Exploring Response Variable Distributional Consequences Following Alterations in the Level of a Multilevel Model

Distributional assumptions made in respect of the variables and parameters of single or multi-level models often include those relating to the response or explanatory variables. It is anticipated that erroneous and misleading conclusions could be drawn on the distribution of the response variable if differing multi-level models predict the response variable values. This study explores, using educational data sets for illustrative analysis, distributional consequences that could be ascribed to the response variable of a multi-level model if the level of a model varies. It is shown how response variable population distribution parameter estimates can vary with varying levels in the K-level Model and also how inferences on confidence interval limits of the response variable can also be misleading in an inappropriate K-level Multi-level Modeling Framework.