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Effective and efficient access to multiparty meeting recordings requires techniques for meeting analysis and indexing. Since meeting participants are generally stationary, speaker location information may be used to identify meeting events e.g., detect speaker changes. Time-delay estimation (TDE) utilizing cross-correlation of multichannel speech recordings is a common approach for deriving speech source location information. Research improved TDE by calculating TDE from linear prediction (LP) residual signals obtained from LP analysis on each individual speech channel. This paper investigates the use of LP residuals for speech TDE, where the residuals are obtained from jointly modeling the multiple speech channels. Experiments conducted with a simulated reverberant room and real room recordings show that jointly modeled LP better predicts the LP coefficients, compared to LP applied to individual channels. Both the individually and jointly modeled LP exhibit similar TDE performance, and outperform TDE on the speech alone, especially with the real recordings.