Spatial Flows and Spatial Patterns

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

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.

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.

Understanding of fish growth, the spatial variability in individual growth, and the potential drivers of such variability is a fundamental component of many ecological investigations. However, sampling gears are always size-selective, and this selectivity can result in biased parameter estimates that can lead to, for example, biased stock assessments that use growth estimates. Using seven flathead catfish (Pylodictis olivaris) populations from across the USA as an example, we investigated to what degree the incorporation of gear selectivity in growth models reduces size-selective bias in the estimation of growth parameters during macroscale investigations of fish growth. We developed a series of simulation scenarios by combining different sampling methods to obtain fish samples and different gear selectivity assumptions to estimate parameters. Results showed that the efficacy of incorporating gear selectivity in growth models to reduce size-selective sampling bias during macroscale investigations depends on multiple factors, including (i) the size distribution of small and large fish in the sample (which is a function of sampling methods), and (ii) consistency of sampling methods across populations. Incorporation of gear selectivity may reduce bias when data are lacking for large fish and when sampling methods are inconsistent across populations. Demographics of the sampled populations and the growth parameter of interest can also affect the utility of directly incorporating gear selectivity into growth models. Because multiple factors can influence the efficacy of incorporating gear selectivity into growth models, the decision to do so likely needs to be made on a case-by-case basis. This study extends the existing gear selectivity research by focusing on macroscale fish growth investigations across multiple populations and provides guidance on how to handle gear selectivity assumptions during such investigations.

Respondent-driven sampling (RDS) is a study design used to investigate populations for which a probabilistic sampling frame cannot be efficiently generated. Biases in parameter estimates may result from systematic non-random recruitment within social networks by geography. We investigate the spatial distribution of RDS recruits relative to an inferred social network among heterosexual adults in New York City in 2010. Mean distances between recruitment dyads are compared to those of network dyads to quantify bias. Spatial regression models are then used to assess the impact of spatial structure on risk and prevalence outcomes. In our primary distance metric, network dyads were an average of 1.34 (95 % CI 0.82–1.86) miles farther dispersed than recruitment dyads, suggesting spatial bias. However, there was no evidence that demographic associations with HIV risk or prevalence were spatially confounded. Therefore, while the spatial structure of recruitment may be biased in heterogeneous urban settings, the impact of this bias on estimates of outcome measures appears minimal.

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

In their influential paper, Wichmann and Hill (2001) have shown that the threshold and slope estimates of a psychometric function may be severely biased when it is assumed that the lapse rate equals zero but lapses do, in fact, occur. Based on a large number of simulated experiments, Wichmann and Hill claim that threshold and slope estimates are essentially unbiased when one allows the lapse rate to vary within a rectangular prior during the fitting procedure. Here, I replicate Wichmann and Hill's finding that significant bias in parameter estimates results when one assumes that the lapse rate equals zero but lapses do occur, but fail to replicate their finding that freeing the lapse rate eliminates this bias. Instead, I show that significant and systematic bias remains in both threshold and slope estimates even when one frees the lapse rate according to Wichmann and Hill's suggestion. I explain the mechanisms behind the bias and propose an alternative strategy to incorporate the lapse rate into psychometric function models, which does result in essentially unbiased parameter estimates.

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.

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 Individual's Choice of Facility for Maternal Health and Family Planning Services in a Dense Urban Environment: The Case of Senegal

Aguirre-Urreta and Marakas (A&M) suggest in their simulation “Revisiting Bias Due to Construct Misspecification: Different Results from Considering Coefficients in Standardized Form,” that, like Jarvis et al. (2003), MacKenzie et al. (2005), and Petter et al. (2007) before them, bias does occur when formative constructs are misspecified as reflective. But A&M argue that the level of bias in prior simulation studies has been exaggerated. They parameterize their simulation models using standardized coefficients in contrast to Jarvis et al., MacKenzie et al., and Petter et al., who parameterize their simulation models using unstandardized coefficients. Thus, across these four simulation studies, biases in parameter estimates are likely to result in misspecified measurement models (i.e., using either unstandardized or standardized coefficients); yet, the biases are greater in magnitude when unstandardized coefficients are used to parameterize the misspecified model. We believe that regardless of the extent of the bias, it is critically important for researchers to achieve correspondence between the measurement specification and the conceptual meaning of the construct so as to not alter the theoretical meaning of the construct at the operational layer of the model. Such alignment between theory and measurement will safeguard against threats to construct and statistical conclusion validity.

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

Detection of bias in observer-based estimates of retained and discarded catches from a multi species trawl fishery

The recursive least squares technique is often extended with exponential forgetting as a tool for parameter estimation in time-varying systems. The distribution of the resulting parameter estimates is, however, unknown when the forgetting factor is less than one. In this paper an approximative expression for bias of the recursively obtained parameter estimates in a time-invariant AR(na) process with arbitrary noise is given, showing that the bias is non-zero and giving bounds on the approximation errors. Simulations confirm the approximation expressions.

Since its introduction, the joint maximum likelihood (JML) has been widely used as an estimation method for Rasch measurement models. As is well known, when the JML method is used, all item and person parame- ters are regarded as unknowns to be estimated. In this paper we focus on some drawbacks of the JML for the Rasch model: viz. i) the occasional non-existence of estimates, and ii) the bias of item parameter estimates. We propose a new estimation method which is based on the Minimum Divergence Estimation approach and consists in appropriately modifying the empirical distribution function. We provide empirical evidence that this method can solve the problem of the non-existence of the estimates and, at the same time, can reduce the bias of item parameter estimates compared to those obtained with both traditional JML estimation and the ( k − 1) /k correction factor (where k is the number of items) commonly applied in JML software.