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Small Area Estimation Using a Multinomial Logit Mixed Model with Category Specific Random Effects

The Analytical Services Branch (ASB) recently published a research paper entitled "Small Area Estimation Using a Multinomial Logit Mixed Model with Category Specific Random Effects". Authored by Janice Scealy, the paper describes a model based approach to producing small area estimates of counts for different categories of Australian labour force based status (employed, unemployed and not in the labour force (NILF)), on a multinomial logit mixed model with category-specific random effects. The term 'category-specific' means that within each small area there are two correlated random effects, one associated with the employed category and the other associated with the unemployed category.

In this application the Multinomial Logit Mixed Model gave similar estimates and mean squared errors (MSEs) to that of the Binomial Logit Mixed Model fitted separately to each labour force status variable. However, the main advantage of the multinomial approach in the general case is that it has the capability to produce more accurate small area estimates where there are reasonably strong correlations between the categories, such as the employed and the unemployed. Another advantage is that once the explanatory variables have been selected for each category response variable, model estimation can be carried out simultaneously for all categories. A third advantage is that the estimates of proportion for each category are guaranteed to add to one, which is not assured when applying separate binomial models to each category.

In the study undertaken by Scealy, estimates of the model parameters were produced using penalised quasi-likelihood combined with approximated restricted maximum likelihood estimation and using these, estimated counts were then produced for each small area. MSE estimates, which measure the statistical accuracy of the estimated counts, were approximated using two methods: the parametric bootstrap and analytical approximations. The performance of these methods was then compared. Using a parametric bootstrap we also examine the properties of the combined penalized quasi-likelihood and restricted maximum likelihood estimators and discuss model goodness of fit measures and diagnostics.

For a copy of the paper, visit the ABS website and search for Catalogue Number 1351.0.55.029 - Research Paper: Small Area Estimation Using a Multinomial Logit Mixed Model with Category Specific Random Effects, Jan 2010. For further information on the analysis, contact Janice Scealy on (02) 6252 5764 or janice.scealy@abs.gov.au.