Comparison of four performance models in quantifying the inequality of leaf and fruit size distribution

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t-tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution.

An accelerated failure time regression model for illness-death data: A frailty approach

This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well-known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided expectation-maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty-based illness-death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.

An information ratio-based goodness-of-fit test for copula models on censored data

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness.

Introduction to the Use of Linear and Nonlinear Regression Analysis in Quantitative Biological Assays

Biological assays are essential tools in biomedical and pharmaceutical research. In simplest terms, such an assay is an analytical method used to measure or predict a response in a biological system in the presence of a given stimulus (e.g., drug). The inherent complexity involved in evaluating a biological system requires the use of rigorous and appropriate tools for data analysis. Linear and nonlinear regression models represent critically important statistical analyses used to define the relationships between variables of interest in biological systems. Recent challenges relating to the reproducibility of published data suggest the absence of standardized and routine use of statistics to support experimental results across a wide range of scientific disciplines. The current situation warrants an introductory review of basic regression concepts using current, practical examples, along with references to in-depth resources. The goal is to provide the necessary information to help standardize the analysis of biological assays in academic research and drug discovery and development, elevating their utility and increasing data transparency and reproducibility. © 2023 The Authors. Current Protocols published by Wiley Periodicals LLC.

Is the Area Under Curve Appropriate for Evaluating the Fit of Psychometric Models?

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as χ2, M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian information criterion (BIC) for relative comparisons. Recent developments show a merging trend of psychometric and machine learnings, yet there remains a gap in the model fit evaluation, specifically the use of the area under curve (AUC). This study focuses on the behaviors of AUC in fitting IRT models. Rounds of simulations were conducted to investigate AUC's appropriateness (e.g., power and Type I error rate) under various conditions. The results show that AUC possessed certain advantages under certain conditions such as high-dimensional structure with two-parameter logistic (2PL) and some three-parameter logistic (3PL) models, while disadvantages were also obvious when the true model is unidimensional. It cautions researchers about the dangers of using AUC solely in evaluating psychometric models.

Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment

Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators' level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered.

Using Multivariate Adaptive Regression Splines to Estimate the Body Weight of Savanna Goats

The Savanna goat breed is an indigenous goat breed in South Africa that is reared for meat production. Live body weight is an important tool for livestock management, selection and feeding. The use of multivariate adaptive regression splines (MARS) to predict the live body weight of Savanna goats remains poorly understood. The study was conducted to investigate the influence of linear body measurements on the body weight of Savanna goats using MARS. In total, 173 Savanna goats between the ages of two and five years were used to collect body weight (BW), body length (BL), heart girth (HG), rump height (RH) and withers height (WH). MARS was used as a data mining algorithm for data analysis. The best predictive model was achieved from the training dataset with the highest coefficient of determination and Pearson's correlation coefficient (0.959 and 0.961), respectively. BW was influenced positively when WH > 63 cm and HG >100 cm with a coefficient of 0.51 and 2.71, respectively. The interaction of WH > 63 cm and BL < 75 cm, WH < 68 cm and HG < 100 cm with a coefficient of 0.28 and 0.02 had a positive influence on Savanna goat BW, while male goats had a negative influence (-4.57). The findings of the study suggest that MARS can be used to estimate the BW in Savanna goats. This finding will be helpful to farmers in the selection of breeding stock and precision in the day-to-day activities such as feeding, marketing and veterinary services.

Goodness-of-fit test for a parametric mixture cure model with partly interval-censored data

Partly interval-censored event time data arise naturally in medical, biological, sociological and demographic studies. In practice, some patients may be immune from the event of interest, invoking a cure model for survival analysis. Choosing an appropriate parametric distribution for the failure time of susceptible patients is an important step to fully structure the mixture cure model. In the literature, goodness-of-fit tests for survival models are usually restricted to uncensored or right-censored data. We fill in this gap by proposing a new goodness-of-fit test dealing with partly interval-censored data under mixture cure models. Specifically, we investigate whether a parametric distribution can fit the susceptible part by using a Cramér-von Mises type of test, and establish the asymptotic distribution of the test . Empirically, the critical value is determined from the bootstrap resamples. The proposed test, compared to the traditional leveraged bootstrap approach, yields superior practical results under various settings in extensive simulation studies. Two clinical data sets are analyzed to illustrate our method.

Goodness of fit tests for random multigraph models

Goodness of fit tests for two probabilistic multigraph models are presented. The first model is random stub matching given fixed degrees (RSM) so that edge assignments to vertex pair sites are dependent, and the second is independent edge assignments (IEA) according to a common probability distribution. Tests are performed using goodness of fit measures between the edge multiplicity sequence of an observed multigraph, and the expected one according to a simple or composite hypothesis. Test statistics of Pearson type and of likelihood ratio type are used, and the expected values of the Pearson statistic under the different models are derived. Test performances based on simulations indicate that even for small number of edges, the null distributions of both statistics are well approximated by their asymptotic χ 2 -distribution. The non-null distributions of the test statistics can be well approximated by proposed adjusted χ 2 -distributions used for power approximations. The influence of RSM on both test statistics is substantial for small number of edges and implies a shift of their distributions towards smaller values compared to what holds true for the null distributions under IEA. Two applications on social networks are included to illustrate how the tests can guide in the analysis of social structure.

Reliability of Calculation of Dynamic Modulus for Asphalt Mixtures Using Different Master Curve Models and Shift Factor Equations

To develop a mechanistic-empirical pavement design system for Norwegian conditions, this paper evaluates the influence of the adoption of different models and shifting techniques on the determination of dynamic modulus master curves of asphalt mixtures. Two asphalt mixture types commonly used in Norway, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA) containing neat bitumen and polymer-modified bitumen, were prepared by the roller compactor, and their dynamic moduli were determined by the cyclic indirect tensile test. The dynamic modulus master curves were constructed using the standard logistic sigmoidal model, a generalized logistic sigmoidal model and the Christensen–Anderson–Marasteanu model. The shifting techniques consisted of log-linear, quadratic polynomial function, Arrhenius, William–Landel–Ferry and Kaelble methods. The absolute error, normalised square error and goodness-of-fit statistics encompassing standard error ratio and coefficient of determination were used to appraise the models and shifting methods. The results showed that the standard logistic sigmoidal model and the Williams–Landel–Ferry equation had the most suitable fits for the specimens tested. The asphalt mixtures containing neat bitumen had a better fit than the ones containing polymer-modified bitumen. The Kaelble equation and log-linear equation led to similar results. These findings provide a relevant recommendation for the mechanistic-empirical pavement design system.

Noninvasive detection of fetal genetic variations through polymorphic site sequencing of maternal plasma DNA

BACKGROUND

Noninvasive prenatal testing (NIPT) for common fetal aneuploidies has been widely adopted in clinical practice for its sensitivity and accuracy. However, detection of pathogenic copy number variations (pCNVs) or monogenic disorders (MDs) is inaccurate and not cost effective. Here we developed an assay, the noninvasive prenatal testing based on goodness-of-fit and graphical analysis of polymorphic sites (GGAP-NIPT), to simultaneously detect fetal aneuploidies, pCNVs, and MDs.

METHODS

Polymorphic sites were amplicon sequenced, followed by fetal fraction estimation using allelic reads counts and a robust linear regression model. The genotype of each polymorphic site or MD variant was then determined by allelic goodness-of-fit test or graphical analysis of its different alleles. Finally, aneuploidies and pCNVs were detected using collective goodness-of-fit test to select each best fit from all possible chromosomal models.

RESULTS

Of the simulated 1,692 chromosomes and 1,895 pCNVs, all normals and variants were correctly identified (accuracy 100%, sensitivity 100%, specificity 100%). Of the 713,320 simulated MD variants, more than 90% of the genotypes were determined correctly (accuracy: 98.3 ± 1.0%; sensitivity: 98.7 ± 1.96%; specificity: 99.7 ± 0.6%). The detection accuracies of three public MD datasets were 95.70%, 93.43%, and 96.83%. For an MD validation dataset, 75% detection accuracy was observed when a site with sample replicates was analyzed individually, and 100% accuracy was achieved when analyzed collectively.

CONCLUSIONS

Fetal aneuploidies, pCNVs, and MDs could be detected simultaneously and with high accuracy through amplicon sequencing of polymorphic and target sites, which showed the potential of extending NIPT to an expanded panel of genetic disorders.

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.

The Hellinger Distance within Posterior Predictive Assessment for Investigating Multidimensionality in IRT Models

Under the Bayesian approach, posterior predictive model checking (PPMC) has become a popular tool for fit assessment of item response theory (IRT) models. In this study, we propose the use of the Hellinger distance within PPMC to quantify the distance between the realized and the predictive distribution of the model-based covariance for item pairs. Specifically, the case of multidimensional data analyzed with a unidimensional approach is taken into account. The results of the simulation study show the effectiveness of the method in detecting model misfit and the sensitivity to the trait correlations. An application to real data on tourism perceptions shows the feasibility of the method in practice and especially the capability of detecting potential misfit attributed to specific items.

Associations of temperament types and gender of early adolescents and teachers with adolescents' school well-being

This study examined the role of temperament type and gender of adolescents and teachers in adolescents' well-being in school. The sample consisted of 677 Finnish students and 56 classroom teachers. Parents rated adolescent temperament and teachers rated their own temperament in autumn of Grade 6. Self-reports of school well-being among adolescents were obtained in autumn and the fall of Grade 6. The results showed that being a girl and having resilient temperament type predicted higher school well-being. In turn, boys with undercontrolled temperament, who were otherwise at risk for decreased school well-being, particularly benefited from having a female teacher with resilient temperament. Overall, the results suggest that both adolescent temperament type and gender play important roles in adolescents' well-being in school.

Rosalie Kane: Honoring Her Contributions to the Development of Assisted Living

This article reflects on the foundational contributions of Rosalie A. Kane to the rise of assisted living in the 1980s and 90s. The author, called the founder of the "Oregon model of assisted living," offers an insider's perspective of how Dr. Kane's insights - and personality-inspired a shift in the options for long term care from a model based on safety and medical treatment to one based on personal choice and independence. Along the way, the article offers an example of how sustained dialogue between theory and practice can spark concrete change. The article also assesses the personality traits that made Rosalie Kane a gifted collaborator and a generator of ideas that reached beyond the academy into real life. A brief glance at Dr. Kane's unfinished agenda speaks to her vision for today's gerontologists and social workers.

Goat Milk Nutritional Quality Software-Automatized Individual Curve Model Fitting, Shape Parameters Calculation and Bayesian Flexibility Criteria Comparison

Simple Summary

The high costs of genotyping normally compel researchers to work with reduced sample sizes. Contextually, population observations may no longer compensate for the lack of sufficient data to fit lactation curves, hindering model efficiency, explicative ability, and predictive potential. Individualized lactation curve analyses may save these drawbacks, but may be time-demanding, which may be prevented through computational automatization. An SPSS model syntax was defined and used to evaluate the individual performance of 49 linear and non-linear models to fit the curve described by the milk components of the milk of 159 Murciano-Granadina does selected for genotyping analyses. Protein, fat, dry matter, lactose, and somatic cell counts curves were evaluated and modelled, while peak and persistence were estimated to maximize the ability to understand and anticipate productive responses in Murciano-Granadina goats, which may translate into improved profitability of goat milk as a product.

Abstract

SPSS syntax was described to evaluate the individual performance of 49 linear and non-linear models to fit the milk component evolution curve of 159 Murciano-Granadina does selected for genotyping analyses. Peak and persistence for protein, fat, dry matter, lactose, and somatic cell counts were evaluated using 3107 controls (3.91 ± 2.01 average lactations/goat). Best-fit (adjusted R²) values (0.548, 0.374, 0.429, and 0.624 for protein, fat, dry matter, and lactose content, respectively) were reached by the five-parameter logarithmic model of Ali and Schaeffer (ALISCH), and for the three-parameter model of parabolic yield-density (PARYLDENS) for somatic cell counts (0.481). Cross-validation was performed using the Minimum Mean-Square Error (MMSE). Model comparison was performed using Residual Sum of Squares (RSS), Mean-Squared Prediction Error (MSPE), adjusted R² and its standard deviation (SD), Akaike (AIC), corrected Akaike (AICc), and Bayesian information criteria (BIC). The adjusted R² SD across individuals was around 0.2 for all models. Thirty-nine models successfully fitted the individual lactation curve for all components. Parametric and computational complexity promote variability-capturing properties, while model flexibility does not significantly (p > 0.05) improve the predictive and explanatory potential. Conclusively, ALISCH and PARYLDENS can be used to study goat milk composition genetic variability as trustable evaluation models to face future challenges of the goat dairy industry.

Model Comparison Metrics Require Adaptive Correction if Parameters Are Discretized: Proof-of-Concept Applied to Transient Signals in Dynamic PET

Linear parametric neurotransmitter PET (lp-ntPET) is a novel kinetic model that estimates the temporal characteristics of a transient neurotransmitter component in PET data. To preserve computational simplicity in estimation, the parameters of the nonlinear term that describe this transient signal are discretized, and only a limited set of values for each parameter are allowed. Thus, linear estimation can be performed. Linear estimation is implemented using predefined basis functions that incorporate the discretized parameters. The implementation of the model using discretized parameters poses unique challenges for significance testing. Significance testing employs model comparison metrics to determine the significance of the improvement of the fit accomplished by including a basis function, i.e. it determines the presence of a transient signal in the PET data. A false positive occurs when the bases overfit data that do not contain a transient component. The number of parameters in a model, p, is necessary to determine the degrees of freedom in the model. In turn, p is crucial for the calculation of model selection metrics and controlling the false positive rate (FPR). In this work, we first explore the effect of parameter discretization on FPR by fitting simulated null data with varying numbers of bases. We demonstrate the dependence of FPR on number of bases. Then, we propose a correction to the number of parameters in the model, p^eff , which adapts to the number of bases used. Implementing model selection with p^eff maintains a stable FPR independent of number of bases.

Reliability assessment for blood oxygen saturation levels measured with optoacoustic imaging

SIGNIFICANCE

Quantitative optoacoustic (OA) imaging has the potential to provide blood oxygen saturation (SO2) estimates due to the proportionality between the measured signal and the blood's absorption coefficient. However, due to the wavelength-dependent attenuation of light in tissue, a spectral correction of the OA signals is required, and a prime challenge is the validation of both the optical characterization of the tissue and the SO2.

AIM

We propose to assess the reliability of SO2 levels retrieved from spectral fitting by measuring the similarity of OA spectra to the fitted blood absorption spectra.

APPROACH

We introduce a metric that quantifies the trends of blood spectra by assigning a pair of spectral slopes to each spectrum. The applicability of the metric is illustrated with in vivo measurements on a human forearm.

RESULTS

We show that physiologically sound SO2 values do not necessarily imply a successful spectral correction and demonstrate how the metric can be used to distinguish SO2 values that are trustworthy from unreliable ones.

CONCLUSIONS

The metric is independent of the methods used for the OA data acquisition, image reconstruction, and spectral correction, thus it can be readily combined with existing approaches, in order to monitor the accuracy of quantitative OA imaging.

Planning and analyzing clinical trials with competing risks: Recommendations for choosing appropriate statistical methodology

In the analysis of time-to-event data, competing risks occur when multiple event types are possible, and the occurrence of a competing event precludes the occurrence of the event of interest. In this situation, statistical methods that ignore competing risks can result in biased inference regarding the event of interest. We review the mechanisms that lead to bias and describe several statistical methods that have been proposed to avoid bias by formally accounting for competing risks in the analyses of the event of interest. Through simulation, we illustrate that Gray's test should be used in lieu of the logrank test for nonparametric hypothesis testing. We also compare the two most popular models for semiparametric modelling: the cause-specific hazards (CSH) model and Fine-Gray (F-G) model. We explain how to interpret estimates obtained from each model and identify conditions under which the estimates of the hazard ratio and subhazard ratio differ numerically. Finally, we evaluate several model diagnostic methods with respect to their sensitivity to detect lack of fit when the CSH model holds, but the F-G model is misspecified and vice versa. Our results illustrate that adequacy of model fit can strongly impact the validity of statistical inference. We recommend analysts incorporate a model diagnostic procedure and contingency to explore other appropriate models when designing trials in which competing risks are anticipated.

Restricted Recalibration of Item Response Theory Models

In item response theory (IRT), it is often necessary to perform restricted recalibration (RR) of the model: A set of (focal) parameters is estimated holding a set of (nuisance) parameters fixed. Typical applications of RR include expanding an existing item bank, linking multiple test forms, and associating constructs measured by separately calibrated tests. In the current work, we provide full statistical theory for RR of IRT models under the framework of pseudo-maximum likelihood estimation. We describe the standard error calculation for the focal parameters, the assessment of overall goodness-of-fit (GOF) of the model, and the identification of misfitting items. We report a simulation study to evaluate the performance of these methods in the scenario of adding a new item to an existing test. Parameter recovery for the focal parameters as well as Type I error and power of the proposed tests are examined. An empirical example is also included, in which we validate the pediatric fatigue short-form scale in the Patient-Reported Outcome Measurement Information System (PROMIS), compute global and local GOF statistics, and update parameters for the misfitting items.

Psychometric evaluation of the Chinese version of the Snizek-revised Hall's Professionalism Inventory Scale

Objective

This study was performed to assess the reliability and validity of the Chinese version of the Snizek-revised Hall’s Professionalism Inventory Scale (C-SR-HPIS).

Methods

Exploratory factor analysis and confirmatory factor analysis were used to evaluate the construct validity of the C-SR-HPIS. The average variance extracted (AVE) and square root of the AVE were calculated and correlation analyses were performed to test the convergent validity and discriminant validity, respectively. Cronbach’s alpha (α) coefficient was used to test the internal consistency reliability.

Results

Data for 355 clinical nurses in mainland China were collected. Five factors were extracted, accounting for 58.86% of the total explained variance, and 20 items were selected for the C-SR-HPIS. The confirmatory factor analysis suggested good fitness of the modified model. The AVE was acceptable for convergent validity. The square roots of the AVE of the five factors were larger than their correlation coefficients with other factors, showing suitable discriminant validity. Cronbach’s α coefficient of internal consistency reliability of the overall scale was 0.76, indicating good reliability of the scale.

Conclusions

This study demonstrated good reliability and validity of the C-SR-HPIS and provides a quantitative tool for the assessment of nursing professionalism in China.

Clinical utility of ICD-11 diagnostic guidelines for high-burden mental disorders: results from mental health settings in 13 countries

In this paper we report the clinical utility of the diagnostic guidelines for ICD-11 mental, behavioural and neurodevelopmental disorders as assessed by 339 clinicians in 1,806 patients in 28 mental health settings in 13 countries. Clinician raters applied the guidelines for schizophrenia and other primary psychotic disorders, mood disorders (depressive and bipolar disorders), anxiety and fear-related disorders, and disorders specifically associated with stress. Clinician ratings of the clinical utility of the proposed ICD-11 diagnostic guidelines were very positive overall. The guidelines were perceived as easy to use, corresponding accurately to patients' presentations (i.e., goodness of fit), clear and understandable, providing an appropriate level of detail, taking about the same or less time than clinicians' usual practice, and providing useful guidance about distinguishing disorder from normality and from other disorders. Clinicians evaluated the guidelines as less useful for treatment selection and assessing prognosis than for communicating with other health professionals, though the former ratings were still positive overall. Field studies that assess perceived clinical utility of the proposed ICD-11 diagnostic guidelines among their intended users have very important implications. Classification is the interface between health encounters and health information; if clinicians do not find that a new diagnostic system provides clinically useful information, they are unlikely to apply it consistently and faithfully. This would have a major impact on the validity of aggregated health encounter data used for health policy and decision making. Overall, the results of this study provide considerable reason to be optimistic about the perceived clinical utility of the ICD-11 among global clinicians.

Summed Score Likelihood-Based Indices for Testing Latent Variable Distribution Fit in Item Response Theory

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood-based statistics may be useful for testing latent variable distribution fit. We develop Satorra-Bentler type moment adjustments to approximate the test statistics' tail-area probability. A simulation study was conducted to examine the calibration and power of the unadjusted and adjusted statistics in various simulation conditions. Results show that the proposed indices have tail-area probabilities that can be closely approximated by central chi-squared random variables under the null hypothesis. Furthermore, the test statistics are focused. They are powerful for detecting latent variable distributional assumption violations, and not sensitive (correctly) to other forms of model misspecification such as multidimensionality. As a comparison, the goodness-of-fit statistic M ₂ has considerably lower power against latent variable nonnormality than the proposed indices. Empirical data from a patient-reported health outcomes study are used as illustration.

Snug as a Bug: Goodness of Fit and Quality of Models

In elucidating risk factors, or attempting to make predictions about the behavior of subjects in our biomedical studies, we often build statistical models. These models are meant to capture some aspect of reality, or some real-world process underlying the phenomena we are examining. However, no model is perfect, and it is thus important to have tools to assess how accurate models are. In this commentary, we delve into the various roles that our models can play. Then we introduce the notion of the goodness of fit of models and lay the ground work for further study of diagnostic tests for assessing both the fidelity of our models and the statistical assumptions underlying them.

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded

The coefficient of determination R² quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R² for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R² that we called for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.

Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects exist or whether they are empirically meaningful. Hence, raising conclusions from the outcomes of statistical analyses is subject to limitations. NHST has been criticized for its misuse and the misconstruction of its outcomes, also stressing its inability to meet expectations that it was never designed to fulfil. Ironically, alternatives to NHST are identical in these respects, something that has been overlooked in their presentation. Three of those alternatives are discussed here (estimation via confidence intervals and effect sizes, quantification of evidence via Bayes factors, and mere reporting of descriptive statistics). None of them offers a solution to the problems that NHST is purported to have, all of them are susceptible to misuse and misinterpretation, and some bring around their own problems (e.g., Bayes factors have a one-to-one correspondence with p values, but they are entirely deprived of an inferential framework). Those alternatives also fail to cover a broad area of inference not involving distributional parameters, where NHST procedures remain the only (and suitable) option. Like knives or axes, NHST is not inherently evil; only misuse and misinterpretation of its outcomes needs to be eradicated.

The Indecision Model of Psychophysical Performance in Dual-Presentation Tasks: Parameter Estimation and Comparative Analysis of Response Formats

Psychophysical data from dual-presentation tasks are often collected with the two-alternative forced-choice (2AFC) response format, asking observers to guess when uncertain. For an analytical description of performance, psychometric functions are then fitted to data aggregated across the two orders/positions in which stimuli were presented. Yet, order effects make aggregated data uninterpretable, and the bias with which observers guess when uncertain precludes separating sensory from decisional components of performance. A ternary response format in which observers are also allowed to report indecision should fix these problems, but a comparative analysis with the 2AFC format has never been conducted. In addition, fitting ternary data separated by presentation order poses serious challenges. To address these issues, we extended the indecision model of psychophysical performance to accommodate the ternary, 2AFC, and same-different response formats in detection and discrimination tasks. Relevant issues for parameter estimation are also discussed along with simulation results that document the superiority of the ternary format. These advantages are demonstrated by fitting the indecision model to published detection and discrimination data collected with the ternary, 2AFC, or same-different formats, which had been analyzed differently in the sources. These examples also show that 2AFC data are unsuitable for testing certain types of hypotheses. matlab and R routines written for our purposes are available as Supplementary Material, which should help spread the use of the ternary format for dependable collection and interpretation of psychophysical data.

A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation

The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf‐shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf‐shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf‐shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy.

Goodness of fit tools for dose-response meta-analysis of binary outcomes

Goodness of fit evaluation should be a natural step in assessing and reporting dose-response meta-analyses from aggregated data of binary outcomes. However, little attention has been given to this topic in the epidemiological literature, and goodness of fit is rarely, if ever, assessed in practice. We briefly review the two-stage and one-stage methods used to carry out dose-response meta-analyses. We then illustrate and discuss three tools specifically aimed at testing, quantifying, and graphically evaluating the goodness of fit of dose-response meta-analyses. These tools are the deviance, the coefficient of determination, and the decorrelated residuals-versus-exposure plot. Data from two published meta-analyses are used to show how these three tools can improve the practice of quantitative synthesis of aggregated dose-response data. In fact, evaluating the degree of agreement between model predictions and empirical data can help the identification of dose-response patterns, the investigation of sources of heterogeneity, and the assessment of whether the pooled dose-response relation adequately summarizes the published results. © 2015 The Authors. Research Synthesis Methods published by John Wiley & Sons, Ltd.

How to discriminate conclusively among different models of decision making?

A popular and successful class of decision-making models (the "evidence accumulator" models) has been recently challenged by a new hypothesis called the urgency-gating model. Hawkins et al. (J Neurophysiol 114: 40-47, 2015) used a sophisticated curve-fitting procedure to show that these models are discriminable and thus testable in constant evidence tasks. In this Neuro Forum article I raise possible limitations of such an approach, discuss some of its implications, and propose alternative solutions.

A new test and graphical tool to assess the goodness of fit of logistic regression models

A prognostic model is well calibrated when it accurately predicts event rates. This is first determined by testing for goodness of fit with the development dataset. All existing tests and graphic tools designed for the purpose suffer several drawbacks, related mainly to the subgrouping of observations or to heavy dependence on arbitrary parameters. We propose a statistical test and a graphical method to assess the goodness of fit of logistic regression models, obtained through an extension of similar techniques developed for external validation. We analytically computed and numerically verified the distribution of the underlying statistic. Simulations on a set of realistic scenarios show that this test and the well-known Hosmer-Lemeshow approach have similar type I error rates. The main advantage of this new approach is that the relationship between model predictions and outcome rates across the range of probabilities can be represented in the calibration belt plot, together with its statistical confidence. By readily spotting any deviations from the perfect fit, this new graphical tool is designed to identify, during the process of model development, poorly modeled variables that call for further investigation. This is illustrated through an example based on real data.

LOGISTIC NETWORK REGRESSION FOR SCALABLE ANALYSIS OF NETWORKS WITH JOINT EDGE/VERTEX DYNAMICS

Change in group size and composition has long been an important area of research in the social sciences. Similarly, interest in interaction dynamics has a long history in sociology and social psychology. However, the effects of endogenous group change on interaction dynamics are a surprisingly understudied area. One way to explore these relationships is through social network models. Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Although early studies of such processes were primarily descriptive, recent work on this topic has increasingly turned to formal statistical models. Although showing great promise, many of these modern dynamic models are computationally intensive and scale very poorly in the size of the network under study and/or the number of time points considered. Likewise, currently used models focus on edge dynamics, with little support for endogenously changing vertex sets. Here, the authors show how an existing approach based on logistic network regression can be extended to serve as a highly scalable framework for modeling large networks with dynamic vertex sets. The authors place this approach within a general dynamic exponential family (exponential-family random graph modeling) context, clarifying the assumptions underlying the framework (and providing a clear path for extensions), and they show how model assessment methods for cross-sectional networks can be extended to the dynamic case. Finally, the authors illustrate this approach on a classic data set involving interactions among windsurfers on a California beach.

Assessing the goodness of fit of personal risk models

We describe a flexible family of tests for evaluating the goodness of fit (calibration) of a pre-specified personal risk model to the outcomes observed in a longitudinal cohort. Such evaluation involves using the risk model to assign each subject an absolute risk of developing the outcome within a given time from cohort entry and comparing subjects' assigned risks with their observed outcomes. This comparison involves several issues. For example, subjects followed only for part of the risk period have unknown outcomes. Moreover, existing tests do not reveal the reasons for poor model fit when it occurs, which can reflect misspecification of the model's hazards for the competing risks of outcome development and death. To address these issues, we extend the model-specified hazards for outcome and death, and use score statistics to test the null hypothesis that the extensions are unnecessary. Simulated cohort data applied to risk models whose outcome and mortality hazards agreed and disagreed with those generating the data show that the tests are sensitive to poor model fit, provide insight into the reasons for poor fit, and accommodate a wide range of model misspecification. We illustrate the methods by examining the calibration of two breast cancer risk models as applied to a cohort of participants in the Breast Cancer Family Registry. The methods can be implemented using the Risk Model Assessment Program, an R package freely available at http://stanford.edu/~ggong/rmap/.

A diversity index for model space selection in the estimation of benchmark and infectious doses via model averaging

In chemical and microbial risk assessments, risk assessors fit dose-response models to high-dose data and extrapolate downward to risk levels in the range of 1-10%. Although multiple dose-response models may be able to fit the data adequately in the experimental range, the estimated effective dose (ED) corresponding to an extremely small risk can be substantially different from model to model. In this respect, model averaging (MA) provides more robustness than a single dose-response model in the point and interval estimation of an ED. In MA, accounting for both data uncertainty and model uncertainty is crucial, but addressing model uncertainty is not achieved simply by increasing the number of models in a model space. A plausible set of models for MA can be characterized by goodness of fit and diversity surrounding the truth. We propose a diversity index (DI) to balance between these two characteristics in model space selection. It addresses a collective property of a model space rather than individual performance of each model. Tuning parameters in the DI control the size of the model space for MA.

On assessing model fit for distribution-free longitudinal models under missing data

The generalized estimating equation (GEE), a distribution-free, or semi-parametric, approach for modeling longitudinal data, is used in a wide range of behavioral, psychotherapy, pharmaceutical drug safety, and healthcare-related research studies. Most popular methods for assessing model fit are based on the likelihood function for parametric models, rendering them inappropriate for distribution-free GEE. One rare exception is a score statistic initially proposed by Tsiatis for logistic regression (1980) and later extended by Barnhart and Willamson to GEE (1998). Because GEE only provides valid inference under the missing completely at random assumption and missing values arising in most longitudinal studies do not follow such a restricted mechanism, this GEE-based score test has very limited applications in practice. We propose extensions of this goodness-of-fit test to address missing data under the missing at random assumption, a more realistic model that applies to most studies in practice. We examine the performance of the proposed tests using simulated data and demonstrate the utilities of such tests with data from a real study on geriatric depression and associated medical comorbidities.

Introduction to statistical modelling: linear regression

In many studies we wish to assess how a range of variables are associated with a particular outcome and also determine the strength of such relationships so that we can begin to understand how these factors relate to each other at a population level. Ultimately, we may also be interested in predicting the outcome from a series of predictive factors available at, say, a routine clinic visit. In a recent article in Rheumatology, Desai et al. did precisely that when they studied the prediction of hip and spine BMD from hand BMD and various demographic, lifestyle, disease and therapy variables in patients with RA. This article aims to introduce the statistical methodology that can be used in such a situation and explain the meaning of some of the terms employed. It will also outline some common pitfalls encountered when performing such analyses.

Somatotopic finger mapping using MEG: toward an optimal stimulation paradigm

OBJECTIVE

In non-invasive somatotopic mapping based on neuromagnetic source analysis, the recording time can be shortened and accuracy improved by applying simultaneously vibrotactile stimuli at different frequencies to multiple body sites and recording multiple steady-state responses. This study compared the reliability of sensory evoked responses, source localization performance, and reproducibility of digit maps for three different stimulation paradigms.

METHODS

Vibrotactile stimuli were applied to the fingertip and neuromagnetic steady-state responses were recorded. Index and middle fingers were stimulated either sequentially in separate blocks, simultaneously at different frequencies, or in alternating temporal order within a block.

RESULTS

Response amplitudes were largest and source localization was most accurate between 21 and 23 Hz. Separation of adjacent digits was significant for all paradigms in all participants. Suppressive interactions occurred between simultaneously applied stimuli. However, when frequently alternating between stimulus sites, the higher stimulus novelty resulted in increased amplitudes and superior localization performance.

CONCLUSIONS

When receptive fields are strongly overlapping, the alternating stimulation is preferable over recording multiple steady state responses.

SIGNIFICANCE

The new paradigm improved the measurement of the distance of somatotopic finger representation in human primary somatosensory cortex, which is an important metric for neuroplastic reorganization after learning and rehabilitation training.

Using Markov chain Monte Carlo (MCMC) to visualize and test the linearity assumption of the Bradley-Terry class of models

The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley-Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley-Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011, PLoS One, 6, e17817) should be considered.

Use the Correlation Coefficient to Summarize Regression Performance?

The correlation coefficient is commonly used to indicate the quality of fit in regression. This practice is questionable.

Analyzing Competing Risk Data Using the R timereg Package

In this paper we describe flexible competing risks regression models using the comp.risk() function available in the timereg package for R based on Scheike et al. (2008). Regression models are specified for the transition probabilities, that is the cumulative incidence in the competing risks setting. The model contains the Fine and Gray (1999) model as a special case. This can be used to do goodness-of-fit test for the subdistribution hazards' proportionality assumption (Scheike and Zhang 2008). The program can also construct confidence bands for predicted cumulative incidence curves.We apply the methods to data on follicular cell lymphoma from Pintilie (2007), where the competing risks are disease relapse and death without relapse. There is important non-proportionality present in the data, and it is demonstrated how one can analyze these data using the flexible regression models.

Low inhibitory control and restrictive feeding practices predict weight outcomes

OBJECTIVE

A priority for research is to identify individuals early in development who are particularly susceptible to weight gain in the current, obesogenic environment. This longitudinal study investigated whether early individual differences in inhibitory control, an aspect of temperament, predicted weight outcomes and whether parents' restrictive feeding practices moderated this relation.

STUDY DESIGN

Participants included 197 non-Hispanic white girls and their parents; families were assessed when girls were 5, 7, 9, 11, 13, and 15 years old. Measures included mothers' reports of girls' inhibitory control levels, girls' reports of parental restriction in feeding, girls' body mass indexes (BMIs), and parents' BMIs, education, and income.

RESULTS

Girls with lower inhibitory control at age 7 had higher concurrent BMIs, greater weight gain, higher BMIs at all subsequent time points, and were 1.95 times more likely to be overweight at age 15. Girls who perceived higher parental restriction exhibited the strongest inverse relation between inhibitory control and weight status.

CONCLUSION

Variability in inhibitory control could help identify individuals who are predisposed to obesity risk; the current findings also highlight the importance of parenting practices as potentially modifiable factors that exacerbate or attenuate this risk.

Family and neighborhood fit or misfit and the adaptation of Mexican Americans

In this study, a person-environment fit model was used to understand the independent and combined roles of family and neighborhood characteristics on the adjustment of adults and children in a sample of 750 Mexican American families. Latent class analysis was used to identify six qualitatively distinct family types and three quantitatively distinct neighborhood types using socioeconomic and cultural indicators at each level. The results showed that members of single-parent Mexican American families may be particularly at-risk, members of the lowest-income immigrant families reported fewer adaptation problems if they lived in low-income neighborhoods dominated by immigrants, members of economically successful immigrant families may be more at-risk in integrated middle class neighborhoods than in low-income neighborhoods dominated by immigrants, and members of two-parent immigrant families appear to be rather resilient in most settings despite their low socioeconomic status.

Temperament-Based Intervention: Re-examining Goodness of Fit

The purpose of this paper is to discuss how recent advances in the temperament field have contributed to the scientific foundation of temperament-based intervention. A presentation of the historical origins of temperament-based intervention is followed by examples of recent studies that add to its empirical support. Guidelines for developing and adapting temperament-based interventions are offered. The goodness of fit model, frequently used as a basis for temperament-based intervention, is re-examined through the lens of self-regulation.

Use of resampling to select among alternative error structure specifications for GLMM analyses of repeated measurements

Autocorrelated error and missing data due to dropouts have fostered interest in the flexible general linear mixed model (GLMM) procedures for analysis of data from controlled clinical trials. The user of these adaptable statistical tools must, however, choose among alternative structural models to represent the correlated repeated measurements. The fit of the error structure model specification is important for validity of tests for differences in patterns of treatment effects across time, particularly when maximum likelihood procedures are relied upon. Results can be affected significantly by the error specification that is selected, so a principled basis for selecting the specification is important. As no theoretical grounds are usually available to guide this decision, empirical criteria have been developed that focus on mode fit. The current report proposes alternative empirical criteria that focus on bootstrap estimates of actual type I error an power of tests for treatment effects. Results for model selection before and after the blind is broken are compared. Goodness-of-fit statistics also compare favourably for models fitted to the blinded or unblinded data, although the correspondence to actual type I error and power depends on the particular fit statistic that is considered.