Abstract:
It can be frequently observed that the data arising in
our environment have a hierarchical or a nested structure attached
with the data. Multilevel modelling is a modern approach to handle
this kind of data. When multilevel modelling is combined with a
binary response, the estimation methods get complex in nature and
the usual techniques are derived from quasi-likelihood method. The
estimation methods which are compared in this study are, marginal
quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized
quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical
model is of no use if it does not reflect the given dataset. Therefore,
checking the adequacy of the fitted model through a goodness-of-fit
(GOF) test is an essential stage in any modelling procedure.
However, prior to usage, it is also equally important to confirm that
the GOF test performs well and is suitable for the given model. This
study assesses the suitability of the GOF test developed for binary
response multilevel models with respect to the method used in model
estimation. An extensive set of simulations was conducted using
MLwiN (v 2.19) with varying number of clusters, cluster sizes and
intra cluster correlations. The test maintained the desirable Type-I
error for models estimated using PQL2 and it failed for almost all the
combinations of MQL. Power of the test was adequate for most of the
combinations in all estimation methods except MQL1. Moreover,
models were fitted using the four methods to a real-life dataset and
performance of the test was compared for each model
