# Discrete response model FAQs

## How can I specify a binomial response model using a macro?

The Manual Supplement (available to download for free) gives an example of running a logistic regression from a macro on pp 86-87, and this is followed by more information about the special commands needed (pp 88-89) which allow you to specify that you have a binomial response, which link function you want to use, the estimation method, and the denominator.

## What is the command for specifying the denominator when fitting a binomial or multinomial model?

The command is DOFFs. For documentation see p88 of the MLwiN manual supplement.

Note that although the documentation for the command is in the manual supplement for version 2.10, this command does also work in version 2.02, as do most of the other commands documented under the heading 'Other useful commands for specifying discrete response models in macros'.

## Why is the log-likelihood value not displayed in the Equation Window when a Binomial or Poisson model has been fitted?

For these models the likelihood value produced by the IGLS algorithm is an approximation, and could be unreliable in some extreme cases. For making statistical inference, you may use Wald test from the Interval and Tests window. But you can still get an approximate 2log-likelihood value for a model using the command LIKE from the Command Interface window

## MLwiN gives different results to SAS and Stata

Example question: I have a logistic multilevel model (random intercept) and calculated the same model in Stata (xtmelogit), in SAS (proc glimmix) and in MLwiN. The fixed effects are quite similar but the random effects and the intercept differ. They are the same for SAS and Stata but not for MLwiN. In Stata and SAS I do get significant random variation in the intercept but in MLwiN I don't. How could that be? Do you have explanations?

SAS and Stata use maximum likelihood estimation for discrete response models while MLwiN uses quasi-likelihood methods (see p128 of the User's Guide for more details). The different estimation methods can produce slightly different results, and in the case where results lie close to the borderline for significance it is possible to find parameter values significantly different from 0 using one estimation method but not the other.

It is known that quasi-likelihood methods give estimates for the random parameters which are biased downwards (see Rodríguez and Goldman, 2001). For this reason, we do not recommend that users take results from these estimation methods as final, but instead recommend that they should use MCMC estimation (after using quasi-likelihood estimation to get starting values). MCMC estimation gives unbiased parameter estimates; note however that the parameter chains and other diagnostics should be carefully checked so as to be sure that the burn in has been long enough for the chains to move away from what will probably be bad starting values, and that after burn in the chains have been run long enough to get accurate estimates. See MCMC estimation in MLwiN for more details of the diagnostics available and how to tell whether burn-ins and chains are long enough; and see our free online training materials (Section C 7.7 and the Technical Appendix to Module 7*) for more detailed discussion of estimation methods for binary response models.

Reference: Rodríguez G. and Goldman N. (2001) Improved estimation procedures for multilevel models with binary response: a case-study. Journal of the Royal Statistical Society, Series A, 164, 339-355

## How do I calculate variance functions for multinomial models?

Example question: I have a multinomial model with categorical explanatory variables. How do I use the Variance function window to calculate the variance for this model?

See our guide to this: Using the Variance Function Window with Multinomial Models with Categorical Explanatory Variables (PDF, 880kB) and if required download dataset used in the unordered multinomial section (.wsz, MLwiN data file, 0.1 mb )

## How do I interpret the estimates for the fixed part parameters in a Poisson model?

The interpretation of the output depends on how you have set your model up, in particular on what you have used as the offsets. If you have set your model up so that the response variable is for example the number of deaths and the offset variable is the log of the number at risk, then the estimates that you see in the Equations window for the coefficients (in the fixed part of the model) will be the effects on the log rate, so that you need to take the exponential of each coefficient to get the effect on the rate. If on the other hand you do as in the example in Chapter 12 of the User's Guide and use as the offset variable the log of the expected number of deaths, then the estimates that you see in the Equations window for the coefficients of the fixed part of the model will be the effects on the log ratio of observed to expected deaths, and the exponentials of the coefficients will be the effects on the ratio of observed to expected deaths. (Note that it is more usual to use the log of the number at risk rather than the log of the expected number of deaths as the offset variable where information on the number at risk is available). So you will need to interpret your results based on how your model is set up.