Continuous, binary, ordinal, count, and survival-time outcomes
Point estimates and standard errors adjusted for survey design
Sampling weights for each stage of a multiple-stage design
Primary and secondary sampling units
Finite population corrections
Fully integrated with Stata's svyset command and svy prefix
Multilevel models are fit to data that can be divided into groups. These may be patients treated at the same hospital, cars manufactured at the same plant, students attending the same school, and so on.
As a more concrete example, suppose an educational researcher has given a test to a sample of students in Texas and wants to analyze the results. The students can be grouped into schools, and the schools can be grouped into school districts. If we believe unobserved characteristics of the individual schools as well as characteristics of the school districts are likely to impact the test results, we can fit a multilevel model with school-level and district-level random effects.
What if we want to fit a multilevel model to data collected using a complex survey design rather than a simple random sample? We need to take into account characteristics of the survey design—clustering, stratification, sampling weights, and finite-population corrections—to obtain appropriate point estimates and standard errors. Adjusting for survey design in multilevel models is unique in that we need weights for each level of the model, assuming those levels correspond to stages of the sampling design.
Continuing with our testing example, we will suppose that the researcher first took a sample of school districts. Then, schools were sampled from within each selected school district. Finally, students were selected from within each selected school. We have a multiple-stage sampling design. We also have sampling weights for each stage of the design related to the probabilities of school districts, individual schools, and students being included in the sample.
Throughout Stata, analyzing complex survey data is as simple as using svyset to declare aspects of the survey design and then adding the svy: prefix to the estimation command for the model you want to fit. We can now use svyset and the svy: prefix when fitting multilevel models to survey data.
You can read another worked example of multilevel analysis of survey data in the Stata manual entry for the multilevel mixed-effects generalized linear model; see [ME] meglm.