A Recursive Regression for High-Dimensional Models, with Application to Growth Curves and Repeated Measures

Abstract

Abstract A fixed-effects formulation of repeated-measures and growth-curve problems usually leads to an unwieldy linear model, so mixed models are widely used for inference that the conditional linear error model could otherwise support with weaker distributional assumptions. Very high-dimensional regressions (not necessarily arising this way) can be fitted by the proposed alternating algorithm, which partitions the design matrix into singly manageable strips and recursively calls a regression routine with low-dimensional subproblems. Convergence to the full least squares solution with modest memory and time requirements is a consequence of the behavior of cyclically iterated projections of linear spaces. The partitioning can be implicitly and transparently done for a wide class of growth-curve problems. The method does not hinge on any balance or completeness properties of the design. In all cases coefficients and residuals are recoverable from standard regression output after convergence, but package-supplied covariances of fitted coefficients are not directly usable. Circumvention of the difficulty is described in conjunction with a case study involving a special error structure.