Modelling the decline of pH in muscles of lamb carcases

Assuming an exponential decay model (EDM) for pH decline as a function of temperature, ideal shortening (i.e. neither hot nor cold shortening) for an individual carcase occurs if and only if that carcaseʹs model parameters fall within a specific sub-region of three dimensional space. This paper demonstrates that simply fitting EDMs to a sample of carcases and using the proportion of sampled carcases with estimated parameters within the specific sub-region can lead to seriously biassed estimates for the proportion of carcases ideally shortened. This is particularly so if the EDMs are fitted separately to each sampled carcase but also remains the case, to a lesser extent, if the models are fitted jointly using random effects modelling. A preferred estimate is based on the probability that an independently selected carcase has model parameters within the specific region, based on the distribution of the EMD parameters. The distribution of EMD parameters is obtained via the fitted random effects exponential decay model.