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In this paper we study the type IV Knorr Held space time models. Such modelstypically apply intrinsic Markov random fields and constraints are imposed foridentifiability. INLA is an efficient inference tool for such models whereconstraints are dealt with through a conditioning by kriging approach. When thenumber of spatial and/or temporal time points become large, it becomescomputationally expensive to fit such models, partly due to the number ofconstraints involved. We propose a new approach, HyMiK, dividing constraintsinto two separate sets where one part is treated through a mixed effectapproach while the other one is approached by the standard conditioning bykriging method, resulting in a more efficient procedure for dealing withconstraints. The new approach is easy to apply based on existingimplementations of INLA.  We run the model on simulated data, on a real data set containing denguefever cases in Brazil and another real data set of confirmed positive testcases of Covid-19 in the counties of Norway. For all cases we get very similarresults when comparing the new approach with the tradition one while at thesame time obtaining a significant increase in computational speed, varying on afactor from 2 to 4, depending on the sizes of the data sets.

Faster estimation of the Knorr-Held Type IV space-time model