, written out on page 133 of the manual. The macro does not work in the case of the multinomial model (as mlwin models it as a three level model). I am wondering if Goldstein, Browne and Rasbash (2002) simulation method can be extended for the multinomial case through the following method:
1. use the higher level variances (of the categories of the dependent variable) to simulate a large number m of higher level residuals from N(0,s²(k)) for each category of the dependent variable. As the dependent variables has k categories, I will do this k-1 times.
2. For each category of the dependent variable, calculate the probability (Pk) for some values of the independent variables. Similarly, calculate the corresponding level 1 variance for each category: V1k=Pk(1-Pk). Is the formula for the variance correct in the multinomial case?
3. From here on it is straightforward to calculate the VPC for each category of the dependent variable.
Would this be a correct approach to model the VPC for each category? Is it sensible to do? And does it also hold if I’m modeling in MCMC?
Kind regards,
Pim Verbunt