Use Of Mixed Models Research Articles

Predicting forest parameters through generalized linear mixed models using GEDI metrics in a temperate forest in Oaxaca, Mexico

ABSTRACT Lidar sensors are active remote sensing instruments that provide data on forest structure, which serve as inputs in the prediction of forest parameters. The objective of this study was to evaluate the performance of mixed-effects models to predict basal area (BA), aboveground biomass (AGB), and wood volume (VOL) from GEDI (Global Ecosystem Dynamics Investigation) predictor variables. Linear mixed and generalized linear mixed models (LMM and GLMM) were fitted with a clustering structure as a random effect between forest parameters and GEDI metrics. LMM and GLMM performed similarly regarding root mean square error (RMSE) and correlation coefficients (r) between observed and predicted data. Our results showed moderate correlations between RH50 and BA (r = 0.53), AGB (r = 0.54), and RH80 with VOL (r = 0.62). Another finding was the correlation between GEDI predictions of the AGB density and the biomass predicted in this study, with an agreement of 79% and 77% and a RMSE of 76.95 and 82.34 Mg ha−1 for LMM and GLMM, respectively. We conclude that the use of mixed models allowed for the inclusion of both fixed and random effects that capture the systematic and random variation in the data, and they provide a flexible framework for modelling forest parameters.

Analysing postprandial amino acid responses in crossover studies with the aaresponse package for R

Nowadays, a healthier and more sustainable lifestyle is the subject of much research. One example is the use of crossover trials to investigate the uptake of proteins, usually from alternatives to animal-based sources, by healthy volunteers. The data analysis is complex and requires many decisions on the part of the scientists involved. Such a process can be streamlined and made more objective and reproducible through bespoke software. This paper describes such a software package, aaresponse\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{aaresponse}$$\\end{document}, for the R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{R}$$\\end{document} environment, available as open source. It features ample visualization functions, supports consistent curation strategies, and compares amino acid uptake of different protein meals (interventions) through the use of mixed models analysing parameters of interest like the area under the curve (AUC). The defining feature is the use of parametric curves to fit the amino acid levels over time, increasing the robustness of the approach and allowing for more strict quality control strategies.

Methodological Aspects for Applied Linguistic Research – Mixed Methods, Triangulation

Abstract Discovering human reality requires a complex methodological culture. Besides the quantitative and qualitative paradigms, this accentuates the role of mixed methods, which is a way of generating complex meanings. This paper addresses the issues of using mixed methods from a theoretical and practical perspective, delineates the development of the theory of mixed methods, and speaks for the necessity of theoretical multilingualism and the use of mixed models. It also details the triangulation typologies that give overall information about the object, subject, process, and structure of the research, and then it presents the links between mixed methods and methodological triangulation. The paper is recommended to anyone who ventures to conduct empirical studies with methodological awareness.

Using particle-resolved aerosol model simulations to guide the interpretations of cloud condensation nuclei experimental data

Ambient aerosol particles can undergo dynamic mixing processes as they coagulate with particles from other air masses and emission sources. Therefore, aerosols exist in a spectrum, from externally mixed to internally mixed. The mixing state of aerosols can affect their ability to uptake water (hygroscopicity) and their cloud condensation nuclei (CCN) activity, modifying their contribution to the planet’s total radiative budget. However, current water-uptake measurement methods may not be able to capture the complex mixing state. In this research, the dynamic mixing process was simulated by the particle-resolved aerosol model PartMC and also created by experiments in a laminar flow mixing tube. The mixing evolution of ammonium sulfate and sucrose binary mixtures were observed along with the changes in their water uptake properties expressed as the single hygroscopicity parameter, κ. The use of a mixing simulation in conjunction with experiments allow for better identification of the particle mixing state and the particle water uptake and show that no one kappa value can capture the complexity of mixing across the mixed particle size distribution. In other words, the PartMC simulations can be used as a guiding tool to interpret a system’s mixing state based on its experimental droplet activation spectra. This work demonstrates the importance of the integration and use of mixing models to aid in mixing state determination and hygroscopicity measurements of mixed systems.Copyright © 2023 American Association for Aerosol Research

On Construction and Estimation of Mixture of Log-Bilal Distributions

Recently, the use of mixed models for analyzing real data sets with infinite domains has gained favor. However, only a specific type of mixture model using mostly maximum likelihood estimation technique has been exercised in the literature, and fitting the mixture models for bounded data (between zero and one) has been neglected. In statistical mechanics, unit distributions are widely utilized to explain practical numeric values ranging between zero and one. We presented a classical examination for the trade share data set using a mixture of two log-Bilal distributions (MLBDs). We examine the features and statistical estimation of the MLBD in connection with three techniques. The sensitivity of the presented estimators with respect to model parameters, weighting proportions, sample size, and different evaluation methodologies has also been discussed. A simulation investigation is also used to endorse the estimation results. The findings on maximum likelihood estimation were more persuasive than those of existing mixture models. The flexibility and importance of the proposed distribution are illustrated by means of real datasets.

Signal processing in BCIs: An GAM-based Approach to EEG/ERP Analysis using Python

The goal of this research is to use non-linear linkages to analyze event-related potentials (ERP) in a regression framework (using splines, and General Additive Models - GAMs). The addition of extra information (such as data at the single-trial, - and even single-channel - level), as well as the computation of marginal means and contrasts, provide for a flexible and powerful manner of analyzing differences between circumstances when combined with the use of mixed models. Keywords: - Invasive; Non- Invasive; Electroencephalogram (EEGs) ; Event-Related Potentials (ERPs).

MIXED-EFFECT MODELS FOR VOLUMETRIC ESTIMATION OF LUMBER FROM NATIVE AMAZONIAN SPECIES

The objective of the present work is to test fixed effect models and compare them with different configurations of mixed models to predict lumber volume. The database came from a medium-sized sawmill located in the rural area of the municipality of Porto Grande, Amapá, Brazil. A total of 50 logs of 9 native species were used, with their volume being measured by the Smalian method. A fixed effect model proposed by Lima et al. (2018) was fitted andcompared to mixed linear models with species as a random effect. The fitting of the fixed model and the mixed models were performed using the maximum restricted likelihood method. Akaike information criteria (AIC), correlation coefficient, Maximum Likelihood Ratio Test, Square Root of the Mean Square Error (RMSE), absolute mean distance and bias were used to select the best model. According to the established criteria, the mixed models obtained better fits when compared to the fixed model, providing a reduction in the RMSE of 0.3 for an average between the mixed models of 0.26. According to the results achieved, the mixed linear models were more efficient and accurate for volume estimation. The M7 mixed model was the best fit model. The use of mixed models enables greater accuracy in estimating volume.

CONTENT-SEMANTIC FIELD OF THE CONCEPT «BLENDED LEARNING» AND MODELS OF BLENDED LEARNING

Annotation. The COVID-19 pandemic and the war in Ukraine have revealed the shortcomings of distance learning, which is why using it as a basic form of learning in basic educational programs has become not entirely effective. The most promising form of organizing the educational process in the conditions of its digital transformation is mixed learning, which involves alternating online and face-to-face learning formats. The content field and components of the concept of "blended learning" are characterized. Through mixed learning, we understand educational technology with mandatory components, which include contact classes of students with teachers, distance classes containing online communication between the teacher and students, and independent educational work of students, which is effectively organized by teachers. Pedagogical aspects of mixed learning related to its organization and implementation in an educational institution in the joint activity of the teacher and students of education are considered. An analysis of existing approaches to the selection and classification of blended learning models has been carried out. The typology of mixed learning models, which are implemented at different levels: the curriculum, the educational subject, the educational session, and the out-of-class learning technology, are substantiated. It is noted that blended learning models have their own name, and a certain internal integrity and mostly fit into one or another scientific theory. Six models of blended learning are described, which are widely presented by domestic scientists. The proposed typology is based on the joint work of a network of experimental sites. The relationship between the proposed typology of organizational and didactic models of blended learning with other typologies and separate models presented in foreign and domestic publications is shown. The problems of the typology of blended learning models were elaborated and their systematic justification was carried out. A set of criteria for delineating and considering one or another model of blended learning is singled out. It was concluded that technological and pedagogical aspects are combined in blended learning; the use of mixed models of education requires different approaches to the selection and development of educational content, educational materials and their means; the presented typology of blended learning models is an important component of the new digital didactics.

Selection of superior sweet potato genotypes for human consumption via mixed models

The growing consumer demand for sweet potato roots results in the need for genotypes with higher yields and better root quality. Thus, the objective of this study was to agronomically evaluate sweet potato genotypes via mixed models to select superior genotypes for human consumption and predict their selection gains. The study had a partially balanced triple lattice design with three replicates. As treatments, 92 sweet potato genotypes from the Universidade Federal de Lavras germplasm bank selected in the first selection cycle were evaluated along with eight controls, namely, Brazlândia Roxa, Princesa, Uruguaiana, BRS Amélia, Beauregard, UFVJM-57, UFVJM-58, and UFVJM-61. The treatments were ranked by the mixed linear model via restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP). We highlighted the 15 best genotypes for each agronomic trait, then identified the best ones overall considering all quantitative and qualitative traits. High heritability was found for the trait commercial root yield (56.31%). For all traits, there were selection gains relative to the population mean. The use of mixed models was efficient for the selection of superior sweet potato genotypes. The genotypes 2018-19-464, 2018-72-1409, 2018-72-1428, 2018-19-443, 2018-36-807, 2018-72-1418, 2018-19-455, 2018-72-1376, 2018-54-1137, 2018-54-1114, 2018-65-1249, and 2018-28-556 have good traits related to commercial root yield and root quality and may be recommended for human consumption.

Genetic variability, adaptability and, stability of safflower genotypes developed for the Brazilian conditions by REML/BLUP

AbstractSafflower (Carthamus tinctorius L.) has stood out as an oilseed crop with potential for cultivation in Brazil and can be inserted in the already consolidated production systems. However, obtaining adapted genotypes is essential for crop development, and the study of genetic variability and agronomic performance in different regions contributes to the recommendation of new cultivars. However, the genotype × environment interaction can influence the selection and recommendation of a given genotype for a region of cultivation and hinder the breeder's work. The use of mixed models allows the evaluation of genotype performance without the influence of the genotype × environment interaction, which makes recommending a genotype for a region more accurate. Four experiments were carried out in different regions of Brazil (Bauru‐SP, Botucatu‐SP and, Campo Novo do Parecis‐MT) to evaluate 10 safflower genotypes in the final stage of breeding. The genetic variability of genotypes was analyzed through similarity analysis, as well as the stability and adaptability of genotypes through mixed models. Wide variability was found between the evaluated genotypes. The use of mixed models allowed the identification of safflower genotypes with high stability and adaptability of the grain and oil yield for cultivation in Brazil.

Simulation studies comparing fixed effect and mixed models in data sets with multiple measurements in individual sampling units

Use of mixed models is advocated almost ubiquitously when regression analysis is applied in data sets that contain multiple measurements in individual sampling units that lead to intercorrelation amongst the residuals. Using two examples, simulation studies were undertaken comparing models that contained fixed effects only with mixed models in which random effects identified the sampling units within the data set. Both approaches resulted in unbiased estimates of the parameters. The choice of a suitable parameterization for the mixed model proved difficult. It was found that use of either an appropriate mixed model or a lesser-known method (‘adjusted ordinary least squares regression’) to fit models with fixed effects only could yield unbiased estimates of the standard errors of the parameter estimates. However, difficulties remain with computational methods in both cases and it cannot be assumed, a priori, that either approach is necessarily superior to the other for any particular data set.

Errors on a Speech-in-Babble Sentence Recognition Test Reveal Individual Differences in Acoustic Phonetic Perception and Babble Misallocations.

The ability to recognize words in connected speech under noisy listening conditions is critical to everyday communication. Many processing levels contribute to the individual listener's ability to recognize words correctly against background speech, and there is clinical need for measures of individual differences at different levels. Typical listening tests of speech recognition in noise require a list of items to obtain a single threshold score. Diverse abilities measures could be obtained through mining various open-set recognition errors during multi-item tests. This study sought to demonstrate that an error mining approach using open-set responses from a clinical sentence-in-babble-noise test can be used to characterize abilities beyond signal-to-noise ratio (SNR) threshold. A stimulus-response phoneme-to-phoneme sequence alignment software system was used to achieve automatic, accurate quantitative error scores. The method was applied to a database of responses from normal-hearing (NH) adults. Relationships between two types of response errors and words correct scores were evaluated through use of mixed models regression. Two hundred thirty-three NH adults completed three lists of the Quick Speech in Noise test. Their individual open-set speech recognition responses were automatically phonemically transcribed and submitted to a phoneme-to-phoneme stimulus-response sequence alignment system. The computed alignments were mined for a measure of acoustic phonetic perception, a measure of response text that could not be attributed to the stimulus, and a count of words correct. The mined data were statistically analyzed to determine whether the response errors were significant factors beyond stimulus SNR in accounting for the number of words correct per response from each participant. This study addressed two hypotheses: (1) Individuals whose perceptual errors are less severe recognize more words correctly under difficult listening conditions due to babble masking and (2) Listeners who are better able to exclude incorrect speech information such as from background babble and filling in recognize more stimulus words correctly. Statistical analyses showed that acoustic phonetic accuracy and exclusion of babble background were significant factors, beyond the stimulus sentence SNR, in accounting for the number of words a participant recognized. There was also evidence that poorer acoustic phonetic accuracy could occur along with higher words correct scores. This paradoxical result came from a subset of listeners who had also performed subjective accuracy judgments. Their results suggested that they recognized more words while also misallocating acoustic cues from the background into the stimulus, without realizing their errors. Because the Quick Speech in Noise test stimuli are locked to their own babble sample, misallocations of whole words from babble into the responses could be investigated in detail. The high rate of common misallocation errors for some sentences supported the view that the functional stimulus was the combination of the target sentence and its babble. Individual differences among NH listeners arise both in terms of words accurately identified and errors committed during open-set recognition of sentences in babble maskers. Error mining to characterize individual listeners can be done automatically at the levels of acoustic phonetic perception and the misallocation of background babble words into open-set responses. Error mining can increase test information and the efficiency and accuracy of characterizing individual listeners.

Wood volume estimation strategies for trees from a Dry Forest/Savannah transition area in Piauí, Brazil

Prediction of aboveground wood volume is one of most important stages when conducting a forest inventory and making forest management decisions. This is more difficult for native forest than for plantations given the high variability of the former (trees of different species and age groups). The objective of this work was to evaluate different strategies to estimate aboveground standing tree wood volume (v) using its diameter at breast height (DBH) and total height (h), comparing the use of form factors, volume equations fitted by ordinary least squares and mixed modelling, as well as the options from the literature. To achieve this, 351 trees were scaled during field campaigns, with 158 felled trees and 193 measured using Criterion equipment. The data collected from each scaled tree was: h, DBH, v and identification of the botanical species. We found that the best application of form factors occurred when the trees were divided by diameter classes. However, regression models, regardless of the fitting technique, presented better volume estimates than form factors. Mixed models, with either the species or diameter class as the random variable, provided the lowest errors when estimating tree volume. Thus, we recommend the use of mixed models as the best strategy to estimate volume of standing trees. The following equation can be used to estimate aboveground wood volume for trees from vegetation types similar to the ones of this study: ln(v) = −9.06013 + 1.91756 ln(DBH) + 0.69846 ln(h).

A Novel Time-Activity Information-Sharing Approach Using Nonlinear Mixed Models for Patient-Specific Dosimetry with Reduced Imaging Time Points: Application in SPECT/CT After 177Lu-DOTATATE.

Multiple-time-point SPECT/CT imaging for dosimetry is burdensome for patients and lacks statistical efficiency. A novel method for joint kidney time-activity estimation based on a statistical mixed model, a prior cohort of patients with complete time-activity data, and only 1 or 2 imaging points for new patients was compared with previously proposed single-time-point methods in virtual and clinical patient data. Methods: Data were available for 10 patients with neuroendocrine tumors treated with 177Lu-DOTATATE and imaged up to 4 times between days 0 and 7 using SPECT/CT. Mixed models using 1 or 2 time points were evaluated retrospectively in the clinical cohort, using the multiple-time-point fit as the reference. Time-activity data for 250 virtual patients were generated using parameter values from the clinical cohort. Mixed models were fit using 1 (∼96 h) and 2 (4 h, ∼96 h) time points for each virtual patient combined with complete data for the other patients in each dataset. Time-integrated activities (TIAs) calculated from mixed model fits and other reduced-time-point methods were compared with known values. Results: All mixed models and single-time-point methods performed well overall, achieving mean bias < 7% in the virtual cohort. Mixed models exhibited lower bias, greater precision, and substantially fewer outliers than did single-time-point methods. For clinical patients, 1- and 2-time-point mixed models resulted in more accurate TIA estimates for 94% (17/18) and 72% (13/18) of kidneys, respectively. In virtual patients, mixed models resulted in more than a 2-fold reduction in the proportion of kidneys with |bias| > 10% (6% vs. 15%). Conclusion: Mixed models based on a historical cohort of patients with complete time-activity data and new patients with only 1 or 2 SPECT/CT scans demonstrate less bias on average and significantly fewer outliers when estimating kidney TIA, compared with popular reduced-time-point methods. Use of mixed models allows for reduction of the imaging burden while maintaining accuracy, which is crucial for clinical implementation of dosimetry-based treatment.

Dielectric Spectroscopy and Application of Mixing Models Describing Dielectric Dispersion in Clay Minerals and Clayey Soils.

The number of sensors, ground-based and remote, exploiting the relationship between soil dielectric response and soil water content continues to grow. Empirical expressions for this relationship generally work well in coarse-textured soils but can break down for high-surface area and intricate materials such as clayey soils. Dielectric mixing models are helpful for exploring mechanisms and developing new understanding of the dielectric response in porous media that do not conform to a simple empirical approach, such as clayey soils. Here, we explore the dielectric response of clay minerals and clayey soils using the mixing model approach in the frequency domain. Our modeling focuses on the use of mixing models to explore geometrical effects. New spectroscopic data are presented for clay minerals (talc, kaolinite, illite and montmorillonite) and soils dominated by these clay minerals in the 1 MHz–6 GHz bandwidth. We also present a new typology for the way water is held in soils that we hope will act as a framework for furthering discussion on sensor design. We found that the frequency-domain response can be mostly accounted for by adjusting model structural parameters, which needs to be conducted to describe the Maxwell–Wagner (MW) relaxation effects. The work supports the importance of accounting for soil structural properties to understand and predict soil dielectric response and ultimately to find models that can describe the dielectric–water content relationship in fine-textured soils measured with sensors.

Temporal Response to Drought Stress in Several Prunus Rootstocks and Wild Species

Prunus species are important crops in temperate regions. In these regions, drought periods are predicted to occur more frequently due to climate change. In this sense, to reduce the impact of climate warming, obtaining new tolerant/resistant cultivars and rootstocks is a mandatory goal in Prunus breeding. Therefore, the current study assembled three Prunus species including almond, (P. dulcis Mill D.A. Webb), apricot (P. armeniaca L.) and peach (P. persica L.) to model the temporal effects of drought. A hybrid peach × almond and a wild almond-relative species Prunus webbii were also included in the study. Physiological traits associated with photosynthetic activity, leaf water status, and chlorophyll content were assessed under three watering treatments. Results showed that effects of time, genotype, and treatment interact significantly in all traits. In addition, results confirmed that P. webbii have a greater tolerance to drought than commercial rootstocks. However, “Real Fino” apricot showed the fastest recovery after re-irrigation while being one of the most affected cultivars. In addition, from the better response to these watering treatments by the almond genotypes, two different trends were observed after re-irrigation treatment that clearly differentiate the response of the almond cultivar “Garrigue” from the rest of Prunus genotypes. A better characterization of the short-term drought response in Prunus, an accurate and more efficient evaluation of the genotype effect was obtained from the use of mixed models considering appropriate variance–covariance structures. Although the advantages of these approaches are rarely used in Prunus breeding, these methodologies should be undertaken in the future by breeders to increase efficiency in developing new breeding materials.

Use of mixing models to explain groundwater quality time and space variation in a narrowed fluctuating alluvial aquifer

Hydrogeochemical studies can provide insights to pursue a flexible and responsive groundwater resources management.Origin of water, mixing and reactive processes are three key parameters that allow to understand hydrological systems and resulting groundwater quality.However, those parameters may evolve strongly and quickly over time and space, especially for hydrological system impacted by pumping activities and seasonal variations.Within this framework, the current study aims to pursue a survey of the hydrological parameters in a small dynamic alluvial aquifer fed by 3 contrasted end-members and used for water supply.The variations of the end-members and the alluvial groundwaters quality (Ca2+, Mg2+, K+, Na+, Cl−, CO32−, NO3−, δ2H and δ18O) will be used as a record of those parameters. 26 sampling campaigns were carried out fortnightly from October 2017 to October 2018 and data processed with two distinct mixing models: GLUE-EMMA model, which define likelihood of each mixing component, and PHREEQC inverse modeling, which account for the reactive processes that occur as water chemistry evolves. For each studied groundwater, appropriate time variant end members signatures as well as analytical uncertainties were accounted and models constrained to fit within 5.0% for the major ions and 0.5‰ for water stable isotopes.With suitable models for all alluvial groundwater samples, both GLUE-EMMA and PHREEQC highlight the mixing process between two end-members as the main parameter of the alluvial groundwater quality. Nonetheless, Mg2+ and K+ reactive fluxes are needed to fit with the required constraints.Hence, the alluvial groundwater quality variations are either associated with the typical seasonal variations of the end-member signature and the change of the mixing processes.For both models, mixing process exhibits slow and small as well as strong and sudden changes. The first can be related with the relative capacity of the end members to feed the aquifer according to their individual high and low water periods. The second to the effects of alternative pumping regime between sampling campaign.The capacity of both models to evaluate and monitor main hydrological processes, over time and space, confirms the interest to combine them as a flexible multi process investigation suited for dynamic hydrological system.

Omitting Routine Radiography of Traumatic Ankle Fractures After Initial 2-Week Follow-up Does Not Affect Outcomes: The WARRIOR Trial: A Multicenter Randomized Controlled Trial.

The clinical consequences of routine follow-up radiographs for patients with ankle fracture are unclear, and their usefulness is disputed. The purpose of the present study was to determine if routine radiographs made at weeks 6 and 12 can be omitted without compromising clinical outcomes. This multicenter randomized controlled trial with a noninferiority design included 246 patients with an ankle fracture, 153 (62%) of whom received operative treatment. At 6 and 12 weeks of follow-up, patients in the routine-care group (n = 128) received routine radiographs whereas patients in the reduced-imaging group (n = 118) did not. The primary outcome was the Olerud-Molander Ankle Score (OMAS). Secondary outcomes were the American Academy of Orthopaedic Surgeons (AAOS) foot and ankle questionnaire, health-related quality of life (HRQoL) as measured with the EuroQol-5 Dimensions-3 Levels (EQ-5D-3L) and Short Form-36 (SF-36), complications, pain, health perception, self-perceived recovery, the number of radiographs, and the indications for radiographs to be made. The outcomes were assessed at baseline and at 6, 12, 26, and 52 weeks of follow-up. Data were analyzed with use of mixed models. Reduced imaging was noninferior compared with routine care in terms of OMAS scores (difference [β], -0.9; 95% confidence interval [CI], -6.2 to 4.4). AAOS scores, HRQoL, pain, health perception, and self-perceived recovery did not differ between groups. Patients in the reduced-imaging group received a median of 4 radiographs, whereas those in the routine-care group received a median of 5 radiographs (p < 0.05). The rates of complications were similar (27.1% [32 of 118] in the reduced-imaging group, compared with 22.7% [29 of 128] in the routine-care group, p = 0.42). The types of complications were also similar. Implementation of a reduced-imaging protocol following an ankle fracture has no measurable negative effects on functional outcome, pain, and complication rates during the first year of follow-up. The number of follow-up radiographs can be reduced by implementing this protocol. Therapeutic Level I. See Instructions for Authors for a complete description of levels of evidence.

The use of mixed modeling to evaluate the impact of treatment integrity on learning

Treatment integrity, or the degree to which an intervention is implemented as intended, is a critical feature of skill acquisition tasks. Single‐case design consistently demonstrates that low treatment integrity slows or inhibits learning, but the relative impact of different types of instructional errors, or the presence of multiple errors, is less clear. The present study utilized a multilevel modeling approach to evaluate the impact of type of error (omission versus omission and commission) and error component (reinforcer delivery versus feedback) on learning. Findings revealed that learning outcomes worsened based on the type of error and as the complexity of errors increased; more specifically, participants performed better when only a single type of error occurred and when only a single error component was manipulated. Additionally, individual characteristics contributed to learning outcomes, highlighting the use of multilevel modeling as a helpful tool to supplement single‐case design. The differential impact of integrity errors on learning may be due to timing of errors (i.e., commission errors more likely to occur early in learning) or how errors affect reinforcement schedule versus discriminative control.

Taper Function for Pinus nigra in Central Italy: Is a More Complex Computational System Required?

Stem tapers are mathematical functions modelling the relative decrease of diameter (rD) as the relative height (rH) increase in trees and can be successfully used in precision forest harvesting. In this paper, the diameters of the stem at various height of 202 Pinus nigra trees were fully measured by means of an optical relascope (CRITERION RD 1000) by adopting a two-steps non-destructive strategy. Data were modelled with four equations including a linear model, two polynomial functions (second and third order) and the Generalised Additive Model. Predictions were also compared with the output from the TapeR R package, an object-oriented tool implementing the β-Spline functions and widely used in the literature and scientific research. Overall, the high quality of the database was detected as the most important driver for modelling with algorithms almost equivalent each other. The use of a non-destructive sampling method allowed the full measurement of all the trees necessary to build a mathematical function properly. The results clearly highlight the ability of all the tested models to reach a high statistical significance with an adjusted-R squared higher than 0.9. A very low mean relative absolute error was also calculated with a cross validation procedure and small standard deviation were associated. Substantial differences were detected with the TapeR prediction. Indeed, the use of mixed models improved the data handling with outputs not affected by autocorrelation which is one of the main issues when measuring trees profile. The profile data violate one of the basic assumptions of modelling: the independence of sampled units (i.e., autocorrelation of measured values across the stem of a tree). Consequently, the use of simple parametric equations can only be a temporary resource before more complex built-in apps are able to allow basic users to exploit more powerful modelling techniques.