Examining the Robustness of the Graded Response and 2-Parameter Logistic Models to Violations of Construct Normality

2022 ◽  
pp. 001316442110634
Author(s):  
Patrick D. Manapat ◽  
Michael C. Edwards
Keyword(s):  
Logistic Model ◽  
Population Distribution ◽  
Latent Trait ◽  
Logistic Models ◽  
Skewed Distribution ◽  
Parameter Recovery ◽  
Irt Models ◽  
Psychological Theories ◽  
Graded Response ◽  
Computationally Intensive

When fitting unidimensional item response theory (IRT) models, the population distribution of the latent trait (θ) is often assumed to be normally distributed. However, some psychological theories would suggest a nonnormal θ. For example, some clinical traits (e.g., alcoholism, depression) are believed to follow a positively skewed distribution where the construct is low for most people, medium for some, and high for few. Failure to account for nonnormality may compromise the validity of inferences and conclusions. Although corrections have been developed to account for nonnormality, these methods can be computationally intensive and have not yet been widely adopted. Previous research has recommended implementing nonnormality corrections when θ is not “approximately normal.” This research focused on examining how far θ can deviate from normal before the normality assumption becomes untenable. Specifically, our goal was to identify the type(s) and degree(s) of nonnormality that result in unacceptable parameter recovery for the graded response model (GRM) and 2-parameter logistic model (2PLM).

scholarly journals Matching IRT Models to Patient-Reported Outcomes Constructs: The Graded Response and Log-Logistic Models for Scaling Depression

Psychometrika ◽  
2021 ◽  
Author(s):  
Steven P. Reise ◽  
Han Du ◽  
Emily F. Wong ◽  
Anne S. Hubbard ◽  
Mark G. Haviland
Keyword(s):  
Cognitive Ability ◽  
Logistic Model ◽  
Patient Reported Outcomes ◽  
Logistic Models ◽  
Response Model ◽  
Graded Response Model ◽  
Irt Model ◽  
Irt Models ◽  
Graded Response ◽  
Patient Reported

AbstractItem response theory (IRT) model applications extend well beyond cognitive ability testing, and various patient-reported outcomes (PRO) measures are among the more prominent examples. PRO (and like) constructs differ from cognitive ability constructs in many ways, and these differences have model fitting implications. With a few notable exceptions, however, most IRT applications to PRO constructs rely on traditional IRT models, such as the graded response model. We review some notable differences between cognitive and PRO constructs and how these differences can present challenges for traditional IRT model applications. We then apply two models (the traditional graded response model and an alternative log-logistic model) to depression measure data drawn from the Patient-Reported Outcomes Measurement Information System project. We do not claim that one model is “a better fit” or more “valid” than the other; rather, we show that the log-logistic model may be more consistent with the construct of depression as a unipolar phenomenon. Clearly, the graded response and log-logistic models can lead to different conclusions about the psychometrics of an instrument and the scaling of individual differences. We underscore, too, that, in general, explorations of which model may be more appropriate cannot be decided only by fit index comparisons; these decisions may require the integration of psychometrics with theory and research findings on the construct of interest.

Cross-Classification Multilevel Logistic Models in Psychometrics

2003 ◽  
Vol 28 (4) ◽  
pp. 369-386 ◽  
Author(s):  
Wim Van den Noortgate ◽  
Paul De Boeck ◽  
Michel Meulders
Keyword(s):  
Random Sample ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Population Distribution ◽  
Logistic Models ◽  
Educational Measurement ◽  
Random Parameters ◽  
Irt Models ◽  
Cross Classification ◽  
Item Effects

In IRT models, responses are explained on the basis of person and item effects. Person effects are usually defined as a random sample from a population distribution. Regular IRT models therefore can be formulated as multilevel models, including a within-person part and a between-person part. In a similar way, the effects of the items can be studied as random parameters, yielding multilevel models with a within-item part and a between-item part. The combination of a multilevel model with random person effects and one with random item effects leads to a cross-classification multilevel model, which can be of interest for IRT applications. The use of cross-classification multilevel logistic models will be illustrated with an educational measurement application.

scholarly journals The use of the nonlinear models in the growth of pears of ‘Shinseiki’ cultivar

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Thais Destefani Ribeiro ◽  
Taciana Villela Savian ◽  
Tales Jesus Fernandes ◽  
Joel Augusto Muniz
Keyword(s):  
Logistic Model ◽  
Least Squares Method ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Information Criterion ◽  
Fruit Weight ◽  
Coefficient Of Determination ◽  
Pear Fruit ◽  
Asian Pear ◽  
Residual Correlations

ABSTRACT: The goal of this study was to elucidate the growth and development of the Asian pear fruit, on the grounds of length, diameter and fresh weight determined over time, using the non-linear Gompertz and Logistic models. The specifications of the models were assessed utilizing the R statistical software, via the least squares method and iterative Gauss-Newton process (DRAPER & SMITH, 2014). The residual standard deviation, adjusted coefficient of determination and the Akaike information criterion were used to compare the models. The residual correlations, observed in the data for length and diameter, were modeled using the second-order regression process to render the residuals independent. The logistic model was highly suitable in demonstrating the data, revealing the Asian pear fruit growth to be sigmoid in shape, showing remarkable development for three variables. It showed an average of up to 125 days for length and diameter and 140 days for fresh fruit weight, with values of 72mm length, 80mm diameter and 224g heavy fat.

scholarly journals Item Response Theory Analysis of ADHD Symptoms in Children With and Without ADHD

Assessment ◽  
2016 ◽  
Vol 23 (6) ◽  
pp. 655-671 ◽  
Author(s):  
James J. Li ◽  
Steven P. Reise ◽  
Andrea Chronis-Tuscano ◽  
Amori Yee Mikami ◽  
Steve S. Lee
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Trait ◽  
Dimensional Structure ◽  
Adhd Symptoms ◽  
Response Theory ◽  
Confirmatory Factor Analyses ◽  
Item Response Theory Analysis ◽  
Graded Response ◽  
Moderate Range

Item response theory (IRT) was separately applied to parent- and teacher-rated symptoms of attention-deficit/hyperactivity disorder (ADHD) from a pooled sample of 526 six- to twelve-year-old children with and without ADHD. The dimensional structure ADHD was first examined using confirmatory factor analyses, including the bifactor model. A general ADHD factor and two group factors, representing inattentive and hyperactive/impulsive dimensions, optimally fit the data. Using the graded response model, we estimated discrimination and location parameters and information functions for all 18 symptoms of ADHD. Parent- and teacher-rated symptoms demonstrated adequate discrimination and location values, although these estimates varied substantially. For parent ratings, the test information curve peaked between −2 and +2 SD, suggesting that ADHD symptoms exhibited excellent overall reliability at measuring children in the low to moderate range of the general ADHD factor, but not in the extreme ranges. Similar results emerged for teacher ratings, in which the peak range of measurement precision was from −1.40 to 1.90 SD. Several symptoms were comparatively more informative than others; for example, is often easily distracted (“Distracted”) was the most informative parent- and teacher-rated symptom across the latent trait continuum. Clinical implications for the assessment of ADHD as well as relevant considerations for future revisions to diagnostic criteria are discussed.

scholarly journals Analysis of Factors Affecting the High Subjective Well-Being of Chinese Residents Based on the 2014 China Family Panel Study

2019 ◽  
Vol 16 (14) ◽  
pp. 2566 ◽  
Author(s):  
Wen Xu ◽  
Haiyan Sun ◽  
Bo Zhu ◽  
Wei Bai ◽  
Xiao Yu ◽  
...  
Keyword(s):  
Physical Exercise ◽  
Influencing Factors ◽  
Low Income ◽  
Social Trust ◽  
Population Distribution ◽  
Panel Study ◽  
Multivariable Analysis ◽  
Logistic Models ◽  
Well Being ◽  
Subjective Well Being

(1) Purpose: The purpose of our research is to understand the subjective well-being (SWB) of Chinese adult residents and its influencing factors and to identify the key groups and areas to provide a basis for the formulation of relevant policies to improve residents’ happiness. (2) Methods: In this study, we analyzed the influencing factors of SWB of individuals older than 16 years of age, according to the 2014 China Family Panel Study (CFPS). We weighted 27,706 samples in the database to achieve the purpose of representing the whole country. Finally, descriptive statistics were used for the population distribution, chi-square tests were used for univariable analysis, and binary logistic models were used for multivariable analysis. (3) Results: The response rate of SWB was 74.58%. Of the respondents, 71.2% had high SWB (7–10), with a U-shaped distribution between age and SWB. Females are more likely than males to rate themselves as happy. There is a positive ratio between years of education and SWB. Residents who have better self-evaluated income, self-rated health (SRH), psychological well-being (PWB), Body Mass Index (BMI), social trust, social relationships, and physical exercise have higher SWB. (4) Conclusion: The results of the present study indicate that to improve residents’ SWB, we should focus more attention on middle-aged and low-income groups, particularly men in agriculture. The promotion of SWB should be facilitated by improvements in residents’ education, health status, and social support as well as by the promotion of smoking bans and physical exercise.

scholarly journals Growth in weight and of some tissues in the bullfrog: fitting nonlinear models during the fattening phase

2014 ◽  
Vol 38 (6) ◽  
pp. 598-606 ◽  
Author(s):  
Marcelo Maia Pereira ◽  
Cleber Fernando Menegasso Mansano ◽  
Edney Pereira da Silva ◽  
Marta Verardino De Stéfani
Keyword(s):  
Food Intake ◽  
Logistic Model ◽  
Fat Body ◽  
Nonlinear Models ◽  
Logistic Models ◽  
Live Weight ◽  
Initial Weight ◽  
Expected Values ◽  
Growth Of Animals ◽  
Cumulative Food Intake

Knowledge of the growth of animals is important so that zootechnical activity can be more accurate and sustainable. The objective of this study was to describe the live weight, development of liver tissue and fat body, leg growth, and cumulative food intake of bullfrogs during the fattening phase using nonlinear models. A total of 2,375 bullfrog froglets with an initial weight of 7.03 ± 0.16 g were housed in five fattening pens (12 m²). Ten samplings were performed at intervals of 14 days to obtain the variables studied. These data were used to estimate the parameters of Gompertz and logistic models as a function of time. The estimated values of weight (Wm) and food intake (FIm) at maturity and time when the growth rate is maximum (t*) were closer to expected values when the logistic model was used. The Wm values for live weight and liver, adipose and leg weights and the FIm value for food intake were 343.7, 15.7, 19.6, 96.03 and 369.3 g, respectively, with t* at 109, 98, 105, 109 and 107 days. Therefore, the logistic model was the best model to estimate the growth and food intake of bullfrogs during the fattening phase.

Bayesian Inference for IRT Models with Non-Normal Latent Trait Distributions

2020 ◽  
pp. 1-21
Author(s):  
Xue Zhang ◽  
Chun Wang ◽  
David J. Weiss ◽  
Jian Tao
Keyword(s):  
Bayesian Inference ◽  
Latent Trait ◽  
Irt Models

scholarly journals Comparison of particular logistic models’ adoption in the Czech Republic

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Petra Vrbová ◽  
Václav Cempírek
Keyword(s):  
Supply Chain ◽  
Czech Republic ◽  
Lead Time ◽  
Logistic Model ◽  
Logistic Models ◽  
Service Level ◽  
Time Service ◽  
The Czech Republic ◽  
Total Cost ◽  
Challenging Tasks

Abstract Managing inventory is considered as one of the most challenging tasks facing supply chain managers and specialists. Decisions related to inventory locations along with level of inventory kept throughout the supply chain have a fundamental impact on the response time, service level, delivery lead-time and the total cost of the supply chain. The main objective of this paper is to identify and analyse the share of a particular logistic model adopted in the Czech Republic (Consignment stock, Buffer stock, Safety stock) and also compare their usage and adoption according to different industries. This paper also aims to specify possible reasons of particular logistic model preferences in comparison to the others. The analysis is based on quantitative survey held in the Czech Republic.

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