Conferences

Delsing and Out (Statistica Neerlandica, 2008, 62, 1, 58-82) have analysed models for the investigation of reciprocal relationships, e.g. AR cross-lagged models, LT models and the ALT model, a synthesis of features of both the AR and LT models. They argued that each model has its strengths, of course, but also weaknesses, some of which could be overcome with the CALT continuous-time model. CALT incorporates a continuous-time version of the AR model in terms of an SDE which generates the cross-lagged effect functions. SDEs have Markovian properties and therefore the cross-lagged effect functions have limited memories. In order to explore whether some attention has to be payed on this limitation in panel analysis, we extend CALT using an SDDE approach. To estimate a stochastic delay differential equation, prediction-based estimators (PBE) seem to be optimal (U. Küchler & M. Sorensen, 2008, Statistical inference for discrete-time samples from affine stochastic delay differential equations; preprint). However, they are computationally much involved. An alternative with mild efficiency loss is the maximum pseudo-likelihood estimator, a particular case of the PBE. We demonstrate our approach using an empirical example and discuss the CALT and CALT/SDDE models.