Recovering knot placements in Bayesian piecewise growth models with missing data

Fitting N-mixture models to count data with unmodeled heterogeneity: Bias, diagnostics, and alternative approaches

The misspecification of gravity spatial interaction models has recently been described by the author. The bias in parameter estimates that results from such misspecification appears to produce the ‘map pattern effect’ or ‘spatial structure bias’ in estimated distance-decay parameters. A further aspect of the misspecification bias in gravity parameter estimates is explored here. The severity of the bias is shown to vary in a predictable manner with variations in spatial structure. In particular, the bias is shown to be dependent upon the pattern of accessibility that exists within a spatial system. The relevant aspects of this pattern are discussed for intraurban and interurban (or interregional) flow matrices. It is shown that from an examination of the spatial structure of centres in a spatial system it is possible, a priori, to identify whether significant bias will arise in the calibration of a gravity model. Certain configurations of centres are shown theoretically to produce maximal bias. The author thus answers the question, “why do gravity parameter estimates appear to be biased in some systems but not in others?”

This article describes a Monte Carlo study of 2 methods for treating incomplete nonnormal data. Skewed, kurtotic data sets conforming to a single structured model, but varying in sample size, percentage of data missing, and missing-data mechanism, were produced. An asymptotically distribution-free available-case (ADFAC) method and structured-model expectation-maximization (EM) with nonnormality corrections were applied to these data sets, and the 2 methods were then compared in terms of bias in parameter estimates, bias in standard-error estimates, efficiency of parameter estimates, and model chi-squares. The results favored the nonnormality corrected EM over the ADFAC method in almost all respects, the only important exceptions involving (a) bias in standard-error estimates with large samples and (b) mixed results with respect to the efficiency of parameter estimates.

Considerations of sample size in medical research

Cognitive diagnostic models (CDMs) are increasingly being used in various assessment contexts to identify cognitive processes and provide tailored feedback. However, the most commonly used estimation method for CDMs, marginal maximum likelihood estimation with Expectation–Maximization (MMLE-EM), can present difficulties when sample sizes are small. This study compares the results of different estimation methods for CDMs under varying sample sizes using simulated and empirical data. The methods compared include MMLE-EM, Bayes modal, Markov chain Monte Carlo, a non-parametric method, and a parsimonious parametric model such as Restricted DINA. We varied the sample size, and assessed the bias in the estimation of item parameters, the precision in attribute classification, the bias in the reliability estimate, and computational cost. The findings suggest that alternative estimation methods are preferred over MMLE-EM under low sample-size conditions, whereas comparable results are obtained under large sample-size conditions. Practitioners should consider using alternative estimation methods when working with small samples to obtain more accurate estimates of CDM parameters. This study aims to maximize the potential of CDMs by providing guidance on the estimation of the parameters.

This work proposes and evaluates two methods (CM1 and CM2) for detecting non-compliance using concentration-time data and for obtaining estimates of population pharmacokinetic model parameters in a population with prevalent non-compliance. CM1 estimates individual residual variability (RV) and identifies subjects with higher than average RV as non-compliant. Exclusion of subjects with high RV from the analysis dataset reduces the bias in the estimates of the model parameters. Various methods of identification and exclusion of non-compliant subjects were tested, compared, and shown to reduce or eliminate bias in parameter estimates associated with non-compliance. The tested methods were (i) a pre-defined cutoff value of the random effect on RV, (ii) sequential exclusion of subjects with the highest RV percentiles, and (iii) use of a mixture model for RV. CM2 is applicable for the data with a specific sampling pattern that includes a potentially non-compliant outpatient part with several trough samples followed by a dense profile after the inpatient (compliant) dose. It relies only on the doses known to be administered (e.g., inpatient doses). In this method, all concentration measurements during the outpatient part of the study (except the trough value immediately preceding the inpatient dose) are removed from the dataset and an additional parameter (individual relative bioavailability of the outpatient doses) is introduced. For a number of simulated datasets with various sampling schemes and non-compliance patterns the proposed methods allowed to identify subjects with compliance problems and to reduce or eliminate bias in the estimates of the model parameters.

Detection of Mastitis in Dairy Cattle by Use of Mixture Models for Repeated Somatic Cell Scores: A Bayesian Approach via Gibbs Sampling

Researchers often collect longitudinal data to model change over time in a phenomenon of interest. Inevitably, there will be some variation across individuals in specific time intervals between assessments. In this simulation study of growth curve modeling, we investigate how ignoring individual differences in time points when modeling change over time relates to convergence and admissibility of solutions, bias in estimates of parameters, efficiency, power to detect change over time, and Type I error rate. We manipulated magnitude of the individual differences in assessment times, distribution of assessment times, magnitude of change over time, number of time points, and sample size. In contrast to the correct analysis, ignoring individual differences in time points frequently led to inadmissible solutions, especially with few time points and small samples, regardless of the specific magnitude of individual differences that were ignored. Mean intercept and slope were generally estimated without bias. Ignoring individual differences in time points sometimes yielded overestimated intercept and slope variances and underestimated intercept–slope covariance and residual variance. Parameter efficiency as well as power and Type I error rates for the linear slope were unaffected by the type of analysis.

The traditional Stochastic Frontier Model (SFM) suffers from a very restrictive assumption of independence of its error components and also limited ability to address heterogeneity (inefficiency effects) satisfactorily, thereby leading to potential biases in the estimation of model parameters, identification of inefficiency effect variables influencing efficiency and, ultimately, efficiency scores. This paper aims to investigate the consequences of ignoring any dependency in error components and heterogeneity in the stochastic frontier model, and proposes a copula-based SFM with heterogeneity to resolve such weaknesses based on a simulation study to prove its superiority over the traditional SFM, followed by an empirical application on a sample of rice producers from northern Thailand. We demonstrate that the proposed model, i.e., copula-based SFM with dependent error components and heterogeneity, is unbiased and robust. The simulation experiments show that the traditional SFM can cause biases in parameter estimation and severe overestimation of technical efficiency. The traditional SFM with heterogeneity also has similar consequences. However, just ignoring heterogeneity does not have a great impact on parameter estimation and technical efficiency compared to the consequence of ignoring dependency in error components. The empirical application of the proposed model results show that land, labor and material inputs are all significant drivers of rice production in our copula-based SFM with dependent error components and heterogeneity, whereas in the traditional SFM model only the land variable seems to be a significant driver of rice production. The mean technical efficiency (MTE) score was also overestimated by two points in the traditional SFM, i.e., MTE = 0.88 versus 0.86. Finally, results of the copula-based SFM with dependent error components and heterogeneity reveals that both subsistence pressure and the use of hired labor are significantly associated with technical inefficiency, whereas the traditional SFM could identify the effect of hired labor use only. Therefore, caution is necessary when interpreting results from the conventional SFM as the results may be biased, incomplete and/or inadequate.

Non-invasive monitoring techniques like camera traps, autonomous recording units and environmental DNA are increasingly used to collect data for understanding species distribution. These methods have prompted the development of statistical models to suit specific sampling designs and get reliable ecological inferences. Site occupancy models estimate species occurrence patterns, accounting for the possibility that the target species may be present but unobserved. Here, two key processes are crucial: detection, when a species leaves signs of its presence, and identification where these signs are accurately recognized. While both processes are prone to error in general, wrong identifications are often considered as negligible with in situ observations. When applied to passive bio-monitoring data, characterized by datasets requiring automated processing, this second source of error can no longer be ignored as misclassifications at both steps can lead to significant biases in ecological estimates. Several model extensions have been proposed to address these potential errors. We propose an extended occupancy model that accounts for the identification process in addition to detection. Similar to other recent attempts to account for false positives, our model may suffer from identifiability issues, which usually require another source of data with perfect identification to resolve them. As an alternative when such data are unavailable, we propose leveraging existing knowledge of the identification process within a Bayesian framework by incorporating this knowledge through an informative prior. Through simulations, we compare different prior choices that encode varying levels of information, ranging from cases where no prior knowledge is available, to instances with accurate metrics on the performance of the identification, and scenarios based on generally accepted assumptions. We demonstrate that, compared to using a default prior, integrating information about the identification process as a prior reduces bias in parameter estimates. Overall, our approach mitigates identifiability issues, reduces estimation bias, and minimizes data requirements. In conclusion, we provide a statistical method applicable to various monitoring designs, such as camera trap, bioacoustics, or eDNA surveys, alongside non-invasive sampling technologies, to produce ecological outcomes that inform conservation decisions.

BackgroundIn a cross-sectional stepped-wedge cluster randomized trial comparing usual care to a new intervention, treatment allocation and time are correlated by design because participants enrolled early in the trial predominantly receive usual care while those enrolled late in the trial predominantly receive the new intervention. Current guidelines recommend adjustment for time effects when analyzing stepped-wedge cluster randomized trials to remove the confounding bias induced by this correlation. However, adjustment for time effects impacts study power. Within the Frequentist framework, adopting a sample size calculation that includes time effects would ensure the trial having adequate power regardless of the magnitude of the effect of time on the outcome. But if in fact time effects were negligible, this would overestimate the required sample size and could lead to the trial being deemed infeasible due to cost or unavailability of the required numbers of clusters or participants. In this study, we explore the use of prior information on time effects to potentially reduce the required sample size of the trial.MethodsWe applied a Bayesian approach to incorporate the prior information on the time effects into cluster-level statistical models (for continuous, binary, or count outcomes) for the stepped-wedge cluster randomized trial. We conducted simulations to illustrate how the bias in the intervention effect estimate and the trial power vary as a function of the prior precision and the mis-specification of the prior means of the time effects in an example scenario.ResultsWhen a nearly flat prior for the time effects was used, the power or sample size calculated using the Bayesian approach matched the result obtained using the Frequentist approach with time effects included. When a highly precise prior for the time effects (with accurately specified prior means) was used, the Bayesian result matched the Frequentist result obtained with time effects excluded. When the prior means of the time effects were nearly correctly specified, including this information improved the efficiency of the trial with little bias introduced into the intervention effect estimate. When the prior means of the time effects were greatly mis-specified and a precise prior was used, this bias was substantial.ConclusionIncluding prior information on time effects using a Bayesian approach may substantially reduce the required sample size. When the prior can be justified, results from applying this approach could support the conduct of a trial, which would be deemed infeasible if based on the larger sample size obtained using a Frequentist calculation. Caution is warranted as biased intervention effect estimates may arise when the prior distribution for the time effects is concentrated far from their true values.

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines.

ABSTRACTMultivariate regression models, i.e. regression models where the left-hand side of the regression equation denotes a matrix of dependent variables, have long been developed. However, the statistical analysis of empirical data is usually restricted to multivariable regression methods with only one dependent variable. Within the framework of hierarchical Bayesian methods, the present study illustrates (i) how multivariate regression models offer new possibilities of information synthesis and theory testing in survey data analysis, and (ii) how sensitive the results are to different specifications of prior distributions. To this end, a large representative survey is utilized to specify two multivariate hierarchical Bayesian regression models which are calculated under two different prior distribution specifications. The estimation procedures and their implementation in R are described, convergence and predictive power analysis of each model are presented, and the advantages and disadvantages of multivariate regression methods are discussed. In general, the results obtained under each prior specification are to some extent similar, although differences were observed regarding model complexity, efficiency and predictive power. It is concluded that these methods facilitate the development and testing of complex research hypotheses, and are promising alternatives to a more efficient data analysis of large survey data sets.

Objective The Bayesian model plays an important role in diagnostic test evaluation in the absence of the gold standard, which used the external prior distribution of a parameter combined with sample data to yield the posterior distribution of the test characteristics. However, the correlation between diagnostic tests has always been a problem that cannot be ignored in the Bayesian model evaluation. This study will discuss how different Bayesian model, correlation scenarios, and prior distribution affect the outcome. MethodsThe data analyzed in this study was gathered during studies of patients presenting to the Nanjing Chest Hospital with suspected tuberculosis. The diagnostic character of T-SPOT.Tb and KD38 tuberculosis antibody test were evaluated in different Bayesian model, and discharge diagnosis as a gold standard was used to verify the model results in the end. Result The comparison of four models under the conditional independence situation found that Bayesian probabilistic constraint model was consistent with the Conditional Covariance Bayesian model. The results were mainly affected by prior information. The sensitivity and specificity of the two tests in Conditional Covariance Bayesian model in prior constraint situation were considerably higher than the Bayesian probabilistic constraint model in prior constraint situation. The results of the four models under the conditional dependence situation were similar to the conditional independence situation; pD was also negative with no prior constraint situation in both model Bayesian probabilistic constraint model and Conditional Covariance Bayesian model. The Deviance Information Criterion of Bayesian probabilistic constraint model was close to model Conditional Covariance Bayesian model, but pD of Conditional Covariance Bayesian model in Prior constraint situation (pD=2.40) was higher than the Bayesian probabilistic constraint model in Prior constraint situation (pD=1.66). Conclusion The result of Conditional Covariance Bayesian model in prior constraint with conditional independence situation was closest to the result of gold standard evaluation in our data. Both of the two Bayesian methods are the feasible way for the evaluation of diagnostic test in the absence of the gold standard diagnostic. Prior source, priority number, and conditional dependencies should be considered in the method selection, the accuracy of posterior estimation mainly depending on the prior distribution.

The hierarchical linear model (HLM) has become popular in behavioral research, and has been widely used in various educational studies in recent years. Violations of model assumptions can have significant impact on the model estimates. The purpose of this study is to conduct a sensitivity analysis of two-level HLM by exploring the influence of outliers on parameter estimates of HLM under normality assumptions. A simulation study is performed to examine the bias of parameter estimates with different numbers and magnitudes of outliers given different sample sizes. Results indicated that the bias of parameter estimates increased with the magnitudes and number of outliers. The estimates have bias with a few outliers. A robust method Huber sandwich estimator corrected the standard errors efficiently when there was a large proportion of outliers.KeywordsHierarchical linear modelsOutliersRobust method