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Stochastic compartmental models are usually based on continuous-time Markov processes. Markovian models assume that the compartments have exponential retention times, which is known not to hold in certain applications such as calcium clearance from bone. A number of semi-Markov models with restricted families of retention times have been proposed recently. This paper presents a general, tractable procedure for determining from suitable data the estimated retention time distributions for assumed non-Markovian phenomenological models. The procedure is based on using phase-type distributions. These distributions can describe the long tails observed in calcium clearance data, and they frequently lead to complex eigenvalues that are often overlooked in practice. The procedure is illustrated on several proposed models for describing a particular data set.

Millon Clinical Multiaxial Inventory (MCMI) scores from 299 suicidal psychiatric outpatients were cluster analyzed in hopes of identifying clinical subgroups and deriving specific treatment indications. The analysis revealed four personality profiles: Negativistic/Avoidant/Schizoid, Avoidant/Dependent/ Negativistic, Antisocial, and Histrionic/Narcissistic. This grouping was validated by examining demographics, diagnoses, and scores on several psychometric scales. Results showed few differences in demographics, diagnosis, or intelligence, but significant differences in depression severity, hopelessness, anxiety, problem-solving self-appraisal, and alcohol abuse. Implications for tailoring interventions for subtypes of suicidal patients are discussed.

Twenty-four lactating Holstein and Jersey cows were fed concentrate mixtures formulated to supplement total diets with 1) no added sodium chloride, 2) 1.0% sodium chloride, 3) 1.14% calcium chloride, and 4) 1.45% sodium bicarbonate during a 9-wk continuous trial, Experiment 1. Responses measured were body temperature, respiration rate, milk yield, milk composition, and 15 blood variables to evaluate acid-base status and express metabolic profile. Treatments affected body temperature and pH, bicarbonate, total carbon dioxide, and base excess of blood. No treatment affected milk yield and composition. Differences in dietary electrolytes had little influence on responses. In a second experiment immediately following the first, a 1-km walking stress was imposed during midafternoon on 3 days; treatment did not influence change in response variables or recovery from stress although Jerseys recovered faster than Holsteins.

Digesta flow models have been based on linear compartment theory that assumes exponential retention times, and on a generalized theory that incorporates nonexponential (Erlang) retention times (Matis, 1987, Journal of Theoretical Biology 124, 371-376). This paper develops a new family of passage models for heterogeneous digesta by mixing the previous models with assumed parametric, usually gamma, mixing distributions. The utility of the resulting models is demonstrated with experimental data on two treatments, namely a chopped and a ground straw, given to each of four cows. Treatment differences are apparent in the preferred model form and in the means of the estimated mean residence times. The models are relatively easy to fit to data using standard estimation procedures, and they should have broad application to other compartment modeling problems with "heterogeneous particles."