Goodness -of -fit in hierarchical logistic regression models
Hierarchical logistic regression models have gained popularity in recent years as algorithms and computer software for fitting them improved. Little research exists to provide measures for assessing model fit in this area.
We extend goodness-of-fit measures used in the standard logistic setting to the hierarchical case. Using simulation studies we examine the performance of unweighted sums of squares, Pearson residual and Hosmer-Lemeshow statistics at various levels of the hierarchical model. Our results suggest such statistics do not offer reasonable performance in the hierarchical logistic model in terms of Type I error rates.
We also develop Kernel smoothed versions of the statistics using level one residuals and a modified unweighted sum of squares statistic based on residuals at higher levels. Performance of these statistics, using Type I error rates, is satisfactory. We also describe power studies suggesting that these statistics have limited power in certain hierarchical settings.
Finally, we discuss limitations of this work and possible future research.