Conditional mixed models with crossed random effects

The analysis of continuous hierarchical data such as repeated measures or data from meta-analyses can be carried out by means of the linear mixed-effects model. However, in some situations this model, in its standard form, does pose computational problems. For example, when dealing with crossed random-effects models, the estimation of the variance components becomes a non-trivial task if only one observation is available for each cross-classified level. Pseudolikelihood ideas have been used in the context of binary data with standard generalized linear multilevel models. However, even in this case the problem of the estimation of the variance remains non-trivial. In this paper we first propose a method to fit a crossed random-effects model with two levels and continuous outcomes, borrowing ideas from conditional linear mixed-effects model theory. We also propose a crossed random-effects model for binary data combining ideas of conditional logistic regression with pseudolikelihood estimation. We apply this method to a case study with data coming from the field of psychometrics and study a series of items (responses) crossed with participants. A simulation study assesses the operational characteristics of the method.