Random Coefficient Regression Research Articles

Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models

Genomic selection has been widely implemented in many livestock breeding programs, but it remains incipient in buffalo. Therefore, this study aimed to (1) estimate variance components incorporating genomic information in Murrah buffalo; (2) evaluate the performance of genomic prediction for milk-related traits using single- and multitrait random regression models (RRM) and the single-step genomic best linear unbiased prediction approach; and (3) estimate longitudinal SNP effects and candidate genes potentially associated with time-dependent variation in milk, fat, and protein yields, as well as somatic cell score (SCS) in multiple parities. The data used to estimate the genetic parameters consisted of a total of 323,140 test-day records. The average daily heritability estimates were moderate (0.35 ± 0.02 for milk yield, 0.22 ± 0.03 for fat yield, 0.42 ± 0.03 for protein yield, and 0.16 ± 0.03 for SCS). The highest heritability estimates, considering all traits studied, were observed between 20 and 280 d in milk (DIM). The genetic correlation estimates at different DIM among the evaluated traits ranged from -0.10 (156 to 185 DIM for SCS) to 0.61 (36 to 65 DIM for fat yield). In general, direct selection for any of the traits evaluated is expected to result in indirect genetic gains for milk yield, fat yield, and protein yield but also increase SCS at certain lactation stages, which is undesirable. The predicted RRM coefficients were used to derive the genomic estimated breeding values (GEBV) for each time point (from 5 to 305 DIM). In general, the tuning parameters evaluated when constructing the hybrid genomic relationship matrices had a small effect on the GEBV accuracy and a greater effect on the bias estimates. The SNP solutions were back-solved from the GEBV predicted from the Legendre random regression coefficients, which were then used to estimate the longitudinal SNP effects (from 5 to 305 DIM). The daily SNP effect for 3 different lactation stages were performed considering 3 different lactation stages for each trait and parity: from 5 to 70, from 71 to 150, and from 151 to 305 DIM. Important genomic regions related to the analyzed traits and parities that explain more than 0.50% of the total additive genetic variance were selected for further analyses of candidate genes. In general, similar potential candidate genes were found between traits, but our results suggest evidence of differential sets of candidate genes underlying the phenotypic expression of the traits across parities. These results contribute to a better understanding of the genetic architecture of milk production traits in dairy buffalo and reinforce the relevance of incorporating genomic information to genetically evaluate longitudinal traits in dairy buffalo. Furthermore, the candidate genes identified can be used as target genes in future functional genomics studies.

Genetic basis of thermotolerance in 2 local dairy sheep populations in the Iberian Peninsula

Sheep milk production in the Northern Mediterranean countries heavily relies on local breeds subject to selection schemes to improve milk production. Climate change may shift the range of thermal loads on the animals and challenge their adaptation to the new thermal gradient. The objective of this study was to characterize the genetic component of thermal tolerance of 2 local breeds from the Iberian Peninsula, Latxa and Manchega, belonging to different genetic types that have evolved under different climatic environments (Oceanic for Latxa and Continentalized Mediterranean for Manchega). A total of 79,243 and 2,388,853 test day monthly records of milk, fat and protein yields from 12,882 and 277,904 ewes of Latxa and Manchega breeds, respectively, along a 12-yr period, were matched with the value of the average temperature-humidity index (THI) on the day of milk recording of the closest weather station to the flocks. These data were used to fit individual reaction norms (Legendre polynomials) describing changes in yields along the THI gradient. Genetic values for thermal tolerance were obtained from the slopes of those reaction norms under cold or heat stress and variances and covariances between yield and thermal tolerance were derived from the (co)variance matrices of the polynomial random regression coefficients. Results showed differing patterns in the 2 breeds. The Latxa breed showed clearer signs of genotype by environment interaction than did Manchega. Estimated correlations between yields under extremes of cold and heat were always above 0.8 for Manchega and around 0.4 for Latxa for all traits. Estimates of correlations between comfort and thermal stress were again over 0.8 for Manchega and lower for the higher (hot end) values (down to 0.6) than for the lower (cold end) values (down to 0.84) of the THI gradient for Latxa, indicating greater thermal stress expected from high than from low temperatures in this breed. Substantial variability in thermal tolerance under the more extreme THI values was found in both breeds. Estimated genetic correlations between yield and thermal tolerance were close to 0 and 0.2 for Latxa and Manchega in the cold and down to -0.6 and -0.3 in the heat end, although small variation was observed for fat in Latxa. Estimated realized trends from the average estimated breeding value, by year of birth, showed a positive response for yields in both breeds [around 0.1 standard deviation (SD) unit], but a detrimental correlation for thermal tolerance (down to -0.03 SD units for heat tolerance in Latxa). These results can be used to design optimal selection strategies for sustainable improvement of productivity under a rising-temperature scenario associated with climate change.

Power and sample size for random coefficient regression models in randomized experiments with monotone missing data.

Random coefficient regression (also known as random effects, mixed effects, growth curve, variance component, multilevel, or hierarchical linear modeling) can be a natural and useful approach for characterizing and testing hypotheses in data that are correlated within experimental units. Existing power and sample size software for such data are based on two variance component models or those using a two-stage formulation. These approaches may be markedly inaccurate in settings where more variance components (i.e., intercept, rate of change, and residual error) are warranted. We present variance, power, sample size formulae, and software (R Shiny app) for use with random coefficient regression models with possible missing data and variable follow-up. We illustrate sample size and study design planning using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We additionally examine the drivers of variability to better inform studydesign.

Genetic parameters of forage dry matter intake and milk produced from forage in Swedish Red and Holstein dairy cows

High-yielding dairy cows are often fed high proportions of cereal grain and pulses. For several reasons, it would be desirable to replace these feed sources with forage, which is not suitable for human consumption. Feeding large amounts of forage to dairy cows could also make dairy production more publicly acceptable in the future. In this study, we estimated genetic parameters for total dry matter intake (DMI), DMI from forage (DMIFor), energy-corrected milk (ECM), and ECM produced from forage (ECMFor). A total of 1,177 lactations from 575 cows of Swedish Red (SR) and Holstein (HOL) dairy breeds were included in the study. Mixed linear animal random regression models were used, with fixed effect of calving season and lactation week nested within parity 1 and 2+, fixed effect of calving year, and random regression coefficients for breeding value (up to linear) and permanent environmental effect (up to quadratic) of the cow. Heritability for DMI and DMIFor was generally higher for HOL than for SR in all-parity data and in later parities; however, the opposite was true for first parity. Heritability for DMI and DMIFor during the first 8 wk averaged 0.11 and 0.15, respectively, in all-parity data for the 2 breeds. Corresponding values for ECMFor and ECM were 0.21 and 0.29, respectively. In first parity, values were 0.32, 0.36, 0.28, and 0.51, respectively. The genetic correlation between DMI and DMIFor was high, above 0.83, and fairly constant across the lactation. The genetic correlation between ECMFor and ECM was close to unity in the later part of lactation for both breeds, but was around 0.8 in the early lactation for both breeds; it decreased for HOL to 0.54 in wk 17. The genetic correlations between DMI and ECMFor and between DMIFor and ECMFor were low and negative for HOL (absolute value ∼0.2-0.3), but changed for SR from weakly positive in early lactation to negative values and back to positive toward the end of lactation. For most traits, the correlation between wk 1 and wk 8 into the lactation was very high; the lowest value was for DMI in HOL at 0.81. The genetic correlation between parities was rather high in the first part of the lactation. During the first 8 wk, the correlation was lower for HOL than for SR, except for ECM. We found that DMIFor and ECMFor showed reasonably large heritability, and future work should explore the possibility of genomic evaluations.

Computational and motivational mechanisms of human social decision making involving close others

Every day, human beings make decisions with social consequences. These social consequences matter most when they impact those closest to us. Recent research has shown that humans exhibit reliable preferences when deciding between conflicting outcomes involving close others – for example, prioritizing the interests of one's family member over one's friend. However, virtually nothing is known about the mechanisms that drive these preferences. We conducted a pre-registered study in a large (maximum N = 375) sample to quantify the computational and motivational mechanisms of human social decision-making preferences involving close others. By pairing assessment techniques from behavioral economics and psychological science with computational modeling and random coefficient regression, we show that value-based cognitive computations (e.g., risk and loss aversion) drive social decision-making preferences involving financial outcomes, whereas socioemotional motivations (e.g., relationship quality) underlie preferences involving social outcomes. These results imply mechanistic heterogeneity, underscoring a need for greater attention to contextual specificity in social decision-making.

Efficacy and safety of nintedanib in patients with systemic sclerosis-associated interstitial lung disease treated with mycophenolate: a subgroup analysis of the SENSCIS trial

In the Safety and Efficacy of Nintedanib in Systemic Sclerosis (SENSCIS) trial, nintedanib reduced the rate of decline in forced vital capacity (FVC) in patients with systemic sclerosis-associated interstitial lung disease (SSc-ILD). Patients on stable treatment with mycophenolate for at least 6 months before randomisation could participate. The aim of this subgroup analysis was to examine the efficacy and safety of nintedanib by mycophenolate use at baseline. The SENSCIS trial was a randomised, double-blind, placebo-controlled trial, in which patients with SSc-ILD were randomly assigned (1:1) to receive 150 mg of oral nintedanib twice daily or placebo for at least 52 weeks. In a prespecified subgroup analysis, we analysed the primary endpoint of rate of decline in FVC over 52 weeks by mycophenolate use at baseline. In a post-hoc analysis, we analysed the proportion of patients with an absolute decrease in FVC of at least 3·3% predicted at week 52 (proposed minimal clinically important difference estimate for worsening of FVC in patients with SSc-ILD) in subgroups by mycophenolate use at baseline. Adverse events were reported in subgroups by mycophenolate use at baseline. Analyses were done in all participants who received at least one dose of study drug. We analysed the annual rate of decline in FVC using a random coefficient regression model (with random slopes and intercepts) including anti-topoisomerase I antibody status, age, height, sex, and baseline FVC as covariates and terms for baseline-by-time, treatment-by-subgroup, and treatment-by-subgroup-by-time interactions. SENSCIS is registered with ClinicalTrials.gov, NCT02597933, and is now complete. Between Nov 30, 2015, and Oct 31, 2017, 819 participants were screened and 576 were enrolled, randomly assigned to, and treated with nintedanib (n=288) or placebo (n=288). 139 (48%) of 288 in the nintedanib group and 140 (49%) of 288 in the placebo group were taking mycophenolate at baseline. In patients taking mycophenolate at baseline, the adjusted mean annual rate of decline in FVC was -40·2 mL per year (SE 19·8) with nintedanib and -66·5 mL per year (19·3) with placebo (difference: 26·3 mL per year [95% CI -27·9 to 80·6]). In patients not taking mycophenolate at baseline, the adjusted mean annual rate of decline in FVC was -63·9 mL per year (SE 19·3) with nintedanib and -119·3 mL per year (19·0) with placebo (difference: 55·4 mL per year [95% CI 2·3 to 108·5]). We found no heterogeneity in the effect of nintedanib versus placebo on the annual rate of decline in FVC between the subgroups by mycophenolate use (p value for interaction=0·45). In a post-hoc analysis, the proportion of patients with an absolute decrease in FVC of at least 3·3% predicted was lower with nintedanib than with placebo in both patients taking mycophenolate (40 [29%] of 138 vs 56 [40%] of 140; odds ratio 0·61 [0·37 to 1·01]) and those not taking mycophenolate (59 [40%] of 149 vs 70 [47%] of 148; 0·73 [0·46 to 1·16]) at baseline. The adverse event profile of nintedanib was similar between the subgroups. Diarrhoea, the most common adverse event, was reported in 106 (76%) of 139 patients in the nintedanib group and 48 (34%) of 140 in the placebo group among those taking mycophenolate at baseline, and in 112 (75%) of 149 in the nintedanib group and 43 (29%) of 148 in the placebo group among those not taking mycophenolate at baseline. Over the entire trial period, 19 patients died (ten in the nintedanib group and nine in the placebo group). One death in the nintedanib group was considered to be related to study drug. Nintedanib reduced the progression of interstitial lung disease both in patients with SSc-ILD who were and were not using mycophenolate at baseline, with no heterogeneity in its treatment effect detected between the subgroups. The adverse event profile of nintedanib was similar in the subgroups by mycophenolate use. Our findings suggest that the combination of mycophenolate and nintedanib offers a safe treatment option for patients with SSc-ILD. More data are needed on the benefits of initial combination therapy versus a sequential approach to treatment of SSc-ILD. Boehringer Ingelheim.

Influence of climatic conditions on tympanic temperature and milk production in grazing cows

The present study aimed to analyze large volumes of tympanic temperature (TT) data to identify its use as a physiological indicator of climatic conditions and its relationship with milk production in grazing cows under tropical lowland conditions. Three dairy farms and 21 multiparous early lactation cows were included in the study. Seven animals were equipped with tympanic temperature wireless sensors within each farm, and permanent information was collected hourly for 22 days on average. Ambient temperature (AT), relative humidity (RH), wind speed (WS), precipitation (PP), and THI information were obtained from meteorological stations located close to each farm. Statistical analyses included Spearman correlations and random coefficient regression models (P < 0.05). TT presented moderate and significant correlations with AT (0.35 to 0.49), SR (0.25 to 0.32), THI (0.35 to 0.49), and RH (-0.35 to -0.49). Climatic variables like AT, PP, SR, and WS were the most contributing factors to TT prediction (R2 =0.42 to 0.86). Grazing dairy cows in tropical scenarios accumulate heat during the day and dissipate it at nighttime, although higher producing animals deal with more problems to reach thermal homeostasis. Correlations between TT and daily milk production varied according to animal yield; however, higher TT values were related to the most productive cows. The effect of TT on milk production prediction was not conclusive among farms, possibly by animal management or others characteristics of the systems. TT determination through remote sensors allows a reliable diagnosis of the physiological temperature response to climatic conditions.

Estimates of genetic parameters and cluster analysis of the lactation curve of dairy Gyr cattle

The aim of this study was to estimate genetic parameters for month test-day milk yields of dairy Gyr cattle and to explore the additive genetic pattern of the milk production curve using cluster analysis in order to choose subgroups of animals that can result in genetic gain for milk production. The dataset of dairy Gyr cows was provided by the Brazilian Association of Zebu Breeders (ABCZ) and contained 123,035 first-lactation test-day records from 16,318 cows and calvings between 1983 and 2014. Random regression under an animal model was used to predict the breeding values of animals for monthly milk yields from 30 to 305 days, as the sum of breeding values of each day in milk, for coefficients of the lactation curve (intercept, linear, quadratic, and cubic), for peak yield, persistency of lactation, and total milk yield. Two cluster analyses were used to describe the additive genetic structure of the population: the hierarchical (Ward method) and non-hierarchical (k-means method) cluster analyses using the predicted breeding values of the above traits. Cluster analysis were used to figure out the patterns of the additive genetic lactation curves within the population that matched up with pre-defined breeding goals (improve the milk production) to suggest potential selection candidates. The estimates of heritability for test day milk yields ranged from 0.14 ± 0.02 to 0.20 ± 0.02. The intercept of the random regression had strong genetic correlation with peak yield and total milk yield while the linear random regression coefficient had strong genetic correlation with the persistency, as defined in this study, of the lactation curve. Cluster analysis resulted in four groups. The animals from Cluster 1 could be used as selection candidates because their additive genetic pattern presented EBVs above the mean population for all the traits. So, those animals could help to increase the milk production, and the persistency of lactation. Cluster analysis was effective to identify groups of animals suitable to attend the breeding goals, i.e. increase the persistency of lactation and the milk production along the lactation curve in dairy Gyr cattle.

Estimating Residual Life Distributions of Complex Operational Systems Using a Remaining Maintenance Free Operating Period (RMFOP)-Based Methodology.

Recent developments in the area of condition monitoring research have been targeted towards predicting machinery health condition for the purpose of preventative maintenance. Typically, published research uses data collected from rotating components (bearings, cutting tools, etc.) working in an idealized lab environment as the case study for prognosis algorithm validations. However, the operational implementation in industry is still very sporadic, mainly owing to the lack of proper data allowing sufficiently mature development of comprehensive methodologies. The prognosis methodology presented herein bridges the gap between academic research and industrial implementations by employing a novel time period for prognosis and implementing random coefficients regression models. The definition of the remaining maintenance-free operating period (RMFOP) is proposed first, which helps to transform the usefulness of the degradation data that is readily available from data short of failure. Degradation patterns are subsequently extracted from the original degradation data, before fitting into either of two regression models (linear or exponential). The system residual life distributions are then computed and updated by estimating the parameter statistics within the model. This RMFOP-based methodology is validated using real-world degradation data collected from multiple operational railway switch systems across Great Britain. The results indicate that both the linear model and the exponential model can produce residual life distributions with a sufficient prediction accuracy for this specific application. The exponential model gives better predictions, the accuracy of which also improves as more of system life percentage has elapsed. By using the RMFOP methodology, switch system health condition affected by an incipient overdriving fault is recognized and predicted.

Rate-optimal nonparametric estimation for random coefficient regression models

Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper, we obtain the optimal pointwise convergence rate for estimating the density in the linear random coefficient model over Hölder smoothness classes, and in particular show how the tail behavior of the design density impacts this rate. In contrast to previous suggestions, the estimator that we propose and that achieves the optimal convergence rate does not require dividing by a nonparametric density estimate. The optimal choice of the tuning parameters in the estimator depends on the tail parameter of the design density and on the smoothness level of the Hölder class, and we also study adaptive estimation with respect to both parameters.

Motor outcome measures in patients with FKRP mutations: A longitudinal follow-up.

To test the hypothesis that we will be able to detect change in motor outcome measures over time in a cohort with mutations in FKRP. Individuals with documented FKRP mutations were evaluated annually with a battery of established motor outcome measures including limited quantitative myometry and timed function measures. Results were analyzed using random coefficient regression to determine annual change in each measure. Due to the nonlinear progression through the lifespan of the study participants, pediatric (<19 years) and adult (≥19 years) cohorts were analyzed separately. Effect of genotype was evaluated in each cohort. Sixty-nine participants (30 pediatric, 44 adult) with at least 2 evaluations were included. There was a small but statistically significant decline in timed motor function measures in both pediatric and adult cohorts. Genotype significantly affected rate of decline in the pediatric but not the adult cohort. Some pediatric patients who are homozygous for the c.826C>A mutation showed improving motor performance in adolescence. Performance on the 10-meter walk/run was highly correlated with other timed function tests. There is a slow annual decline in motor function in adults with FKRP mutations that can be detected with standard motor outcome measures, while the results in the pediatric population were more variable and affected by genotype. Overall, these analyses provide a framework for development of future clinical trials. The dystroglycanopathies natural history study (Clinical Trial Readiness for the Dystroglycanopathies) may be found on clinicaltrials.gov (NCT00313677).

Is social decision making for close others consistent across domains and within individuals?

Humans make decisions across a variety of social contexts. Though social decision-making research has blossomed in recent decades, surprisingly little is known about whether social decision-making preferences are consistent across different domains. We conducted an exploratory study in which participants made choices about 2 types of close others: parents and friends. To elicit decision making preferences, we pit the interests in parents and friends against one another. To assess the consistency of preferences for close others, decision making was assessed in three domains-risk taking, probabilistic learning, and self-other similarity judgments. We reasoned that if social decision-making preferences are consistent across domains, participants ought to exhibit the same preference in all three domains (i.e., a parent preference, based on prior work), and individual differences in preference magnitude ought to be conserved across domains within individuals. A combination of computational modeling, random coefficient regression, and traditional statistical tests revealed a robust parent-over-friend preference in the risk taking and probabilistic learning domains but not the self-other similarity domain. Preferences for parent-over-friend in the risk-taking domain were strongly associated with similar preferences in the probabilistic learning domain but not the self-other similarity domain. These results suggest that distinct and dissociable value-based and social-cognitive computations underlie social decision making. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Application of multivariate single-step SNP best linear unbiased predictor model and revised SNP list for genomic evaluation of dairy cattle in Australia

The objectives of this study were (1) to evaluate the computational feasibility of the multitrait test-day single-step SNP-BLUP (ssSNP-BLUP) model using phenotypic records of genotyped and nongenotyped animals, and (2) to compare accuracies (coefficient of determination; R2) and bias of genomic estimated breeding values (GEBV) and de-regressed proofs as response variables in 3 Australian dairy cattle breeds (i.e., Holstein, Jersey, and Red breeds). Additive genomic random regression coefficients for milk, fat, protein yield and somatic cell score were predicted in the first, second, and third lactation. The predicted coefficients were used to derive 305-d GEBV and were compared with the traditional parent averages obtained from a BLUP model without genomic information. Cow fertility traits were evaluated from the 5-trait repeatability model (i.e., calving interval, days from calving to first service, pregnancy diagnosis, first service nonreturn rate, and lactation length). The de-regressed proofs were only for calving interval. Our results showed that ssSNP-BLUP using multitrait test-day model increased reliability and reduced bias of breeding values of young animals when compared with parent average from traditional BLUP in Australian Holsten, Jersey, and Red breeds. The use of a custom selection of approximately 46,000 SNP (custom XT SNP list) increased the reliability of GEBV compared with the results obtained using the commercial Illumina 50K chip (Illumina, San Diego, CA). The use of the second preconditioner substantially improved the convergence rate of the preconditioned conjugate gradient method, but further work is needed to improve the efficiency of the computation of the Kronecker matrix product by vector. Application of ssSNP-BLUP to multitrait random regression models is computationally feasible.

1172-P: Impact of Telemedicine Clinics in the Management of Type 1 Diabetes

Background: Our institution began telemedicine clinics at rural hospitals in 2013, with standard office visits delivered synchronously via video conferencing. This project aims to assess the impact of telemedicine clinics in T1D care at our institution. Methods: IRB approval was obtained to access records of people with T1D with three or more telemedicine visits from Nov 2013 to Oct 2019. To assess change in A1c, we used a random coefficient regression model and estimated the effect of time on A1c, controlling for gender and age at start of treatment. Data were collected on change in treatment and prior provider (PCP, outside/academic endocrinologist). Results: The 139 patients evaluated (average age 45 y (range 16-94), 58% F) had an average of 8 A1c values (2-23) over an average duration of 32 mos (4-69). The scatterplot and fitted regression line show a temporal A1c decline. Similarly, random coefficient regression analysis provided overwhelming evidence for an A1c decline (P&amp;lt; 0.001). Each year in telemedicine care was associated with a decline of 0.13 in A1c (95% CI: -0.20, -0.06). Age and gender were not associated with A1c. A1c decline was noted irrespective of prior provider or treatment change (ie, starting CGM/pump therapy). Conclusions: Our data supports the concept that T1D can be effectively managed via telemedicine. Declines in A1c were seen in all groups, irrespective of age, prior provider and additions of diabetes technology. Disclosure L.A. Eiland: None. M. Siahpush: None. P. Akkireddy: None. L. Kuechenmeister: None.

Efficient pseudo-Gaussian and rank-based detection of random regression coefficients

ABSTRACTRandom coefficient regression models are the regression counterparts of the classical random effects models in Analysis of Variance and panel data analysis. While several heuristic methods have been proposed for the detection of such random regression coefficients, little is known on their optimality properties. Based on a nonstandard ULAN property, we are proposing locally asymptotically optimal (in the Hájek-Le Cam sense) parametric, pseudo-Gaussian, and rank-based procedures for this problem. The asymptotic relative efficiencies (with respect to the pseudo-Gaussian procedure) of rank-based tests turn out to be quite high under heavy-tailed and skewed densities, demonstrating the importance of a careful choice of scores. Simulations reveal the excellent finite-sample performances of a class of rank-based procedures based on data-driven scores.

Multi-stage nested classification credibility quantile regression model

In insurance (or in finance) practice, in a regression setting, there are cases where the error distribution is not normal and other cases where the set of data is contaminated due to outlier events. In such cases the classical credibility regression models lead to an unsatisfactory behavior of credibility estimators, and it is more appropriate to use quantile regression instead of the ordinary least squares estimation. However, these quantile credibility models cannot perform effectively when the set of data has nested (hierarchical) structure. This paper develops credibility models for regression quantiles with nested classification as an alternative to Norberg’s (1986) approach of random coefficient regression model with multi-stage nested classification. This paper illustrates two types of applications, one with insurance data and one with Fama/French financial data.

Geometric characterization of [formula omitted]-optimal designs for random coefficient regression models

In this paper we investigate geometric characterization of optimal designs for random coefficient regression models. We establish a generalization of Elving’s theorem for the D-optimality criterion for estimating the population parameters in random coefficient regression models. We also consider the geometric characterization of D-optimal designs for predicting the individual parameters.

Efficient Data Augmentation for Multivariate Probit Models with Panel Data: An Application to General Practitioner Decision Making about Contraceptives

Summary The paper considers the problem of estimating a multivariate probit model in a panel data setting with emphasis on sampling a high dimensional correlation matrix and improving the overall efficiency of the data augmentation approach. We reparameterize the correlation matrix in a principled way and then carry out efficient Bayesian inference by using Hamiltonian Monte Carlo sampling. We also propose a novel antithetic variable method to generate samples from the posterior distribution of the random effects and regression coefficients, resulting in significant gains in efficiency. We apply the methodology by analysing stated preference data obtained from Australian general practitioners evaluating alternative contraceptive products. Our analysis suggests that the joint probability of discussing combinations of contraceptive products with a patient shows medical practice variation among the general practitioners, which indicates some resistance even to discuss these products, let alone to recommend them.

Formula omitted]-optimal designs for individual prediction in random coefficient regression models

In this paper we consider optimal designs for the R-criterion in random coefficient regression models. We derive two equivalence theorems to characterize the optimal designs for the prediction of the individual parameters and for the individual deviations from the unknown population mean parameters in random coefficient models. Some examples of the R-optimal designs for the straight line regression with random coefficients are presented for illustration.

Using a Random Coefficient Regression Model to Jointly Determine the Optimal Critical Level and Lot Sizing

This paper proposes an integrated preventive maintenance and economic production quantity model. A condition-based maintenance policy is described by a random coefficient regression model, based on which the monitored condition is divided into two parts: the actual condition and random error. Products are produced in batches and the system is monitored at the end of each batch. If the observed system condition either reaches or exceeds the critical level, the system should be renewed by preventive maintenance. However, if the actual system condition reaches the failure level during the production process, the system fails and should be renewed immediately. Based on these two renewal situations, we construct a model of expected cost per unit time using the renewal reward theory. The critical level and production lot size are decision variables, which can be obtained by minimizing the cost model. We also develop a simulation process to obtain the optimal results in another way and validate our proposed cost model. Finally, a real case study is given to demonstrate the model and the simulation process.