I am using multilevel logistic regression, using a hierarchical data set, to determine the risk of occurrence of acute respiratory infection (modeled as a binary  yes, no) for 32 countries. I am initial under taking the analysis at a country level. The models has the following levels
Level 1 Child Characteristics
Level2 – Household and maternal Characteristics
Level 3 – Regions
For most of the countries when I run the model I gain a ‘Variance = 0.0000; Std Error = 0.0000'. To solve this problem I have used the parameter contains settings for random parameters assigning ”to equal” option as 0. Is this an appropriate method to use to solve this problem?
NB: For those countries which work without being constrained the difference between the constrained and nonconstrained models are negligible.
Thank you very much for you time.
Constraining multilevel logistic regression model

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 Joined: Mon Oct 19, 2009 10:34 am
Re: Constraining multilevel logistic regression model
Are you be able to provide some more details regarding what you are trying to do and the problem that you are seeing, as the question isn't clear to us currently?
Re: Constraining multilevel logistic regression model
Thank you very much for your response.
The model set up was a binomial logit model, with three levels, which converged and threelevel hierarchy assumed by the model matches the data (checked through using the hierarchy viewer)
I have attached images out the output to try and explain the problem.
Problem: The random effects variance and standard error are 0.
Propose Solution: Changing the random parameter constraints so that the "to equal" option in the parameter constraints window is assigned a 0. Which gives a variance of 0.2 (SD: 0.1) across regions and a variance of 10.0 (SE: 0.45) across households.
Question: Is this proposed solution an appropriate why of solving the issues with the original (nonconstrained) model that gave the results of 0 variance across the levels?
Link to image: https://drive.google.com/file/d/1Cid99B ... sp=sharing
The model set up was a binomial logit model, with three levels, which converged and threelevel hierarchy assumed by the model matches the data (checked through using the hierarchy viewer)
I have attached images out the output to try and explain the problem.
Problem: The random effects variance and standard error are 0.
Propose Solution: Changing the random parameter constraints so that the "to equal" option in the parameter constraints window is assigned a 0. Which gives a variance of 0.2 (SD: 0.1) across regions and a variance of 10.0 (SE: 0.45) across households.
Question: Is this proposed solution an appropriate why of solving the issues with the original (nonconstrained) model that gave the results of 0 variance across the levels?
Link to image: https://drive.google.com/file/d/1Cid99B ... sp=sharing
Re: Constraining multilevel logistic regression model
Dear KW844529,
What you are doing doesn't make sense at all as in the logistic regression model, value normally used for the level 1 variance stored in that column is in fact the scaling factor for over/underdispersion and set at 1 for a standard logistic regression with binomial variation. It therefore doesn't make sense to try and fix this value at 0 and I'll be honest that I am not sure what this would do to the quasilikelihood algorithm that is being used but I would NOT use the estimates produced. I hope that makes some sense.
Best wishes,
Bill.
What you are doing doesn't make sense at all as in the logistic regression model, value normally used for the level 1 variance stored in that column is in fact the scaling factor for over/underdispersion and set at 1 for a standard logistic regression with binomial variation. It therefore doesn't make sense to try and fix this value at 0 and I'll be honest that I am not sure what this would do to the quasilikelihood algorithm that is being used but I would NOT use the estimates produced. I hope that makes some sense.
Best wishes,
Bill.
Re: Constraining multilevel logistic regression model
Dear Bill,
Thank you very much for your response. I thought this would be the case.
Are there any suggestion or resources that I could be directed to, to be able to solve this problem?
Thank you very much for your response. I thought this would be the case.
Are there any suggestion or resources that I could be directed to, to be able to solve this problem?
Re: Constraining multilevel logistic regression model
If you leave it unconstrained then it is simply pointing to the maximum (quasi)likelihood solution being 0 for the variance i.e. there is probably no influence of the hierarchical structure. You could try fitting the model using MCMC to see what estimates that gives,
Bill.
Bill.