Separating interviewer and area effects by using a cross-classified multilevel logistic model: simulation findings and implications for survey designs

Cross-classified multilevel models deal with data pertaining to two different nonhierarchical classifications. It is unclear how much interpenetration is needed for a crossclassified multilevel model to work well and to estimate the two higher-level effects reliably. The paper investigates this question and the properties of cross-classified multilevel logistic models under various survey conditions. The effects of different membership allocation schemes, total sample sizes, group sizes, number of groups, overall rates of response and the variance partitioning coefficient on the properties of the estimators and the power of the Wald test are considered. The work is motivated by an application to separate area and interviewer effects on survey non-response which are often confounded. The results indicate that limited interviewer dispersion (around three areas per interviewer) provides sufficient interpenetration for good estimator properties. Further dispersion yields only very small or negligible gains in the properties. Interviewer dispersion also acts as a moderating factor on the effect of the other simulation factors (sample size, the ratio of interviewers to areas, the overall probability and the variance values) on the properties of the estimators and test statistics. The results also indicate that a higher number of interviewers for a set number of areas and a set total sample size improves these properties.