Bootstrapping for variance estimation in multi-level models fitted to survey data

For estimation of parameters of a multi-level model fitted to hierarchical survey data, the standard assumptions are that the survey weights are available at all sampling levels and that the hierarchy of sampling levels coincides with the hierarchy used in modeling. Under these two assumptions, we propose two bootstrap methods for the variance estimation of the estimated parameters in the multi-level model. These methods are essentially modifications of the well-known survey bootstrap methods of Rao and Wu (1988). In a simulation study designed according to the Canadian Workplace and Employee Survey (CWES), we study and compare the properties of these methods, and in turn we compare them to the more prevalent Taylor linearization method