Important: Read this before posting to this forum

  1. This forum is for questions related to the use of Apollo. We will answer some general choice modelling questions too, where appropriate, and time permitting. We cannot answer questions about how to estimate choice models with other software packages.
  2. There is a very detailed manual for Apollo available at http://www.ApolloChoiceModelling.com/manual.html. This contains detailed descriptions of the various Apollo functions, and numerous examples are available at http://www.ApolloChoiceModelling.com/examples.html. In addition, help files are available for all functions, using e.g. ?apollo_mnl
  3. Before asking a question on the forum, users are kindly requested to follow these steps:
    1. Check that the same issue has not already been addressed in the forum - there is a search tool.
    2. Ensure that the correct syntax has been used. For any function, detailed instructions are available directly in Apollo, e.g. by using ?apollo_mnl for apollo_mnl
    3. Check the frequently asked questions section on the Apollo website, which discusses some common issues/failures. Please see http://www.apollochoicemodelling.com/faq.html
    4. Make sure that R is using the latest official release of Apollo.
  4. If the above steps do not resolve the issue, then users should follow these steps when posting a question:
    1. provide full details on the issue, including the entire code and output, including any error messages
    2. posts will not immediately appear on the forum, but will be checked by a moderator first. This may take a day or two at busy times. There is no need to submit the post multiple times.

rho square

Ask questions about the results reported after estimation. If the output includes errors, please include your model code if possible.
Post Reply
maa033
Posts: 35
Joined: 23 Jul 2020, 14:00

rho square

Post by maa033 »

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)?
stephanehess
Site Admin
Posts: 974
Joined: 24 Apr 2020, 16:29

Re: rho square

Post by stephanehess »

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
--------------------------------
Stephane Hess
www.stephanehess.me.uk
LianEnaLiu
Posts: 3
Joined: 02 Jan 2023, 11:19

Re: rho square

Post by LianEnaLiu »

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!
stephanehess
Site Admin
Posts: 974
Joined: 24 Apr 2020, 16:29

Re: rho square

Post by stephanehess »

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
--------------------------------
Stephane Hess
www.stephanehess.me.uk
Post Reply