ApolloChoiceModelling forum

Hi
In the cmcRcode package rho square was reported both as rho square (0) and rhos square (C ) (both incl. the adjusted version).
In the apollo output I only get rho squared (0) reported.

What is the connection between LL (0) and rho square (0), respectively LL (C ) and rho square (C ), and why isn't there a rho square (final)?

What is the difference between rho square (0) and rho square (C )?
How can I change the code in order to retrieve rho square (C ) and rho square (final)?

Hi

rho2(0) is for a model with all parameters at zero, i.e. equal shares for all alternatives, while rho2(C) is for a model with alternative specific constants only. We had included rho2(C) in the old code but this meant making an assumption of equal availability of all alternatives, which we did not want to retain in Apollo.

if you want to calculate rho2(C), then you should estimate a separate model in which you only estimate the alternative specific constants, getting LL(C). Then calculate the new rho2 as:

rho2(C) = 1-(LL(beta)/LL(C))

where LL(beta) is your LL for the full model.

If you want an adjusted rho2(C), it would be

adj.rho2(C) = 1-((LL(beta)-kb)/(LL(C)-kc))

where kb is the number of parameters in the full model, and kc is the number of parameters in the model with constants only

Stephane

Hi,

Currently, I am working on understanding and interpreting the estimation results of my MNL model. In the output, the following is given:

LL(start) : -2145.59
LL at equal shares, LL(0) : -2145.59
LL at observed shares, LL(C) : -2097.69
LL(final) : -1828.9
Rho-squared vs equal shares : 0.1476
Adj.Rho-squared vs equal shares : 0.1443
Rho-squared vs observed shares : 0.1281
Adj.Rho-squared vs observed shares : 0.1248
AIC : 3671.81
BIC : 3710.85

I am struggling to understand the difference between the four rho-squared given. I assume that rho-squared vs equal shares is the same as rho2(0) and rho-squared vs observed shares as rho2(c)? But I still do not understand the explanation of rho2(0) and rho2(c). I've tried to find some explanation on the different rho-squared options and how to determine which one to use to examine the model fit, but I could not find any explanation. So therefore I was wondering:

1. What is the difference between the four different rho-squared options presented in the model outputs?

Thanks in advance!

Hi

the difference was explained in the post below, and also in the manual. Maybe also look at https://doi.org/10.1016/j.jocm.2016.02.001

Stephane