Standard Errors Of Parameter Estimates Research Articles

A novel correction method for modelling parameter-driven autocorrelated time series with count outcome

BackgroundCount time series (e.g., daily deaths) are a very common type of data in environmental health research. The series is generally autocorrelated, while the widely used generalized linear model is based on the assumption of independent outcomes. None of the existing methods for modelling parameter-driven count time series can obtain consistent and reliable standard error of parameter estimates, causing potential inflation of type I error rate.MethodsWe proposed a new maximum significant ρ correction (MSRC) method that utilizes information of significant autocorrelation coefficient ρ estimate within 5 orders by moment estimation. A Monte Carlo simulation was conducted to evaluate and compare the finite sample performance of the MSRC and classical unbiased correction (UB-corrected) method. We demonstrated a real-data analysis for assessing the effect of drunk driving regulations on the incidence of road traffic injuries (RTIs) using MSRC in Shenzhen, China. Moreover, there is no previous paper assessing the time-varying intervention effect and considering autocorrelation based on daily data of RTIs.ResultsBoth methods had a small bias in the regression coefficients. The autocorrelation coefficient estimated by UB-corrected is slightly underestimated at high autocorrelation (≥ 0.6), leading to the inflation of the type I error rate. The new method well controlled the type I error rate when the sample size reached 340. Moreover, the power of MSRC increased with increasing sample size and effect size and decreasing nuisance parameters, and it approached UB-corrected when ρ was small (≤ 0.4), but became more reliable as autocorrelation increased further. The daily data of RTIs exhibited significant autocorrelation after controlling for potential confounding, and therefore the MSRC was preferable to the UB-corrected. The intervention contributed to a decrease in the incidence of RTIs by 8.34% (95% CI, -5.69–20.51%), 45.07% (95% CI, 25.86–59.30%) and 42.94% (95% CI, 9.56–64.00%) at 1, 3 and 5 years after the implementation of the intervention, respectively.ConclusionsThe proposed MSRC method provides a reliable and consistent approach for modelling parameter-driven time series with autocorrelated count data. It offers improved estimation compared to existing methods. The strict drunk driving regulations can reduce the risk of RTIs.

Benefits of multinomial processing tree models with discrete and continuous variables in memory research: an alternative modeling proposal to Juola et al. (2019).

Signal detection theory (SDT) and two-high threshold models (2HT) are often used to analyze accuracy data in recognition memory paradigms. However, when reaction times (RTs) and/or confidence levels (CLs) are also measured, they usually are analyzed separately or not at all as dependent variables (DVs). We propose a new approach to include these variables based on multinomial processing tree models for discrete and continuous variables (MPT-DC) with the aim to compare fits of SDT and 2HT models. Using Juola et al.'s (2019, Memory & Cognition, 47[4], 855-876) data we have found that including CLs and RTs reduces the standard errors of parameter estimates and accounts for interactions among accuracy, CLs, and RTs that classical versions of SDT and 2HT models do not. In addition, according to the simulations, there is an increase in the proportion of correct model selections when relevant DV are included. We highlight the methodological and substantive advantages of MPT-DC in the disentanglement of contributing processes in recognition memory.

Comparing Several Missing Data Estimation Methods in Linear Regression;Real Data Example and A Simulation Study

Analysis on incomplete could lead to biased estimation when using standard statistical procedure since it ignores the missing observations. The disadvantage of ignoring missing data is that the researcher might not have enough data to conduct an analysis. The main objective of the study is to compare the performance between listwise deletion (LD), mean substitution (MS) and multiple imputation (MI) method in estimating parameters. The performance will be measured through bias, standard error and 95% confidence interval of interested estimates for handling missing data with 10% missing observations. A complete empirical data set was used and assumed as population data. Ten percent of total observations in the population ere set as missing arbitrarily by generating random numbers from a uniform distribution, . Then, bias of parameter estimates and confidence interval of parameter estimates are calculated to compare the three methods. A Monte Carlo simulation was carried out to know the properties of missing data and investigated using simulated random numbers. Simulation of 1000 sampled data with 20, 50, and 100 observations and each sample is set to have 10% missing observations. Standard statistical analyses are run for each missing data and get the average of parameter estimates to calculate the bias and standard error of parameter estimates for every missing data method. The analysis was conducted by using SAS version 9.2. It was found that the MI method provided the smallest bias and standard error of parameter estimates and a narrower confidence interval compared to the LD and MS methods Meanwhile, the LD method gives a smaller bias of parameter estimates and standard error for small sample size of missing data. And, MS method is strongly recommended not to use for handling missing data because it will result in large bias and standard error of parameter estimates.

Performance of Multiple Imputation Using Modern Machine Learning Methods in Electronic Health Records Data.

Missing data are common in studies using electronic health records (EHRs)-derived data. Missingness in EHR data is related to healthcare utilization patterns, resulting in complex and potentially missing not at random missingness mechanisms. Prior research has suggested that machine learning-based multiple imputation methods may outperform traditional methods and may perform well even in settings of missing not at random missingness. We used plasmode simulations based on a nationwide EHR-derived de-identified database for patients with metastatic urothelial carcinoma to compare the performance of multiple imputation using chained equations, random forests, and denoising autoencoders in terms of bias and precision of hazard ratio estimates under varying proportions of observations with missing values and missingness mechanisms (missing completely at random, missing at random, and missing not at random). Multiple imputation by chained equations and random forest methods had low bias and similar standard errors for parameter estimates under missingness completely at random. Under missingness at random, denoising autoencoders had higher bias than multiple imputation by chained equations and random forests. Contrary to results of prior studies of denoising autoencoders, all methods exhibited substantial bias under missingness not at random, with bias increasing in direct proportion to the amount of missing data. We found no advantage of denoising autoencoders for multiple imputation in the setting of an epidemiologic study conducted using EHR data. Results suggested that denoising autoencoders may overfit the data leading to poor confounder control. Use of more flexible imputation approaches does not mitigate bias induced by missingness not at random and can produce estimates with spurious precision.

Three Sample Estimates of Fraction of Missing Information From Full Information Maximum Likelihood.

In missing data analysis, the reporting of missing rates is insufficient for the readers to determine the impact of missing data on the efficiency of parameter estimates. A more diagnostic measure, the fraction of missing information (FMI), shows how the standard errors of parameter estimates increase from the information loss due to ignorable missing data. FMI is well-known in the multiple imputation literature (Rubin, 1987), but it has only been more recently developed for full information maximum likelihood (Savalei and Rhemtulla, 2012). Sample FMI estimates using this approach have since then been made accessible as part of the lavaan package (Rosseel, 2012) in the R statistical programming language. However, the properties of FMI estimates at finite sample sizes have not been the subject of comprehensive investigation. In this paper, we present a simulation study on the properties of three sample FMI estimates from FIML in two common models in psychology, regression and two-factor analysis. We summarize the performance of these FMI estimates and make recommendations on their application.

Extending finite mixtures of [formula omitted] linear mixed-effects models with concomitant covariates

The issue of model-based clustering of longitudinal data has attracted increasing attention in past two decades. Finite mixtures of Student’s-t linear mixed-effects (FM-tLME) models have been considered for implementing this task especially when data contain extreme observations. This paper presents an extended finite mixtures of Student’s-t linear mixed-effects (EFM-tLME) model, where the categorical component labels are assumed to be influenced by the observed covariates. As compared with the naive methods assuming the mixing proportions to be fixed but unknown, the proposed EFM-tLME model exploits a logistic function to link the relationship between the prior classification probabilities and the covariates of interest. To carry out maximum likelihood estimation, an alternating expectation conditional maximization (AECM) algorithm is developed under several model reduction schemes. The technique for extracting the information-based standard errors of parameter estimates is also investigated. The proposed method is illustrated using simulation experiments and real data from an AIDS clinical study.

A skew factor analysis model based on the normal mean–variance mixture of Birnbaum–Saunders distribution

This paper presents a robust extension of factor analysis model by assuming the multivariate normal mean–variance mixture of Birnbaum–Saunders distribution for the unobservable factors and errors. A computationally analytical EM-based algorithm is developed to find maximum likelihood estimates of the parameters. The asymptotic standard errors of parameter estimates are derived under an information-based paradigm. Numerical merits of the proposed methodology are illustrated using both simulated and real datasets.

Quantitative Prediction of Interactions Mediated by Transporters and Cytochromes: Application to Organic Anion Transporting Polypeptides, Breast Cancer Resistance Protein and Cytochrome 2C8.

The in vivo mechanistic static model (IMSM) is an effective method to predict the magnitude of drug-drug interactions (DDIs) mediated by cytochromes. The aim of this study was to extend the IMSM paradigm to DDIs mediated by organic anion transporting polypeptide (OATP)1Bs, breast cancer resistance protein (BCRP) and cytochrome 2C8. First, a generic model for this kind of interaction was established, and a literature search was then conducted to retrieve the area under the concentration-time curve (AUC) ratio of a large set of DDIs involving OATP1B1, OATP1B3, BCRP and cytochromes 2C8 or 3A4. The model was fitted to the data to estimate the characteristic parameters (contribution ratios [CRs] and inhibition or induction potencies [IXs]) by nonlinear regression, and the model was qualified by external validation on a different dataset. Lastly, the model was used to identify the risks of overexposure by DDIs of this type. A total of 27 substrates, 26 inhibitors, 3 inducers and 3 genetic variants were considered in the regression analysis. The number of observations (AUC ratios, denoted as Robs) was 101. Forty-six CRs and 47 IXs were estimated. The proportions of predictions within 0.67- to 1.5-fold and 0.5- to twofold Robs were 90% and 99%, respectively, for the internal validation, and 78% and 96%, respectively, for the external validation. The median fold-error was 1.03 (the ideal value is 1). The interquartile range of fold-error was 0.31, and the relative standard error of parameter estimates was, at most, 17%. The IMSM approach was successfully extended to DDIs mediated by OATP1Bs, BCRP and cytochromes 2C8 or 3A4. The method revealed good predictive performances by internal and external validation.

Development of a linear mixed-effects individual-tree basal area increment model for masson pine in Hunan Province, South-central China

ABSTRACT An individual-tree basal area increment model was developed for masson pine based on 26276 observations of 13,138 trees in 987 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, South-central China. The model was built using a linear mixed-effects approach with sample plots included as random effects since the data have a hierarchical stochastic structure and biased estimates of the standard error of parameter estimates could be a consequence of applying ordinary least square (OLS) for regression. In addition, within-plot heteroscedasticity and autocorrelation were also considered. The final mixed-effects model was determined according to the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik), and the likelihoodratio test (LRT). The results revealed that initial diameter (DBH), the sum of the basal area (m2/ha) in trees with DBHs larger than the DBH of the subject tree (BAL), number of trees per hectare (NT), and elevation (EL) had a significant impact on individual-tree basal area increment. The mixed-effects model performed much better than the basic model produced using OLS. Additionally, the variance structure of the model errors was successfully modeled using the power function. However, the autocorrelation structures were not defined because there was no autocorrelation amongst the data. It is believed that the final model will contribute to the scientific management of the masson pine.

Fitting Large Factor Analysis Models With Ordinal Data.

A simulation study was conducted to investigate the model size effect when confirmatory factor analysis (CFA) models include many ordinal items. CFA models including between 15 and 120 ordinal items were analyzed with mean- and variance-adjusted weighted least squares to determine how varying sample size, number of ordered categories, and misspecification affect parameter estimates, standard errors of parameter estimates, and selected fit indices. As the number of items increased, the number of admissible solutions and accuracy of parameter estimates improved, even when models were misspecified. Also, standard errors of parameter estimates were closer to empirical standard deviation values as the number of items increased. When evaluating goodness-of-fit for ordinal CFA with many observed indicators, researchers should be cautious in interpreting the root mean square error of approximation, as this value appeared overly optimistic under misspecified conditions.

A Bayesian spatial hierarchical model for extreme precipitation in Great Britain

AbstractIntense precipitation events are commonly known to be associated with an increased risk of flooding. As a result of the societal and infrastructural risks linked with flooding, extremes of precipitation require careful modeling. Extreme value analysis is typically used to model large precipitation events, although an independent analysis of neighboring sites can produce very different estimates of risk. In reality, one would expect neighboring locations to exhibit similar extremal behavior. A common method of inducing spatial similarity of extremal behavior is to define a spatial structure on the parameters of a generalized Pareto distribution in a Bayesian hierarchical modeling framework. These methods are often implemented under the assumption of conditional independence in time and space, with the consequence that standard errors of parameter estimates are too small. We present an approach for accounting for spatial and temporal dependence when quantifying the uncertainty in Bayesian hierarchical models when the misspecification of conditional independence has been made. We also present comparisons of performance between this class of models and alternative approaches, applied to precipitation data in Great Britain.

A Generic Model for Quantitative Prediction of Interactions Mediated by Efflux Transporters and Cytochromes: Application to P-Glycoprotein and Cytochrome 3A4.

The In Vivo Mechanistic Static Model (IMSM) is a powerful method used to predict the magnitude of drug-drug interactions (DDIs) mediated by cytochromes. The objective of this study was to extend the IMSM paradigm to DDIs mediated by efflux transporters and cytochromes. First, a generic model for this kind of interaction was devised. A flexible approach was then developed to estimate the characteristic parameters [the contribution ratios (CRs) and inhibition or induction potencies (IXs)] from clinical data by non-linear regression. Next, this approach was applied to the DDIs mediated by P-glycoprotein (P-gp) and cytochrome P450 (CYP) 3A4/3A5 in a large set of victim drugs and interactors. Lastly, the model and associated parameters were used to identify the DDIs most at risk of overexposure. A total of 25 substrates and 26 interactors (three inducers, 23 inhibitors) could be considered in the regression analysis. The number of observations [area under the plasma concentration-time curve ratios or renal clearance ratios (Robs)] was 138. Fifty CRs and 57 IXs were estimated. The proportions of predictions within 0.67- to 1.5-fold Robs and within 0.5- to 2-fold Robs were 79% and 93% for the internal validation and 76% and 88% for the external validation, respectively. The median fold error was 0.98 (the ideal value is 1) and the interquartile range of the fold error was 0.36. The relative standard error of parameter estimates was a maximum of 15%. The IMSM approach was successfully extended to DDIs mediated by P-gp and CYP3A4/3A5. The method revealed good predictive performances by internal and external validation.

Optimal design for dynamical modeling of pest populations.

We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

Seasonal habitat use in three species of wild ungulates in Sikkim Himalaya

Ungulates face increasing seasonal fluctuations in climate and forage availability with increasing latitude. While ungulates in the temperate regions address this by migrating across latitude and elevation, the strategies used by ungulates in the sub-tropical mountains is very little studied. We examined the influence of season, elevation, aspect and slope on the use of habitat by three species of ungulates in the Himalaya. The study area, Kyongnosla Alpine Sanctuary in Sikkim in India, covered 31km2. We deployed camera traps in 16 trails in an elevation range of 3000m to 4200m and used photo-captures in weeklong sessions as indicator of habitat use during the winter and post-winter during 2011–12. We used zero-inflated negative binomial regression in a model selection approach and model averaged parameter estimates to examine the relative influence of covariates on photo-captures. Zero captures or species absence was closely associated with winter and more northern aspects in the Himalayan musk deer (Moschus chrysogaster), higher elevation in the Himalayan goral (Naemorhedus goral) and both winter and more northern aspects in the Himalayan serow (Capricornis thar). The non-zero photo-captures increased with elevation and decreased with northerly aspects in musk deer, decreased with increasing elevation in goral, while no pattern was evident in serow. Thus, the three species have different strategies to deal with drastic seasonal changes: goral is a resident at low elevations, musk deer is a commuter between aspects at higher elevations, and serow is probably a migrant between high and low elevations. The lack of sampling ≪3000m, might have been the reason for low photo-captures of serow, especially in winter. Overall, we had few captures for all species due to the use of a limited number of cameras. This probably accounts for large standard errors of parameter estimates in the count models.

Multivariate normal mean-variance mixture distribution based on Lindley distribution

ABSTRACTThis article introduces a new asymmetric distribution constructed by assuming the multivariate normal mean-variance mixture model. Called normal mean-variance mixture of the Lindley distribution, we derive some mathematical properties of the new distribution. Also, a feasible maximum likelihood estimation procedure using the EM algorithm and the asymptotic standard errors of parameter estimates are developed. The performance of the proposed distribution is illustrated by means of real datasets and simulation analysis.

Nonlinear regression models based on the normal mean–variance mixture of Birnbaum–Saunders distribution

This paper presents a new extension of nonlinear regression models constructed by assuming the normal mean–variance mixture of Birnbaum–Saunders distribution for the unobserved error terms. A computationally analytical EM-type algorithm is developed for computing maximum likelihood estimates. The observed information matrix is derived for obtaining the asymptotic standard errors of parameter estimates. The practical utility of the methodology is illustrated through both simulated and real data sets.

Severity of pedestrian injuries due to traffic crashes at signalized intersections in Hong Kong: a Bayesian spatial logit model

SummaryThe present study intended to (1) investigate the injury risk of pedestrian casualties involved in traffic crashes at signalized intersections in Hong Kong; (2) determine the effect of pedestrian volumes on the severity levels of pedestrian injuries; and (3) explore the role of spatial correlation in econometric crash‐severity models. The data from 1889 pedestrian‐related crashes at 318 signalized intersections between 2008 and 2012 were elaborately collected from the Traffic Accident Database System maintained by the Hong Kong Transport Department. To account for the cross‐intersection heterogeneity, a Bayesian hierarchical logit model with uncorrelated and spatially correlated random effects was developed. An intrinsic conditional autoregressive prior was specified for the spatial correlation term. Results revealed that (1) signalized intersections with greater pedestrian volumes generally exhibited a lower injury risk; (2) ignoring the spatial correlation potentially results in reduced model goodness‐of‐fit, an underestimation of variability and standard error of parameter estimates, as well as inconsistent, biased, and erroneous inference; (3) special attention should be paid to the following factors, which led to a significantly higher probability of pedestrians being killed or sustaining severe injury: pedestrian age greater than 65 years, casualties with head injuries, crashes that occurred on footpaths that were not obstructed/overcrowded, heedless or inattentive crossing, crashes on the two‐way carriageway, and those that occurred near tram or light‐rail transit stops. Copyright © 2017 John Wiley & Sons, Ltd.

The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables.

Three estimation methods with robust corrections-maximum likelihood (ML) using the sample covariance matrix, unweighted least squares (ULS) using a polychoric correlation matrix, and diagonally weighted least squares (DWLS) using a polychoric correlation matrix-have been proposed in the literature, and are considered to be superior to normal theory-based maximum likelihood when observed variables in latent variable models are ordinal. A Monte Carlo simulation study was carried out to compare the performance of ML, DWLS, and ULS in estimating model parameters, and their robust corrections to standard errors, and chi-square statistics in a structural equation model with ordinal observed variables. Eighty-four conditions, characterized by different ordinal observed distribution shapes, numbers of response categories, and sample sizes were investigated. Results reveal that (a) DWLS and ULS yield more accurate factor loading estimates than ML across all conditions; (b) DWLS and ULS produce more accurate interfactor correlation estimates than ML in almost every condition; (c) structural coefficient estimates from DWLS and ULS outperform ML estimates in nearly all asymmetric data conditions; (d) robust standard errors of parameter estimates obtained with robust ML are more accurate than those produced by DWLS and ULS across most conditions; and (e) regarding robust chi-square statistics, robust ML is inferior to DWLS and ULS in controlling for Type I error in almost every condition, unless a large sample is used (N = 1,000). Finally, implications of the findings are discussed, as are the limitations of this study as well as potential directions for future research. (PsycINFO Database Record

The Impact of Ignoring the Level of Nesting Structure in Nonparametric Multilevel Latent Class Models.

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In the present study, a simulation study was conducted to investigate the impact of ignoring the higher-level nesting structure. Three criteria-the model selection accuracy, the classification quality, and the parameter estimation accuracy-were used to evaluate the impact of ignoring the nested data structure. The results of the simulation study showed that ignoring higher-level nesting structure in an MLCM resulted in the poor performance of the Bayesian information criterion to recover the true latent structure, the inaccurate classification of individuals into latent classes, and the inflation of standard errors for parameter estimates, while the parameter estimates were not biased. This article concludes with remarks on ignoring the nested structure in nonparametric MLCMs, as well as recommendations for applied researchers when LCM is used for data collected from a multilevel nested structure.

Seasonal Resource Selection and Distributional Response by Elk to Development of a Natural Gas Field

Global energy demand is predicted to increase dramatically, suggesting the need to understand the role of disturbance from energy development better and to develop more efficient conservation strategies for affected wildlife populations. We evaluated elk (Cervus elaphus) response to disturbance associated with natural gas development in summer and winter, including shifts in resource selection and concomitant distribution. We collected elk locations prior to (1992–1995) and during (2008–2010) coal bed natural gas (CBNG) development in the ∼ 498-km2 Fortification Creek Area (FCA) of northeastern Wyoming, USA, where approximately 700 CBNG wells and 542 km of collector, local, and resource roads were developed from 2000 through 2010. We developed resource selection functions for summer and winter using coordinate data from VHF-collared female elk prior to CBNG development and similar location data from GPS-collared female elk during CBNG development to assess spatial selection shifts. By pooling across all locations we created population level models for each time period (e.g., pre- and during development) and incorporated individual variation through bootstrapping standard errors for parameter estimates. Comparison of elk resource selection prior to and during natural gas development demonstrated behavioral and distributional shifts whereby during development, elk demonstrated a higher propensity to use distance and escape cover to minimize exposure to roads. Specifically, during-development elk selected areas with greater Rocky Mountain juniper (Juniperus scopulorum Sarg.) cover, increased terrain ruggedness, and farther from CBNG roads than prior to development. Elk distributional changes resulting from avoidance behavior led to a loss of high-use areas by 43.1% and 50.2% in summer and winter, respectively. We suggest reducing traffic, protecting woody escape cover, and maintaining refugia within the energy-development footprint to promote persistence of elk within energy fields.