  Continuous response variables often need to be transformed to meet regression
modeling assumptions; however, finding the optimal transformation is
challenging and results may vary with the choice of transformation. When a
continuous response variable is measured repeatedly for a subject or the
continuous responses arise from clusters, it is more challenging to model the
continuous response data due to correlation within clusters. We extend a widely
used ordinal regression model, the cumulative probability model (CPM), to fit
clustered continuous response variables based on generalized estimating
equation (GEE) methods for ordinal responses. With our approach, estimates of
marginal parameters, cumulative distribution functions (CDFs), expectations,
and quantiles conditional on covariates can be obtained without
pre-transformation of the potentially skewed continuous response data.
Computational challenges arise with large numbers of distinct values of the
continuous response variable, and we propose two feasible and computationally
efficient approaches to fit CPMs for clustered continuous response variables
with different working correlation structures. We study finite sample operating
characteristics of the estimators via simulation, and illustrate their
implementation with two data examples. One studies predictors of CD4:CD8 ratios
in an HIV study. The other uses data from The Lung Health Study to investigate
the contribution of a single nucleotide polymorphism to lung function decline.
